Algebra 2 Practice Book

NAME ______________________________________________ DATE______________ PERIOD _____1-1 Practice Expressions and Formulas Find the value of each expression. 1. 3(4 3. 1 5. 20 7. 18 9. 11. 1 [6 2 8(13 6 7) 2 (5 {5 42] 11 3(4) 3) [34 2 52(3) (17 11)]} 2. 4(12 4. 12 6. ( 2)3 8. [4(5 10. 1 [ 5 4 ( 8)2 9 42) [20 2(62 3 22)] 3) 2(4 8)] 16 5( 3)] ( 1)2 4( 9) 1 . 3 37) 12. 5 3 ,b 4 Evaluate each expression if a 13. ab2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 8, c 14. (c 16. 2, d d)b 3, and e d d2 de)e2 (c 1 e 9 C 5 15. ab c d(b c) ac 17. (b 19. 18. ac3 d) 2 ] 20. ac4 d b2de c e2 b[a 21. 9bc 22. 2ab2 (d 3 c) 23. TEMPERATURE The formula F 32 gives the temperature in degrees Fahrenheit for a given temperature in degrees Celsius. What is the temperature in degrees Fahrenheit when the temperature is 40 degrees Celsius? 24. PHYSICS The formula h 120t 16t2 gives the height h in feet of an object t seconds after it is shot upward from Earth’s surface with an initial velocity of 120 feet per second. What will the height of the object be after 6 seconds? 25. AGRICULTURE Faith owns an organic apple orchard. From her experience the last few seasons, she has developed the formula P 20x 0.01x2 240 to predict her profit P in dollars this season if her trees produce x bushels of apples. What is Faith’s predicted profit this season if her orchard produces 300 bushels of apples? Chapter 1 9 Glencoe Algebra 2 Lesson 1-1 (3)(8) (5)(10) NAME ______________________________________________ DATE______________ PERIOD _____ 1-2 Practice Properties of Real Numbers Name the sets of numbers to which each number belongs. 1. 6425 25 36 2. 7 3. 2 4. 0 5. 6. 16 7. 35 8. 31.8 Name the property illustrated by each equation. 9. 5x (4y 3x) 5x (3x 4y) 10. 7x (9x 8) (7x 9x) 8 11. 5(3x y) 5(3x 1y) 12. 7n 2n (7 2)n 13. 3(2x)y 1 4 (3 2)(xy) 14. 3x 2y 3 2 x y 15. (6 6)y 0y 16. 4y 1y 17. 5(x y) 5x 5y 18. 4n 0 4n Name the additive inverse and multiplicative inverse for each number. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 19. 0.4 21. 11 16 20. 22. 5 1.6 5 6 Simplify each expression. 23. 5x 25. 8x 27. 3(r 29. 2(4 3y 7y 10s) 2x 2x (3 3y 6y) 4(7s y) 4(5 2r) x y) 24. 11a 2c 13b (4c 15) 12y 7a 2c) 1 (8 2 1 (2x 4 3b 26. 4c 28. 30. 1 (10a 5 5 3 x 6 5 4a) 12y) 31. TRAVEL Olivia drives her car at 60 miles per hour for t hours. Ian drives his car at 50 miles per hour for (t 2) hours. Write a simplified expression for the sum of the distances traveled by the two cars. 32. NUMBER THEORY Use the properties of real numbers to tell whether the following statement is true or false: If a b, it follows that a 1 a 1 . Explain your reasoning. b b Chapter 1 16 Glencoe Algebra 2 NAME ______________________________________________ DATE______________ PERIOD _____ 1-3 Practice Solving Equations Write an algebraic expression to represent each verbal expression. 1. 2 more than the quotient of a number and 5 2. the sum of two consecutive integers 3. 5 times the sum of a number and 1 4. 1 less than twice the square of a number Write a verbal expression to represent each equation. 5. 5 2x 4 6. 3y 4y3 7. 3c 2(c 1) 8. m 5 3(2m 1) Name the property illustrated by each statement. 9. If t 11. If h 13 12 52, then 52 22, then h t 10. 13. 10. If 8(2q 12. If 4m 1) 4, then 2(2q 12m 1) 45. 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 15, then 13. 14 15. 17. 3 4 8 1 n 2 6r 5 8 14. 9 16. 7.8 v 21 5 s 6 4n 3 4 59 11 12 1.6r 5 4v) 18. 6x 20. 6y 5 5 2d 3 7 9x 3(2y 1) 19. 5(6 Solve each equation or formula for the specified variable. 21. E 23. h mc2, for m vt gt2, for v 22. c 24. E 1 , for d U, for I 1 2 Iw 2 Define a variable, write an equation, and solve the problem. 25. GEOMETRY The length of a rectangle is twice the width. Find the width if the perimeter is 60 centimeters. 26. GOLF Luis and three friends went golfing. Two of the friends rented clubs for $6 each. The total cost of the rented clubs and the green fees for each person was $76. What was the cost of the green fees for each person? Chapter 1 23 Glencoe Algebra 2 Lesson 1-3 Solve each equation. Check your solution. ⏐2 5. A poll with a stated margin of error of 3% predicts that candidate Tonwe will receive 51% of an upcoming vote. ⏐6a⏐ 3. ⏐a Solve each equation.NAME ______________________________________________ DATE______________ PERIOD _____ 1-4 Practice Solving Absolute Value Equations 1. c 2. 5⏐2r 22. Check your solutions. 13⏐ 3⏐ 4⏐ 2y⏐ 1⏐ 3y⏐ 2 42 6 9 5w 6 37 14 7 4 19. ⏐4d⏐ 12. 3 2⏐7 7⏐ s⏐ 3⏐ 3⏐2 5⏐2d 2w⏐ 3⏐ 29. ⏐2b 8. Chapter 1 31 Glencoe Algebra 2 Lesson 1-4 . 5 28. ⏐1 10. a poll with a margin of error of 5% is considered accurate to within plus or minus 5% of the actual value. 5. ⏐4w 24. ⏐2y 17. Inc. 26.5c b⏐ 11. 2⏐4 27. ⏐n 15. ⏐17c⏐ 6. WEATHER A thermometer comes with a guarantee that the stated temperature differs from the actual temperature by no more than 1. 13. ⏐10d 6⏐10a 7⏐ ⏐ 8b ⏐a⏐ 2a⏐ 3⏐b⏐ 7. ⏐3u Copyright © Glencoe/McGraw-Hill. ⏐8 23. ⏐5a 9. OPINION POLLS Public opinion polls reported in newspapers are usually given with a margin of error.4 degrees Fahrenheit. Write and solve an equation describing the minimum and maximum percent of the vote that candidate Tonwe is expected to receive. 3⏐0. 7⏐x 18. Write and solve an equation to find the minimum and maximum actual temperatures when the thermometer states that the temperature is 87. 30. ⏐x 16. a division of The McGraw-Hill Companies. 4⏐ 3⏐ 6⏐ 13 29 42 9⏐ 2p 5 3s 5 0 24 3 9 14. Evaluate each expression if a 1. 3⏐4x p⏐ 6⏐5 21.5b⏐ a⏐ 4. ⏐5x 20.5 degrees Fahrenheit. 4⏐2y 25. For example. ⏐2b a⏐ 12⏐ ⏐3c 2⏐ ⏐b 4⏐ ⏐ 0.4. and d 4⏐ ⏐3b 1⏐ 7c⏐ ⏐5 2d⏐ 5⏐ 5⏐ 1. b 8. 9x 11 6x 9 6. a division of The McGraw-Hill Companies.NAME ______________________________________________ DATE______________ PERIOD _____ 1-5 Practice Solving Inequalities Solve each inequality. .5 4 3 19 2 2. Then. Hotel parking is $12 per day. 23 2 4u 1 0 1 11 2 3 4 5 6 3. 4n 5(n 3) 3(n 1) 4 Define a variable and write an inequality for each problem. Inc. 16 4 3 8r 2 0 1 0 1 2 3 4 4. 3(4w 1) 18 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 7. q 2(2 q) 0 13. 4x 2 3 3.1)x 12x 30 600 to find how many nights the Lincoln’s can stay at the hotel without exceeding total hotel costs of $600.5 times that same number.5 12. BANKING Jan’s account balance is $3800. graph the solution set on a number line. Jan wants to keep a balance of at least $500. 1. Describe the solution set using set-builder or interval notation. An additional 10% tax is added. Four times the sum of twice a number and 3 is less than 5. 18. Twenty less than a number is more than twice the same number.5x 1 0 1 2 3 4 9. 1 4 8u 3 2 3u 1 0 10 1 2 3 4 8. Of this. 9(2r Copyright © Glencoe/McGraw-Hill. Then solve. Solve the inequality 90x 90(0. Chapter 1 39 Glencoe Algebra 2 Lesson 1-5 17. 36 2(w 77) 4(2w 52) 14. 16. 15. $750 is for rent. The Lincoln’s expect to spend $30 in tips during their stay. Write and solve an inequality describing how much she can withdraw and still meet these conditions. 14s 4 9s 3 2 5 1 0 1 2 3 4 5. 17. 8x 4 6 3 2 10 1 0 1 2 3 4 2. HOTELS The Lincoln’s hotel room costs $90 a night. 1 5(x 8) 2 (x 5) 11. 5) 3 7r 4 10. 08 ounces. MANUFACTURING A company’s guidelines call for each can of soup produced not to vary from its stated volume of 14. 18. ⏐3b 5⏐ 2 16.5 and 1. 1. ⏐3n 2⏐ 2 1 17. 2x 3 15 or 3 7x 17 8. all numbers greater than 4 or less than 2.5 4 8 6 4 2 0 2 4 6 8 1. Graph the solution set on a number line.5 fluid ounces by more than 0.NAME ______________________________________________ DATE______________ PERIOD _____ 1-6 Practice Solving Compound and Absolute Value Inequalities Write an absolute value inequality for each of the following. all numbers between 1. 3. ⏐x⏐ x 1 15. a division of The McGraw-Hill Companies. 5. Inc. ⏐2w⏐ 4 3 5 2 1 0 1 2 3 4 10. 3(5x 2 0 2) 2 4 24 or 6x 6 4 4 5x 8 12 16 20 24 28 32 8 10 12 14 7. 15 5x 0 and 5x 6 14 4 3 2 1 0 1 2 3 4 4 3 2 1 0 1 2 3 4 Copyright © Glencoe/McGraw-Hill. Then graph the solution set on a number line.5. Chapter 1 46 Glencoe Algebra 2 .5 and 1.5 inches from its mean value of 24 inches. 9. 20 10 0 10 20 4. 8 0 4 3y 20 52 6. including Write an absolute value inequality for each graph. Write and solve an absolute value inequality to describe acceptable can volumes. ⏐2z 2⏐ 3 13. the rainfall at Shell Beach has varied no more than 6. ⏐2x 2⏐ 7 5 14. ⏐y 8 5⏐ 7 6 2 5 4 3 2 1 0 11. Write and solve an absolute value inequality to describe the rainfall in the other 10% of the last 30 years. RAINFALL In 90% of the last 30 years. 4 3 2 1 0 1 2 3 4 Solve each inequality. ⏐x 8⏐ 3 12. f( 4) 11.NAME ______________________________________________ DATE______________ PERIOD _____ 2-1 2-1 Practice Relations and Functions Determine whether each relation is a function. a division of The McGraw-Hill Companies. Write yes or no. f(m 2) 13. (4. 48) represent the cost of buying various numbers of CDs through a music club. 1. How long would it take the computer to do 5 billion calculations? Chapter 2 9 Glencoe Algebra 2 Lesson 2-1 3. 1). {( 4. 16). (2. 16). (0. 3). then the function T(n) 0. 0). Domain 2 8 Range 21 25 30 2. Inc. and (5.0000000015 second. 0)} y 6. 32). f(3) 10. (4. 1 2 7. Then determine whether the relation or equation is a function. 32). g 12. MUSIC The ordered pairs (1. g( 6) 9. Is the relation discrete or continuous? Is the relation a function? 14. 4. f( 2) 8. COMPUTING If a computer can do one calculation in 0. (3. (2. Next determine if the relation is discrete or continuous. Domain 5 10 15 Range 105 110 x 3 1 0 2 3 y 0 1 0 2 4 y O x Graph each relation or equation and find the domain and range. Identify the domain and range of the relation. y 2x y 1 O O x x Find each value if f(x) 5 x 2 and g(x) 2x 3. 5. . Copyright © Glencoe/McGraw-Hill.0000000015n gives the time required for the computer to do n calculations. 2x 7y y 14 Copyright © Glencoe/McGraw-Hill. If no.54x gives the length in centimeters corresponding to a length x in inches. y 4. y 2x y O 4 12. B. and C. Then graph the equation. What is the length in centimeters of a 1-foot ruler? LONG DISTANCE For Exercises 14 and 15. O O x x 11. Write yes or no. y 2x 4 y 10.05t. 5. 3y 7x 5 5 0 6. where t is the number of minutes talked. 6x 2y 6 y x O x 13. h(x) 3. y 7. x 3 x 8 2 y 7 5 3 4 Find the x-intercept and the y-intercept of the graph of each equation. 9 2 x 3 5xy 2 Write each equation in standard form. What is the effective cost per minute (the total cost divided by the number of minutes talked) of talking 8 hours? of talking 20 hours? Chapter 2 16 Glencoe Algebra 2 . the monthly cost C in dollars is given by the linear function C(t) 6 0. a division of The McGraw-Hill Companies. MEASURE The equation y 2. Identify A. y 5 x 23 2. explain your reasoning. 14. For Meg’s long-distance calling plan. use the following information.NAME ______________________________________________ DATE______________ PERIOD _____ 2-2 Practice Linear Equations State whether each equation or function is linear. What is the total cost of talking 8 hours? of talking 20 hours? 15. 1. Inc. 9. y 8. parallel to a line O x DEPRECIATION For Exercises 13–15. (0. 4) Graph the line passing through the given point with the given slope. 5. Find the average rate of change in value of the machine between the end of 3 years and the end of 8 years. perpendicular 3 to a line whose slope is 2 y O 12. (7. 6) 4. 2) 2) 3. 2) 1) 2. 3). ( 8. 8). m 0 y 10. m y O 3 8. Find the average rate of change in value (depreciation) of the machine between its purchase and the end of 3 years. Interpret the sign of your answers. a division of The McGraw-Hill Companies. 6). 7. passes through ( 3. The same machine has a value of $2800 at the end of 8 years. 3). 2). 2). (3. Practice Slope Find the slope of the line that passes through each pair of points. (8. 3). ( 7. ( 10. (4. m y O 4 5 x O Copyright © Glencoe/McGraw-Hill. (2.NAME ______________________________________________ DATE______________ PERIOD _____ 2-3 1. m y x 3 4 O x 9. (7.600 has a value of $7500 at the end of 3 years. 11. use the following information. Inc. 0). (2. ( 5. whose slope is 1 y x 1). 3). x Graph the line that satisfies each set of conditions. 1). 14. 15. Chapter 2 23 Glencoe Algebra 2 Lesson 2-3 . 6. ( 6. (3. 3). passes through (3. A machine that originally cost $15. 13. (0. (8. 12. y 6. 11) and ( 6. the water level is dropping at a rate of 3 inches per day. passes through (10. Write an equation that gives the profit P when n drives are manufactured. y 4. –2) x O (3. 7). passes through (6. a division of The McGraw-Hill Companies. 3 8) 14. 1) 16. 2) O x O (0. 10) 13. slope 4 . 4) 9. The relationship between the number of drives manufactured and the profit is linear. slope 0. RESERVOIRS The surface of Grand Lake is at an elevation of 648 feet. 2x 3y 10 Write an equation in slope-intercept form for each graph. 20. 3y 8x 7 Practice Writing Linear Equations 3 x 5 State the slope and y-intercept of the graph of each equation. passes through (3. 8) 11. 7. y 5.000 profit if it manufactures 500.000 drives. 3x 0. 5 3) Copyright © Glencoe/McGraw-Hill. Inc. y (4. 10. passes through ( 8. slope 2 . Chapter 2 30 Glencoe Algebra 2 . y 8. y-intercept 2 17. y-intercept 7 18. passes through (0. 5) 15. write an equation that gives the elevation in feet of the surface of Grand Lake after x days. perpendicular to the graph of y 4x 3 19.25x 15 1 5y 3. passes through (7. If this trend continues.000 profit if it manufactures 100.750.000 drives. slope 5. x-intercept 5. –1) x Write an equation in slope-intercept form for the line that satisfies each set of conditions.NAME ______________________________________________ DATE______________ PERIOD _____ 2-4 1. and $1. passes through ( 3. 3) y (0. BUSINESS Tony Marconi’s company manufactures CD-ROM drives. 2) and (3. x-intercept 3. 12 2. During the current drought. The company will make $150. (–3. As Anchara drives into the mountains. Weight (tons) 1. Time (min) 18 24 30 40 42 48 52 60 ? Calories Burned 260 280 320 380 400 440 475 Chapter 2 38 Glencoe Algebra 2 .3 1.5 Weight (tons) 2.8 2 ? 2. HEALTH Alton has a treadmill that uses the time on the treadmill and the speed of walking or running to estimate the number of Calories he burns during a workout. ALTITUDE In most cases.000 8. c.NAME ______________________________________________ DATE______________ PERIOD _____ 2-5 Practice Modeling Real-World Data: Using Scatter Plots For Exercises 1–3.000 10. Use your prediction equation to predict the missing value.5 2. b. a division of The McGraw-Hill Companies. complete parts a–c for each set of data. a. Use two ordered pairs to write a prediction equation.000 9.400 12.0 2.4 1. Draw a scatter plot. 1.5 1.000 Altitude (ft) Temperature Versus Altitude Copyright © Glencoe/McGraw-Hill. Altitude (ft) Temperature ( F) 7500 61 8200 58 8600 56 9200 53 9700 10. temperature decreases with increasing altitude. The table gives workout times and Calories burned for several workouts. FUEL ECONOMY The table gives the approximate weights in tons and estimates for overall fuel economy in miles per gallon for several cars. 50 46 ? 3. Inc.4 17 15 Miles per Gallon 29 24 23 21 Fuel Economy Versus Weight Fuel Economy (mi/gal) 30 25 20 15 10 5 0 0.5 1. her car thermometer registers the temperatures (°F) shown in the table at the given altitudes (feet).000 Temperature ( F) 65 60 55 50 45 0 7.0 1.1 2. h(x) 4 2x h(x) x if x 0 2 if x 0 O x O x 7. Draw a function that represents this situation. g(x) 2⏐x⏐ g (x ) O 4. Inc. 5. f(x) x ⏐x 1⏐ f (x ) O x Copyright © Glencoe/McGraw-Hill.NAME ______________________________________________ DATE______________ PERIOD _____ 2-6 Practice Special Functions Lesson 2-6 5 10 15 20 25 30 35 Pounds Graph each function. Draw a graph of the step $2.50 per pound for 20 or more pounds.00 $40 per hour or any fraction thereof per pound for less than 20 pounds of candy and for labor. Identify the domain and range.5x f (x ) 2. f(x) 0. BUSINESS A wholesaler charges a store $3. 280 240 Total Cost ($) 200 160 120 80 40 0 1 2 3 4 5 Hours 6 7 Cost ($) 105 90 75 60 45 30 15 0 Chapter 2 45 Glencoe Algebra 2 . a division of The McGraw-Hill Companies. f(x) x 2 if x 3x if x 2 f(x) 2 6. BUSINESS A Stitch in Time charges 8. 1. graph of the function that represents this Labor Costs Candy Costs situation. f(x) x 2 f (x ) O O x x 3. y 3 y O 2. The total cost of the computers cannot exceed $80. If the school wants to buy 50 of the desktop computers and 25 of the notebook computers. a division of The McGraw-Hill Companies. use the following information. will they have enough money? 0 10 20 30 40 50 60 70 80 90 100 Desktops Chapter 2 53 Glencoe Algebra 2 Lesson 2-7 . Graph the inequality. x 2 y 3. A school system is buying new computers. 11. and notebook computers costing $1200 per unit. Inc. They will buy desktop computers costing $1000 per unit. x Copyright © Glencoe/McGraw-Hill. Write an inequality that describes this situation. Notebooks Computers Purchased 80 70 60 50 40 30 20 10 10.000.NAME ______________________________________________ DATE______________ PERIOD _____ 2-7 2-7 Practice Graphing Inequalities Graph each inequality. y 1 y x O O x O x x 7. y 1 x 2 3 y 6. y 3x y 5 5. 3y y 6 8. y ⏐x⏐ 1 y 9. 12. x y 4 y O x O x x 4. y 3⏐x y O 1⏐ 2 x O x O x COMPUTERS For Exercises 10–12. 1. 000 plus $500 per additional site license. Location Mapping needs new software.000 20. 2x y y 1 x 2 y 3 9 2 O O x x O x 4. 1.000 12.NAME ______________________________________________ DATE______________ PERIOD _____ 3-1 3-1 Practice Solving Systems of Equations By Graphing Solve each system of equations by graphing. 2x y x 2y y 6 2 O 6. x 2x 2y 3y 4 1 y 3. y y x 1 3 y 5. 2x x y y 2 y O O 4 8. 2y y 8 1 x 2 x 4 y x O x SOFTWARE For Exercises 10–12. 10. Estimate the break-even point of the software costs. If Location Mapping plans to buy 10 additional site licenses.000 8. x y 2y 2x 0 3 y 2.000 11. 5x y 4 2x 6y 4 y x O x O x Copyright © Glencoe/McGraw-Hill. a division of The McGraw-Hill Companies. Software B costs $2500 plus $1200 per additional site license. 7.000 4. Graph each system of equations and describe it as consistent and independent.000 16. Write two equations that represent the cost of each software. Total Cost ($) Software Costs 24. 12. y x y x 2 4 y x 9. use the following information. consistent and dependent. Graph the equations. or inconsistent. Inc. which software will cost less? Chapter 3 0 2 4 6 8 10 12 14 16 18 20 Additional Licenses 9 Glencoe Algebra 2 Lesson 3-1 . Software A costs $13. NAME ______________________________________________ DATE______________ PERIOD _____ 3-2 3-2 Practice Solving Systems of Equations Algebraically Solve each system of equations by using substitution. 1. 2x 3x 4. 2a a 7. u u y 2y 4b 2b 2v 2v 4 1 6 3 1 2 2. x x 5. 2m 5m 8. x 5 4x 3y 2y 9 1 3. g 1 g 3 3h h 3y 2y 3z 5z 8 9 6 7 1 4 n 6 6n 1 3y y 16 9 6. 4x x 9. w 3w Solve each system of equations by using elimination. 10. 2r 3r 13. 3j 4j 16. 2t t Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. s s k k 4v 2v 5 20 10 16 6 3 11. 2m 3m n 2n 1 30 12. 6x 8x 15. 2g 3g 18. 1 x 2 3y 5y 6 12 14. 2x y 4 4x 2y 6 17. 3x 2x 2y 2 y 3 h 6 2h 16 3y 5y 11 17 12 14 8x Solve each system of equations by using either substitution or elimination. 19. 8x 10x 3y 6y 5 1 5 13 20. 8q 4q 23. s s 15r 2r 3y 1 4 56 40 21. 3x 1 x 3 4y 4 y 9 12 4 3 22. 4b 2d 2b d 24. 4m 2p 0 3m 9p 5 27. h 3h z 3 3z 25. 5g 4k 10 3g 5k 7 26. 0.5x 2y 5 x 2y 8 6 SPORTS For Exercises 28 and 29, use the following information. Last year the volleyball team paid $5 per pair for socks and $17 per pair for shorts on a total purchase of $315. This year they spent $342 to buy the same number of pairs of socks and shorts because the socks now cost $6 a pair and the shorts cost $18. 28. Write a system of two equations that represents the number of pairs of socks and shorts bought each year. 29. How many pairs of socks and shorts did the team buy each year? Chapter 3 17 Glencoe Algebra 2 Lesson 3-2 NAME ______________________________________________ DATE______________ PERIOD _____ 3-3 Practice Solving Systems of Inequalities by Graphing Solve each system of inequalities by graphing. 1. y y 1 1 y x 2. x 2y 2 3x 6 y 3. y y 2x 1 x 2 3 2 y O x O x O x 4. x y 3x y 2 2 y 5. ⏐y⏐ 1 y x 1 y 6. 3y 2x 4x 3y y 6 O x O x O x Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Find the coordinates of the vertices of the figure formed by each system of inequalities. 7. y y x 1 x 3 x 1 8. x x x y y 2 2 2 9. y 2x 2 2x 3y 6 y 4 DRAMA For Exercises 10 and 11, use the following information. The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales. 10. Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meets its goal. 11. List three different combinations of tickets sold that satisfy the inequalities. Play Tickets 400 350 Student Tickets 300 250 200 150 100 50 0 100 200 300 Adult Tickets 400 Chapter 3 24 Glencoe Algebra 2 NAME ______________________________________________ DATE ____________ PERIOD _____ 3-4 3-4 Practice Linear Programming Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function for this region. 1. 2x 4 y 2x 4 y y 2 f(x, y) 2x y y 2. 3x 2x y f(x, y y x y) 7 3 3 x y 4y 3. x y y y f(x, 0 0 6 3x y) y 15 3x y O x O x O x Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 4. x y 4x f(x, 0 0 y y) 7 x y O 4y 5. y 3x 6 4y 3x 3 x 2 f(x, y) x y x 3y 6. 2x 2x x y f(x, 3y 6 y 2 0 0 y) x y 4y 3 O x O x PRODUCTION For Exercises 7–9, use the following information. A glass blower can form 8 simple vases or 2 elaborate vases in an hour. In a work shift of no more than 8 hours, the worker must form at least 40 vases. 7. Let s represent the hours forming simple vases and e the hours forming elaborate vases. Write a system of inequalities involving the time spent on each type of vase. 8. If the glass blower makes a profit of $30 per hour worked on the simple vases and $35 per hour worked on the elaborate vases, write a function for the total profit on the vases. 9. Find the number of hours the worker should spend on each type of vase to maximize profit. What is that profit? Chapter 3 31 Glencoe Algebra 2 Lesson 3-4 The sum of three numbers is 4. . 2x y 3z 3 3x 2y 4z 5 6x 3y 9z 9 15. d 3e f 0 d 2e f 4d e f 1 1 12. a division of The McGraw-Hill Companies. x 2y z 1 x 2y z 6 4y 2z 1 19. 2x 2y 4z 3x 3y 6z 2x 3y z 2 3 7 20. The sum of the first and second numbers is 5. Find the numbers. 2g 3h 8j 10 g 4h 1 2g 3h 8j 5 6. p p q 4r 7 3q 8 r 1 10. The team scored 10 times during the game. 2x 3x 4x 5y 2y 3y z 5 z 17 2z 17 8. 4x 3x 2x 4y 5y 2y 2z 8 3z 0 z 4 11. x 4y 3z 2x 2y 3z 4z 16 27 22 3. 4x y 5z x 4y 2z 2x 3y 2z 9 2 21 Copyright © Glencoe/McGraw-Hill. 3x 5x 3x 3y 2y 2y z 10 2z 7 3z 9 16. 24. 5x 2x 5x 9y z 20 y z 21 2y 2z 21 14. 3m 2n 4p 15 m n p 3 m 4n 5p 0 5. 2x x 3x y y y Practice Solving Systems of Equations in Three Variables Solve each system of equations. 2x y z 8 4x y 2z 3 3x y 2z 5 7. How many touchdowns were made during the game? Chapter 3 39 Glencoe Algebra 2 Lesson 3-5 23. the team can earn one point for the extra kick or two points for a 2-point conversion. The first number is one more than the third number. x y 9z 2x 4y z 3x 6y 3z 27 1 27 21.NAME ______________________________________________ DATE______________ PERIOD _____ 3-5 1. The third number is the sum of the first and second numbers. Six points are awarded for each touchdown. 2x 3y 4z 5x 2y 3z x 5y 2z 2 0 4 9. The sum of three numbers is 6. 2u v w 2 3u 2v 3w 7 u v 2w 7 17. The second number decreased by the third is equal to the first. 13. 2z z 2z 15 3 18 2. Find the numbers. SPORTS Alexandria High School scored 37 points in a football game. After each touchdown. 2x 5y 3z 7 4x 10y 2z 6 6x 15y z 19 22. a b a b c 2c 3 3 10 4. x 5y 3z 18 3x 2y 5z 22 2x 3y 8z 28 18. The team scored one fewer 2-point conversions than extra kicks. Inc. Week 1 Week 2 Week 3 Load 1 40 tons Load 1 40 tons Load 1 32 tons Load 2 32 tons Load 2 40 tons Load 2 24 tons Load 3 24 tons Load 3 32 tons Load 3 24 tons 16. ⎣ y ⎡ 3x 21⎤ ⎣ 8y 5⎦ ⎡ y 8⎤ ⎣ 17⎦ ⎡ 0⎤ ⎣ 2⎦ 10. Inc. ⎢ 5 16 ⎣ 4 7 2 3⎤ 0 0⎥ 1 4⎦ Solve each equation. ⎣ 3z] [6x 2y 45] ⎡ 6x⎤ 3⎦ 3⎤ 6y⎦ ⎡ 36⎤ ⎣ 17⎦ ⎡ ⎣ 2y 1⎤ 2⎦ 3x⎤ 16⎦ ⎡7x 7. [ 3 3 7] ⎡ 5 8 2. ⎣ 2y 5 3x 1 3z 8y⎤ 11⎦ ⎡ 5 ⎣ 3y ⎡ 3x⎤ 4⎦ ⎡ 5x 12. ⎣8y 8⎤ 3⎦ 20⎤ ⎡ ⎣2y 3⎦ ⎡ 4x ⎡ ⎡ 6x 12⎤ 9. What are the dimensions of the matrix? Chapter 4 9 Glencoe Algebra 2 Lesson 4-1 4. 1. ⎡ 1⎤ ⎣ y⎦ ⎡ 2x y⎤ 13. a division of The McGraw-Hill Companies. 5. [ 2x 22 6. Write a matrix for the amount of gravel in each load. 15. ⎣ 2 1 1⎤ 8⎦ ⎡ 2 2 3. use the following information. TICKET PRICES The table at the right gives ticket prices for a concert.NAME ______________________________________________ DATE______________ PERIOD _____ 4-1 Practice Introduction to Matrices State the dimensions of each matrix. Child Cost Purchased in Advance Cost Purchased at the Door $6 $8 Student $12 $15 Adult $18 $22 CONSTRUCTION For Exercises 15 and 16. Write a 2 3 matrix that represents the cost of a ticket. ⎣ 3y 6⎦ x 5z 1⎤ 4⎦ 11. ⎣2y 8. During each of the last three weeks. a road-building crew has used three truckloads of gravel. ⎣ 3x 2y⎦ 14. ⎣3x Copyright © Glencoe/McGraw-Hill. [4x 42] [24 6y] . The table at the right shows the amount of gravel in each load. ⎢ 71⎥ ⎣ 18⎦ ⎡2 4. and fiber between Mix B and Mix A expressed as a matrix. PET NUTRITION Use the table that gives nutritional information for two types of dog food. a division of The McGraw-Hill Companies. one for women and one for men. If the matrix does not exist. A Copyright © Glencoe/McGraw-Hill. ECONOMICS For Exercises 13 and 14. ⎡ 2 1. use the table that shows loans by an economic development board to women and men starting new businesses. 15.000 $672. 4B ⎡ 10 ⎣ 6 C A 0.000 $562. Write two matrices that represent the number of new businesses and loan amounts. 4 20⎦ 3C 12. ⎡1 2 ⎣2⎤ ⎦ ⎡0 4 ⎣5⎤ ⎦ 3⎡ 8 12⎤ 4 ⎣ 16 20⎦ Use A 7. fat.5C 8 6⎤ to find the following.000 $902. 11. Find the difference in the percent of protein.000 14. A 10. B 5⎤ . ⎢ 3 ⎣14 3. Women Businesses 2003 2004 2005 27 41 35 Loan Amount ($) $567. % Protein Mix A Mix B 22 24 % Fat 12 8 % Fiber 5 8 Chapter 4 16 Glencoe Algebra 2 .000 Men Businesses 36 32 28 Loan Amount ($) $864. 13. 1 3 ⎡ 17 ⎣ 1⎤ 7⎥ 9⎦ ⎡ 6 ⎢ 7 ⎣ 8 0⎤ 11⎦ 9⎤ 11⎥ 17⎦ ⎡ 4⎤ 2. and C 9⎦ 8.NAME ______________________________________________ DATE______________ PERIOD _____ 4-2 Practice Operations with Matrices Perform the indicated matrix operations. ⎡ 67⎤ ⎢ 45⎥ ⎣ 24⎦ 1 8⎤ 7 9⎦ ⎡ 3 16 4 ⎣ 21 12⎤ ⎦ ⎡10⎤ ⎣18⎦ ⎡ 2 4 ⎣ 1 0 ⎡ 1 4 2⎣ 7 2 2 ⎡27 3 ⎣54 3⎤ 6⎦ 9⎤ 18⎦ 5.000 $777. A 9. 7 ⎣4 6. Inc. Find the sum of the numbers of new businesses and loan amounts for both men and women over the three-year period expressed as a matrix. 3B 2B ⎡ 4 ⎣ 3 B 1 0⎤ 6 2⎦ . write impossible. B ⎡ 4 ⎣ 2 RENTALS For Exercises 19–21. express the income of each of the three complexes as a matrix. ⎣ 7 ⎡3 10. 2-Bedroom Sun Haven Surfside Seabreeze 36 29 18 3-Bedroom 24 32 22 4-Bedroom 22 42 18 19. C ⎡ 1 0⎤ ⎣ 0 1⎦ 1⎦ . ⎣ 2 5⎦ ⎣ 7 ⎡ 1⎤ 11. If so. a division of The McGraw-Hill Companies. Write a matrix that represents the number of each type of unit available at each complex and a matrix that represents the weekly charge for each type of unit. 0⎤ . a 3-bedroom condominium for $2165. ⎢ 3⎥ [4 0 2] ⎣ 1⎦ 14. For their one-week vacation. and scalar c 3 to determine whether the following equations are true for the given matrices. if possible. or a 4-bedroom condominium for $2538. A(B 18. the Montoyas can rent a 2-bedroom condominium for $1796. ⎡2 7. ⎣ 3 4⎤ ⎡3 1⎦ ⎣6 2 0 4⎤ 1⎦ 7⎤ 5⎦ ⎡2 8. 1. 15. A7 4. (A C) C)B BA B(A CA C) ⎡1 3⎤ ⎣3 1⎦ . A3 5. state the dimensions of the product. P1 5 9 M5 Q9 8 1 3. ⎣6 4⎤ ⎡ 3 0⎤ 1⎦ ⎣ 2 5⎦ 2 0 7⎤ ⎡3 5⎦ ⎣6 2 0 7⎤ 5⎦ ⎡ 3 0⎤ ⎡ 2 9. [ 15 ⎡ 6 9] ⎣23 11⎤ 10⎦ Copyright © Glencoe/McGraw-Hill. 20. The table shows the number of units in each of three complexes. [4 0 2] ⎢ 3⎥ ⎣ 1⎦ ⎡ 6 13. P9 1 1 A1 Q1 6 9 Find each product. 21. If all of the units in the three complexes are rented for the week at the rates given the Montoyas.NAME ______________________________________________ DATE______________ PERIOD _____ 4-3 Practice Multiplying Matrices Determine whether each matrix product is defined. What is the total income of all three complexes for the week? Chapter 4 23 Glencoe Algebra 2 Lesson 4-3 . AC 17. M3 4 2 B4 A3 3 2 2. use the following information. M2 6. Inc. (AB)c CA c(AB) 16. ⎣ 3 Use A 2⎤ ⎡5 0⎤ 1⎦ ⎣0 5⎦ ⎡ 1⎤ 12. They place the corners of an island at (2. and Z(3. the Bradleys plot their kitchen plans on a grid with each unit representing 1 foot. and D( 2. Write the coordinates of RST in a vertex matrix. S(3. 4). 2). BUSINESS The design of a business logo calls for locating the vertices of a triangle at (1. Graph the preimage and the image. (3. The vertices of quadrilateral ABCD are A( 3.5. Copyright © Glencoe/McGraw-Hill. Quadrilateral WXYZ with vertices W( 3. y O x 9. 3). 7. O y 5. Y(4. 5). B(0. 8). 4. 10. 5). and (9. X( 2. 4). (8. Find the coordinates of quadrilateral W X Y Z . a division of The McGraw-Hill Companies. O x For Exercises 4–6. 0) is translated 1 unit left and 3 units down. (4. x For Exercises 7–10. The quadrilateral is reflected over the y-axis. ARCHITECTURE Using architectural design software. and T( 2. 1). what will the new coordinates of its corners be? 12. The triangle is dilated so that its perimeter is one half the original perimeter. use the following information. 2). use the following information. use the following information. Write the coordinates of ABCD in a vertex matrix. C(4. Graph ABCD and A B C D . 2. 5). 8). what will the new coordinates of the vertices be? Chapter 4 30 Glencoe Algebra 2 . 3. Inc. RST. Find the coordinates of A B C D . If design changes require rotating the triangle 90º counterclockwise. 11. Graph RST and RST . 1). Write the translation matrix. 0) on a grid. 2). 2).5 feet to the right and 2 feet down. Write the reflection matrix for this situation. The vertices of RST are R(6.NAME ______________________________________________ DATE______________ PERIOD _____ 4-4 Practice Transformations with Matrices y For Exercises 1–3. 8. 1. Find the coordinates of the image 6. and (1. If the Bradleys wish to move the island 1. 3). 11). NAME ______________________________________________ DATE______________ PERIOD _____ 4-5 Practice Determinants Find the value of each determinant. ⎢8 ⎢1 7 4 1 4 0 5 1⎥ 9⎥ 7⎥ 6⎥ 0⎥ 3⎥ ⎢2 15. ⎢ Evaluate each determinant using diagonals.7⎥ 0. 4). ⎢ 2 3 13. ⎢2 ⎢3 4 1 2 1⎥ 3⎥ 1⎥ 0⎥ 1⎥ 5⎥ ⎢ 2 14. ⎢1 ⎢3 ⎢2 23. a division of The McGraw-Hill Companies. ⎢7 ⎢ ⎢ 6. ⎢0. ⎢2 7⎥ ⎢ ⎥ 9 6 2.4 ⎢ ⎢ 7. how many acres is the parcel? Chapter 4 38 Glencoe Algebra 2 . 1 6 1. ⎢ 4 0⎥ 2 9⎥ ⎢ 3 10. ⎢ 2 ⎢ 3⎥ 4⎥ 4⎥ 9⎥ 1⎥ 9. ⎢ 14 2 ⎢ 4 5. (6. 17). 10). 5). ⎢2 5 ⎢ 1 9. ⎢ 12 3 8. ⎢3 2⎥ ⎢ ⎥ 3⎥ 2⎥ 4 3. ⎢ 1 1 1 1⎥ 2⎥ 1⎥ 3⎥ 1⎥ 6⎥ ⎢ 12 0 7 5 4 2 Copyright © Glencoe/McGraw-Hill. ⎢1 ⎢1 18. LAND MANAGEMENT A fish and wildlife management organization uses a GIS (geographic information system) to store and analyze data for the parcels of land it manages. If the coordinates of the corners of a parcel are ( 8. ⎢ 10 0. ⎢ 3 ⎢ 1 ⎢2 17. Inc. 26.5⎥ 1⎥ 5⎥ 5⎥ 11⎥ 11⎥ 2⎥ 0. ⎢1 ⎢2 ⎢2 1 24. ⎢3. ⎢ 0 4 ⎢ 2 5 ⎢0 16. and (2.5 12. All of the parcels are mapped on a grid in which 1 unit represents 1 acre. ⎢ 2 1 ⎢ 4 1 ⎢1 2 22. ⎢3 Evaluate each determinant using expansion by minors. 5). 10). ⎢4 ⎢0 2 1 1 1 0 3 3⎥ 1⎥ 1⎥ 2⎥ 2⎥ 2⎥ ⎢1 21.3⎥ ⎢ 4. ⎢1 4 ⎢2 3 1⎥ 2⎥ 4⎥ 4⎥ 6⎥ 3⎥ ⎢2 20. (6.75 4⎥ 5⎥ ⎢2 11. ⎢1 8 ⎢0 5 4 6 3 1⎥ 2⎥ 1⎥ 3⎥ 0⎥ 1⎥ 25. ⎢ 4 3 19. and ( 4. GEOMETRY Find the area of a triangle whose vertices have coordinates (3. 2x 2x 11. 0.3g 10 4 1. LANDSCAPING A memorial garden being planted in front of a municipal library will contain three circular beds that are tangent to each other. A landscape architect has prepared a sketch of the design for the garden using CAD (computer-aided drafting) software. 6g 3g 3y 2y 6y 8y 5 1 45 13 4. as shown at the right.NAME ______________________________________________ DATE______________ PERIOD _____ 4-6 Practice Cramer’s Rule Use Cramer’s Rule to solve each system of equations. Find the coordinates of a vertex of the parallelogram. 2x 3x y 0 2y 2 2. The distance from A to B is 15 feet. The centers of the three circular beds are represented by points A. 1.5y 3 4 y 3 5. Inc. 3x 2y 5z 3 2x 2y 4z 3 5x 10y 7z 3 24. Find the coordinates of the vertex of the angle.3d 0.2d 16.5y 3y 15. 8a 2a 12. 0.9. Copyright © Glencoe/McGraw-Hill. 5c 2c 9d d 6 22 1 8 11 12 1 9 19 20 3.02x 0.8 0. 18. the distance from B to C is 13 feet. a division of The McGraw-Hill Companies. x x 4x 3y 3z 2y z y 2z 4 1 1 19. 13. x 3y 3x y 8. x x 0. Use Cramer’s Rule to solve each system of equations.5y 1 and 0.6g 0. 2e 3e 3x 2x f 4 5f 15 15y 45 7y 18 3y 8 0. and the distance from A to C is 16 feet. GEOMETRY Two sides of a parallelogram are contained in the lines represented by the equations 0. What is the radius of each of the circular beds? Chapter 4 A 16 15 f t ft B 13 ft C 46 Glencoe Algebra 2 . 17.2x 0. 2x 3x 6.5 10. and C.2x 0.3y 0. 2x 5x 3x y 3z 2y 2z 3y 5z 5 8 17 21. 2c 3d e 17 4c d 5e 9 c 2d e 12 22. 3u 6u 14. 5a b 4c 7 3a 2b c 0 2a 3b c 17 20. B. GEOMETRY The two sides of an angle are contained in the lines whose equations are x 6 and 2x y 1. 20m 3n 28 2m 3n 16 7.6x y 4y 5v 7v 3b 24 b 4 h 4h 0. 5x 9x 9. 2j k 3m 3j 2k 4m 4j k 2m 3 5 4 23. ⎡ 4 7. Q ⎡3 2⎤ ⎣5 3⎦ ⎡3 3. Inc. 1) O (2. B ⎡ 2 ⎣ 3 ⎡1 1⎤ 2⎦ 1 ⎤ 10 3 10 ⎦ Determine whether each pair of matrices are inverses. 17. ⎣ 4 ⎡2 11. 1. Write the vertex matrix A for the rectangle.5 0⎤ ⎣ 0 1. use the figure at the right. Make a conjecture about what transformation B 1 describes on a coordinate plane. ⎣3 5⎦ ⎡ 2 5⎤ 10. 14. Use matrix multiplication to find BA if B ⎡1. 2) (5. All square matrices have multiplicative inverses. M 2. ⎣6 9⎦ y (4. X ⎡ 3 ⎣ 5 ⎡ 6 ⎣ 2 2⎤ 3⎦. ⎣ 1 3⎦ ⎡4 6⎤ 12. A ⎢ 5 2 ⎣5 ⎥ 4. . Y 2⎤ 3⎦. CODES Use the alphabet table below and the inverse of coding matrix C decode this message: 19 | 14 | 11 | 13 | 11 | 22 | 55 | 65 | 57 | 60 | 2 | 1 | 52 | 47 | 33 | 51 | 56 | 55.NAME ______________________________________________ DATE______________ PERIOD _____ 4-7 Practice Identity and Inverse Matrices ⎡2 1⎤ . CODE A H 1 8 B I 2 9 C 3 D 4 E 5 F 6 G 7 ⎡1 2⎤ ⎣2 1⎦ to J 10 Q 17 X 24 K 11 R 18 Y 25 L 12 S 19 Z 26 M 13 T 20 – 0 N 14 U 21 O 15 V 22 P 16 W 23 Chapter 4 53 Glencoe Algebra 2 Lesson 4-7 Determine whether each statement is true or false.5⎦. 5⎤ 3⎦ 3⎤ 7⎦ 5⎤ 1⎦ ⎡2 0⎤ 8. N ⎣3 2⎦ ⎡ 3 1⎤ ⎣ 4 2⎦. P ⎢ 14 1 ⎣ 7 1⎤ 7 3 7⎦ ⎥ 5. 13. Graph the vertices of the transformed triangle on the previous graph. ⎣ 3 Copyright © Glencoe/McGraw-Hill. –1) x 15. 4) GEOMETRY For Exercises 13–16. 6. (1. a division of The McGraw-Hill Companies. ⎣ 4 ⎡ 1 9. 16. All square matrices have multiplicative identities. Find the inverse of each matrix. Describe the transformation. if it exists. 4j 9k 6j 12k 8 5 17. 3x 2y 5x 3y 9 13 2. AIRLINE TICKETS Last Monday at 7:30 A.200. 6x 3x 2y 3y 2 10 3.2 grams of vitamin C. 3⎤ ⎡ a⎤ 4⎦ ⎣ b ⎦ ⎡16⎤ ⎣34⎦ ⎡ 1⎤ ⎣ 1⎦ ⎡ 4 2⎤ ⎡ r ⎤ 11.6 gram of calcium and 1.. 2a 3a b 0 2b 2 4. 5m 2m 3y 2y 9n n 5 1 19 20 14. an airline flew 89 passengers on a commuter flight from Boston to New York.M. 3x 2y 5z 3 x y 4z 2 2x 2y 7z 5 6. If a person wants to take 0. ⎣ 1 5⎦ ⎣ y⎦ ⎡ 5 3⎤ ⎡ c ⎤ 10. How many passengers bought $120 tickets? How many bought $230 tickets? 18. 8d 9f 13 6d 5f 45 16. a division of The McGraw-Hill Companies. how many doses of each supplement should she take? Chapter 4 60 Glencoe Algebra 2 . Some of the passengers paid $120 for their tickets and the rest paid $230 for their tickets. ⎣12 6⎤ ⎣ z ⎦ ⎦ ⎡ 7⎤ ⎣ 10⎦ Copyright © Glencoe/McGraw-Hill.2 gram of calcium and 0. ⎣ 6 4⎦ ⎣ d⎦ ⎡ 8 3 ⎡ y⎤ 12. r 5s 10 2r 3s 7 5. ⎡2 1⎤ ⎡ g ⎤ 7. The total cost of all of the tickets was $14. NUTRITION A single dose of a dietary supplement contains 0. A single dose of a second dietary supplement contains 0. ⎣ 3 ⎡ 0⎤ ⎣ 2⎦ ⎡ 12⎤ ⎣ 11⎦ ⎡ 17⎤ ⎣ 26⎦ ⎡ 2 3⎤ ⎡ x⎤ 8. 2x 3x 15. 1.1 gram of calcium and 0. ⎣3 2⎦ ⎣ h⎦ ⎡ 1 9.4 gram of vitamin C.NAME ______________________________________________ DATE______________ PERIOD _____ 4-8 Practice Using Matrices to Solve Systems of Equations Write a matrix equation for each system of equations.2 gram of vitamin C. Inc. 2m 5m 3m n 3p 2n 2p 3n 5p 5 8 17 Solve each matrix equation or system of equations by using inverse matrices. ⎣ 7 4⎦ ⎣ s ⎦ 13. f(x) x2 4x 12 3. and the x-coordinate of the vertex. 1. f(x) x2 6x 14 6. Find the maximum height reached by the ball and the time that this height is reached. the SportsTime Athletic Club charged $20 to participate in an aerobics class. The club wants to increase the class price this year. a division of The McGraw-Hill Companies. Susan throws a ball upward with a velocity of 32 feet per second. The height h(t) of the ball t seconds after Susan throws it is given by h(t) 16t2 32t 4. Use this information to graph the function. Seventy people attended the classes. f(x) 2 2 x 3 8x 24 10. Find the y-intercept. f(x) x2 8x 15 2. 11. f(x) x2 4x 1 9. Make a table of values that includes the vertex. f(x) 2x2 4x 6 8. Then state the domain and range of the function. What is the maximum income the SportsTime Athletic Club can expect to make? Chapter 5 9 Glencoe Algebra 2 Lesson 5-1 . What price should the club charge to maximize the income from the aerobics classes? b. HEALTH CLUBS Last year. f(x) 2x2 2x 1 16 12 f (x ) 16 12 f (x ) f(x) 8 8 4 4 O 2 4 6 8x –6 –4 –2 O 2x O x Copyright © Glencoe/McGraw-Hill. c. a. the equation of the axis of symmetry. b. They expect to lose one customer for each $1 increase in the price.NAME ______________________________________________ DATE______________ PERIOD _____ 5-1 Practice Graphing Quadratic Functions Complete parts a–c for each quadratic function. Inc. Determine whether each function has a maximum or a minimum value. and find the maximum or minimum value of each function. 4. GRAVITATION From 4 feet above a swimming pool. a. f(x) x2 2x 8 5. v(x) x2 14x 57 7. use the formula h(t) v0t 16t 2. x2 Use the related graph of each equation to determine its solutions. BASEBALL Marta throws a baseball with an initial upward velocity of 60 feet per second. a division of The McGraw-Hill Companies. Their sum is 5. 4. state the consecutive integers between which the roots are located. v0 is the object’s initial velocity in feet per second. VOLCANOES A volcanic eruption blasts a boulder upward with an initial velocity of 240 feet per second. and t is the time in seconds. and their product is f (x ) O 6. 7. 3x2 f (x ) Practice Solving Quadratic Equations By Graphing 2.NAME ______________________________________________ DATE______________ PERIOD _____ 5-2 1. how long after she releases the ball will it hit the ground? 10. 9. Inc. How long will it take the boulder to hit the ground if it lands at the same elevation from which it was ejected? Chapter 5 16 Glencoe Algebra 2 . and their product is 8. If exact roots cannot be found. Use a quadratic equation to find two real numbers that satisfy each situation. f(x) x O x For Exercises 9 and 10. or show that no such numbers exist. where h(t) is the height of an object in feet. 2x2 O x f(x) 6 0 x x O x Copyright © Glencoe/McGraw-Hill. 3 3x 2 3 0 f (x ) x f (x ) 3 0 3x 2 f (x ) 0 O x f (x ) O 3x 2 x 3 f (x ) x2 3x 2 O x x Solve each equation by graphing. 8. 2x2 6x 5 12 8 4 –6 –4 –2 O 0 f (x ) 5. Their sum is 1. x2 10x 24 0 f (x ) 6. Ignoring Marta’s height. 3x2 3. 1. 1 2 8. x2 25. 6. Inc. 7 2 Factor each polynomial. 8a2 2a 6 12. 10. 31. 3. 36x2 4x 6x 4x 9x 12x 25 36 12 8 0 0 0 17. Solve each equation by factoring. 30. 1 . 3 3. Write the equation in standard form. 16r2 169 15.2 3 9. By how many inches will the dimensions of the photograph have to be reduced? Chapter 5 23 Glencoe Algebra 2 Lesson 5-3 . x2 26. x3 8 14.NAME ______________________________________________ DATE______________ PERIOD _____ 5-3 Practice Solving Quadratic Equations by Factoring Write a quadratic equation with the given roots. b4 81 Copyright © Glencoe/McGraw-Hill. Find the dimensions of the rectangle if its area is 63 square feet. NUMBER THEORY Find two consecutive even positive integers whose product is 624. a division of The McGraw-Hill Companies. 10x2 24. 5. c2 49 13. 0. x2 21. r3 3r2 54r 11. 7. 8 5. x2 19. x2 20. x2 22. 16. NUMBER THEORY Find two consecutive odd positive integers whose product is 323. 7x2 23. 8 4. 7. GEOMETRY The length of a rectangle is 2 feet more than its width. 29. x2 18. 4 7. 2 2. 3 6. 2x2 16x 3x 4x 2x 35x 8x 99 60 90 0 0 64 2 0 0 28. PHOTOGRAPHY The length and width of a 6-inch by 8-inch photograph are reduced by the same amount to make a new photograph whose area is half that of the original. 0. 1. 5x2 27. (5 2i) ( 13 8i) 13. 15 33. i 55 11. (7i)2(6i) 9. (6 4i)(6 4i) 18. Practice Complex Numbers 36a3b4 550x 49 2. (28 4i) (10 30i) 17. (10 15i) (48 30i) 16. 8 a6b3 98 32 3. ( 3i)(4i)( 5i) 8. 25. find the voltage E in a circuit when the current I is 3 j amps and the impedance Z is 3 2j ohms. (8 6 11i)(8 5i 2i 11i) 19. i 42 10. Chapter 5 31 Glencoe Algebra 2 Lesson 5-4 . 2 7 8i 23. 4m2 29. ( 12 48i) (15 21i) 15. (7 2i)(9 6i) 21. i 89 12. (7 6i) (9 11i) 14. Inc. 3i)(2 5i) 20. 22. ELECTRICITY The impedance in one part of a series circuit is 1 3j ohms and the impedance in another part of the circuit is 7 5j ohms.NAME ______________________________________________ DATE______________ PERIOD _____ 5-4 Simplify. 1 2 4i 3i Solve each equation. (3m 28i 4) 3m (3 4ni n)i 16 3i 32. 31. ELECTRICITY Using the formula E IZ. 30. a division of The McGraw-Hill Companies. (4 Copyright © Glencoe/McGraw-Hill. 5. (6 34. 5m2 35 76 65 0 0 0 26. 2m2 3 2 x 4 10 6 12 0 0 0 Find the values of m and n that make each equation true. 5n2 27. 2 3 i i 24. (7 m) n) 3ni (4m 12 10)i 27i 3 6i 35. 15 25 4. Add these complex numbers to find the total impedance in the circuit. 2m2 28. 36. 1. 6. 17 81 7. 19. x2 12x c 11. 3x2 24.36x c 16. INVESTMENTS The amount of money A in an account in which P dollars is invested for 2 years is given by the formula A P(1 r)2. 9x2 6x 1 2 Find the value of c that makes each trinomial a perfect square. x2 25. If an investment of $800 in the account grows to $882 in two years. 7x2 6x 2 0 31. What were the dimensions of the original cube? 32.NAME ______________________________________________ DATE______________ PERIOD _____ 5-5 1.2x c 15. x2 10x 25 16 4. x2 11x c 13. x2 1 x 4 c 18. x2 8x 16 8 7. x2 x 14x x 5 2 19 0 0 0 21. GEOMETRY When the dimensions of a cube are reduced by 4 inches on each side. 2x2 6x 18 8x 8 9x 3 0 0 20. x2 26. x2 Practice Completing the Square Solve each equation by using the Square Root Property. Then write the trinomial as a perfect square. x2 14x 49 9 5. x2 27. x2 6x 9 5 8. x2 3x 6 0 29. a division of The McGraw-Hill Companies. at what interest rate was it invested? Chapter 5 38 Glencoe Algebra 2 . 4x2 12x 9 4 6. x2 20x c 12. x2 2. where r is the interest rate compounded annually. x2 6x 9 1 3. x2 0. x2 0. 2x2 5x 16x 10x 2 7 5 0 0 0 28. 10. x2 5 x 3 c Copyright © Glencoe/McGraw-Hill. x2 5 x 6 c 17.8x c 14. 3x2 23. Solve each equation by completing the square. Inc. 2x2 5x 6 0 30. 8x 16 1 2. x2 22. the surface area of the new cube is 864 square inches. x2 2x 1 2 9. 25x2 27.05s2 1. a division of The McGraw-Hill Companies. Find the exact solutions by using the Quadratic Formula. 1. Inc. GRAVITATION The height h(t) in feet of an object t seconds after it is propelled straight up from the ground with an initial velocity of 60 feet per second is modeled by the equation h(t) 16t2 60t. x2 16x 64 0 2.NAME ______________________________________________ DATE______________ PERIOD _____ 5-6 Practice The Quadratic Formula and the Discriminant Lesson 5-6 24x 16 0 7x 0 6x 2 0 3x 6 0 5x 6 0 0 Glencoe Algebra 2 Complete parts a c for each quadratic equation. c. x2 25. 3x2 20. 8x 29. x2 3x 40 5. x2 3x 3. 16x2 8x 1 0 15. 3x2 22. 6x2 2x 1 0 12. STOPPING DISTANCE The formula d 0. Find the value of the discriminant. If a car stops in 200 feet. 7x2 18. 4x2 Copyright © Glencoe/McGraw-Hill. 4x2 28. b. 16. x2 13.1s estimates the minimum stopping distance d in feet for a car traveling s miles per hour. 4x2 1 9 21 0 4x 22x 14x 20x 4x2 7 0 53 6 8 0 12x 30. x2 21. x2 24. 3x2 6 0 14. At what times will the object be at a height of 56 feet? 31. 12x2 2x 4 0 11. 2x2 7. 3x2 9x 2 0 6. 15x2 23. 12x2 x 6 0 9. 5x2 2x 4 0 8. a. 3x2 26. what is the fastest it could have been traveling when the driver applied the brakes? Chapter 5 45 . 4x2 19. 7x2 10. 9x2 4. Describe the number and type of roots. 2x2 Solve each equation by using the method of your choice. Find exact solutions. x2 5x 8x 13x 6x 3 54 4x 4x 17 15 0 0 3 4 0 0 17. What is the maximum height that the baseball reaches.NAME ______________________________________________ DATE______________ PERIOD _____ 5-7 Practice Analyzing Graphs of Quadratic Functions Write each quadratic function in vertex form. 18) 15. 6) 4) 16. Write a quadratic function in vertex form that describes the shape of the outside of the arc. y 2x2 2 3. SCULPTURE A modern sculpture in a park contains a parabolic arc that starts at the ground and reaches a maximum height of 10 feet after a horizontal distance of 4 feet. 13. y x2 y 6x 5 12. where y is the height of a point on the arc and x is its horizontal distance from the left-hand starting point of the arc. y x2 10x 20 5. vertex: ( 3. 4 ft 10 ft Chapter 5 53 Glencoe Algebra 2 Lesson 5-7 . and when does this occur? 19. 3) point: ( 2. 17. 18. y 2x2 y 2x 1 O Copyright © Glencoe/McGraw-Hill. 4) and x-intercept 6. BASEBALL The height h of a baseball t seconds after being hit is given by h(t) 16t2 80t 3. Then identify the vertex. y 2x2 16x 32 8. Write an equation for a parabola with vertex at ( 3. y 3x2 18x 21 9. point: (5. 15) 14. y 3x2 6x 5 7. axis of symmetry. a division of The McGraw-Hill Companies. y 2x2 12x 18 6. y 2x2 16x 29 Graph each function. 10. y (x 3)2 1 y 11. y 6(x 2)2 1 2. Inc. vertex: (10. Write an equation for a parabola with vertex at (4. 1. 0) point: (3. if not already in that form. y 4x2 8x 4. x O x O x Write an equation for the parabola with the given vertex that passes through the given point. vertex: (1. and direction of opening. 1) and y-intercept 2. x2 14x 49 0 11. 5x2 10 27x 18. x2 6 O –6 –12 2 4 6 8x O 8x y 0 5. 4x2 4x 1 0 17. 4 y 2. a division of The McGraw-Hill Companies. What are the possible widths of the play area? 20. x2 15 8x 13. x2 2x y 3 0 6. x2 5x 7 0 14. FENCING Vanessa has 180 feet of fencing that she intends to use to build a rectangular play area for her dog. y 6x 6 y 3. BUSINESS A bicycle maker sold 300 bicycles last year at a profit of $300 each. x2 5x 14 12. x2 10x 16 0 9. Inc. She wants the play area to enclose at least 1800 square feet. x2 O 9x y 14 0 x x Copyright © Glencoe/McGraw-Hill. y x2 Practice Graphing and Solving Quadratic Inequalities x2 2x2 Graph each inequality. 4. Solve each inequality algebraically. How many $20 increases in profit can the maker add in and expect to make a total profit of at least $100. but predicts that each $20 increase in profit will reduce the number of bicycles sold by 10. 7. The maker wants to increase the profit margin this year.NAME ______________________________________________ DATE______________ PERIOD _____ 5-8 1. 9x2 31x 12 0 19. y 4x y 2 O O x x O x Use the graph of its related function to write the solutions of each inequality. x2 x 20 0 8. x2 4x 5 0 10. 9x 12x2 16.000? Chapter 5 60 Glencoe Algebra 2 . 9x2 36x 36 0 15. 7 106 9 1010 25. 19. 1.8 102)(6. Inc. 18.7 102) 24. 8u(2z)3 . 896. Some computers use 32-bit numbers.000.295. 2. LIGHT When light passes through water. TREES Deciduous and coniferous trees are hard to distinguish in a black-and-white photo. to identify each address in their memories. short for binary digit. 15. Express the result in scientific notation. 2x3y2 x2y5 2 3 2 4 4 d f 2 (3x 2y3)(5xy (x 3)4y 2 4 5 3 d f 3 8) 20(m2v)( v)3 5( v)2( m4) Express each number in scientific notation. 13. a division of The McGraw-Hill Companies.000056 21. The largest 32-bit number is nearly 4. ( 2b 4)( 2c3)3 12m8 y6 9my4 27x3( x7) 16x4 10. Each 32-bit number corresponds to a number in our base-ten system. y7 y3 y2 4. 6s5x3 18sx7 2 2 3r2s3z6 (4w 3z 5)(8w)2 14.NAME ______________________________________________ DATE______________ PERIOD _____ 6-1 Practice Properties of Exponents Simplify. 2.7 108 Evaluate. If an infrared wavelength measures about 8 10 7 meters and a blue wavelength measures about 4. (m4n6)4(m3n2p5)6 16.86 105 miles per second. 11. Copyright © Glencoe/McGraw-Hill. at what velocity does it travel through water? Write your answer in scientific notation. 17.5 10 7 meters. was first used in 1946 by John Tukey. 433. 27. (4d 2t5v 9.9 104) 23. n5 n2 3. But because deciduous trees reflect infrared energy better than coniferous trees. (2f 4)6 7. 12. COMPUTING The term bit. A single bit holds a zero or a one. the two types of trees are more distinguishable in an infrared photo. Write this number in scientific notation. Assume that no variable equals 0.7 109)(8. 0. t9 t 5. or strings of 32 consecutive bits. its velocity is reduced by 25%. (4. x 4 8 x 4 x4 6.000. If the speed of light in a vacuum is 1. (3. 26. 22. about how many times longer is the infrared wavelength than the blue wavelength? Chapter 6 9 Glencoe Algebra 2 Lesson 6-1 5dt 3v 1) 8.000 20. 6c 13n2) 2mp 7) (2t2 7w) 3) 4xy 3y2) ( 3m2 12) 9( y2 9r4y2( 3ry7 6a2w(a3w 18. ( 6n 11. 2xy4 6xy 2. (7a 24. (2n4 4s2) 28. 30. aw4) 11w2) 3x) xy 4) (6 (4 (4x2 y2) 7w2) 5x ( 3x2 3u2 2r3y4 3a4w2 4u) 8r10) Copyright © Glencoe/McGraw-Hill. (5x 27.8% and the other grows 6%. (w 6)(v2 8)2 4w)(5x 2s)(w2 4) 22. 1) (8n2 8) ( 3n 6p2) 3t 9n2) 5mp p2) 8. BANKING Terry invests $1500 in two mutual funds. 2x2(x2 xy 2y2) 20. If it is a polynomial. 3 3 2 ab d ( 5ab2d5 5 5ab) 21. 1. 5a2w3(a2w6 9aw6) 19. (u 16. 6. (2x2 14. (v2 23. (6w 10. state the degree of the polynomial. Chapter 6 16 Glencoe Algebra 2 . (3n2 9. GEOMETRY The area of the base of a rectangular box measures 2x2 4x 3 square units. 5x3 4. one fund grows 3. Inc. 12m8n9 (m n)2 5 r 6 s x 78 5. (5t 15. The height of the box measures x units. Write a polynomial to represent the amount Terry’s $1500 grows to in that year if x represents the amount he invested in the fund with the lesser growth rate. Find a polynomial expression for the volume of the box. a division of The McGraw-Hill Companies. (8x2 12. 25x3z Simplify. ( y 25. (x 9y)(2a 5y)2 3)(2n4 y)(x2 y) 3) 2y2) 2ws 3xy 29. 4 ac 3 2 a5d3 c 1 3. (5m2 13. 7. The first year.NAME ______________________________________________ DATE______________ PERIOD _____ 6-2 Practice Operations with Polynomials Determine whether each expression is a polynomial. 17. (x2 4w) 26. ( 30x3y 12x2y2 18x2y) ( 6x2y) 4. GEOMETRY The area of a rectangle is 2x2 11x 15 square feet. (a3 2x3 x 64) (a 4) 10. Inc. What is the height of the triangle? Chapter 6 23 Glencoe Algebra 2 Lesson 6-3 15. 15r10 Practice Dividing Polynomials 5r8 5r4 40r2 6k2m 12k3m2 2km2 9m3 2. What is the width of the rectangle? 26. 1. 3. (3w3 Copyright © Glencoe/McGraw-Hill. ( 6w3z4 3w2z5 4w 5z) (2w2z) 5. (6t3 2h4 5t2 2t 1) (3t 1) 23. 7w2 4w 3) (w 3) 14. (b3 2x3 x 27) (b 3) 11. 6x2 x 7 3x 1 21. 14p 3 3 24.NAME ______________________________________________ DATE______________ PERIOD _____ 6-3 Simplify. h3 h2 h2 1 h 3 25. 7f 2 10 8. (4a3 f2 f 8a2 a2)(4a) 1 6. GEOMETRY The area of a triangle is 15x4 3x3 4x2 x 3 square meters. (28d 3k2 2x2 x d 2k2 4dk2)(4dk2) 1 7. (6y2 5y 15)(2y 3) 1 19. The length of the rectangle is 2x 5 feet. The length of the base of the triangle is 6x2 2 meters. (6y4 15y3 28y 6) (y 2) 17. (x4 3x3 11x2 3x 10) (x 5) 16. (2r3 4p4 5r2 17p2 2p 2r 15) (2r 3) 22. 4x 3 6 13. (3m5 m 1) (m 1) . 3x 14 2 9. 6x 4 152 12. a division of The McGraw-Hill Companies. 4x2 2x 6 2x 3 20. (x4 3x3 5x 6)(x 2) 1 18. p(x) x3 x5 6. Inc. a division of The McGraw-Hill Companies. r(x 2) 15. and c. p(x) 7x2 5x 9 7. p(x) x4 1 3 x 2 1 x 2 10. 2 m2 1)(2x2 3m 12 9) 2. p(8a) 3x2 4 and r(x) 2x2 5x 1. b. 1. 12. Estimate the wind chill temperature at 0 F if the wind speed is 20 miles per hour. determine whether it represents an odd-degree or an even-degree polynomial function. p(x) 1 3 x 3 2 2 x 3 3x If p(x) 11. If it is not a polynomial in one variable. state the number of real zeroes. 13. explain why. 5.013s2 s 7 estimates the wind chill temperature C(s) at 0 F for wind speeds s from 5 to 30 miles per hour. 17. p(x) x5 4x3 8. WIND CHILL The function C(s) 0. f (x ) 19. 5[p(x 2)] For each graph. p(x) 3x3 x2 2x 5 9. p(x2 1) 16. r(a2) 14.NAME ______________________________________________ DATE______________ PERIOD _____ 6-4 Practice Polynomial Functions State the degree and leading coefficient of each polynomial in one variable. f (x ) 18. Chapter 6 30 Glencoe Algebra 2 . find each value. 1 3 a 5 3 2 a 5 4 a 5 4. describe the end behavior. f (x ) O x O x O x 20. (3x2 3. a. 5r(2a) Copyright © Glencoe/McGraw-Hill. 27 3xy3 12x2y2 10y Find p( 2) and p(3) for each function. 4. 6. S. what is the least degree the equation could have? 176 175 174 173 1 2 3 4 5 6 7 8 9 10 11 Months Since September.NAME ______________________________________________ DATE______________ PERIOD _____ 6-5 Practice Analyze Graphs of Polynomial Functions Complete each of the following. 2000 to July.9).5). (5. (7.3). How many turning points would the graph of a polynomial function through these points have? Describe them. 5. 2. use the following information. (3.6). f(x) x 2 1 0 1 2 3 4 O x3 f(x) 3x2 3 f (x ) 2.4). 2000 7.3). The Consumer Price Index (CPI) gives the relative price 179 for a fixed set of goods and services. f(x) x Copyright © Glencoe/McGraw-Hill. Chapter 6 37 Glencoe Algebra 2 Lesson 6-5 0 . 2001 is shown in the graph. 2. a. Describe the turning points of the graph. 5. (6. 1. Estimate the x-coordinates at which the relative and relative minima occur. f(x) x 2 1 x x3 f(x) 1.75x4 f(x) x3 3x2 4 f (x ) 4. 3. 177 Source: U.5x2 6x 1 8 4 f (x ) 0 1 2 3 4 –4 –2 O –4 –8 2 4x 3. Determine consecutive values of x between which each real zero is located. If the graph were modeled by a polynomial equation. The CPI from 178 September. Graph each function by making a table of values. 6. (4.7). LABOR A town’s jobless rate can be modeled by (1.5). f(x) x x4 4x3 f(x) 6x2 4x f (x ) 3 O x O x Consumer Price Index PRICES For Exercises 5 and 6. 0. c. (2. 4. Inc. (8. b. a division of The McGraw-Hill Companies. Bureau of Labor Statistics 5. n4 24. 13. 19. t4 4s4 49n2 21t2 32s3 0 80 0 0 25. 6p2 17p 45 Write each expression in quadratic form. 500x4 x2 18.NAME ______________________________________________ DATE______________ PERIOD _____ 6-6 Practice Solving Polynomial Equations Factor completely. Chapter 6 44 Glencoe Algebra 2 . 8b5 8b3 1 Copyright © Glencoe/McGraw-Hill. 3x3y2 2x2y 5xy 4. 28d6 25d3 16. y4 21. x2 xy 2x 2y 7. y2 20y 96 8. Solve each equation. 21 7t 3r rt 6. The longer leg of the triangle measures 5 miles less than the square of the shorter leg. The county has hired Meghan’s surveying firm to survey the parcel. and the hypotenuse of the triangle measures 13 miles less than twice the square of the shorter leg. if possible. 15a2b 10ab2 2. 3st2 9s3t 6s2t2 3. 2x3y x2y 5xy2 xy3 5. 4ab 2a 6b 3 9. 5x8 x2 6 15. 10b4 3b2 11 14. a division of The McGraw-Hill Companies. which is in the shape of a right triangle. s5 22. What are the x-coordinates of the points on the grid where the proton crosses the x-axis? 26. 1. PHYSICS A proton in a magnetic field follows a path on a coordinate grid modeled by the function f(x) x4 2x2 15. Inc. Find the length of each boundary. 4s8 4s4 7 17. x2 8x 8 12. write prime. SURVEYING Vista county is setting aside a large parcel of land to preserve it as open space. If the polynomial is not factorable. x4 7y3 625 50x2 18y2 0 49 0 0 20. The length of each boundary is a whole number. 6n2 11n 2 10. 6x2 7x 3 11. m4 23. 2x 1 26. x3 5x2 2x 24. what polynomials express the length and width of the pool? Chapter 6 51 Glencoe Algebra 2 Lesson 6-7 . f(x) 5. x 2 29. 17.NAME ______________________________________________ DATE______________ PERIOD _____ 6-7 1. Use synthetic substitution to estimate the population for 2010. f(x) 15. x 3 20. find the remaining factors of the polynomial. f(x) 13. x3 7x2 7x 15. x3 x2 14x 24. x5 x4 5x3 5x2 4x 4. f(x) 3. x 2 24. x 2 22. f(x) x2 x3 x3 x3 x4 2x4 3x4 x6 5x x2 6x2 x2 x3 3x3 4x3 2x5 10 2x 2x 4x 3x2 4x2 3x2 x4 x3 4 x 12 2x 5x 1 3 9x2 20 3 2x4 x5 Given a polynomial and one of its factors. x5 2x4 4x3 8x2 5x 10. f(x) 10. 3x 2 27. x 3 25. f(x) 7. 4x3 12x2 x 3. VOLUME The volume of water in a rectangular swimming pool can be modeled by the polynomial 2x3 9x2 7x 6. 18x3 9x2 2x 1. f(x) 8. x3 Copyright © Glencoe/McGraw-Hill. 30. where x is the number of years since 2005. f(x) 9. x3 9x2 27x 27. 2x 5x 2x2 2x2 3x2 2x2 x3 7x3 3 4 5 2x 2x x 2x2 4x 8 50 7 26 10 2. 6x3 5x2 3x 2. f(x) 4. f(x) 12. x 2 18. Some factors may not be binomials. x 1 28. 3x2 6x 8. 3x3 4x2 17x 6. x3 x2 8x 12. a division of The McGraw-Hill Companies. f(x) 14. If the depth of the pool is given by the polynomial 2x 1. f(x) x2 x2 x3 x3 x3 x4 Practice The Remainder and Factor Theorems Use synthetic substitution to find f( 3) and f(4) for each function. POPULATION The projected population in thousands for a city over the next several years can be estimated by the function P(x) x3 2x2 8x 520. f(x) 11. x 1 19. x 4 23. f(x) 16. x 3 21. f(x) 6. Inc. NAME ______________________________________________ DATE______________ PERIOD _____ 6-8 1. 2. p(x) x3 3x2 9x 7 13. 3i 20. The plans call for the box to be 10 inches by 8 inches by 6 inches. 11. h(x) 7x4 3x3 2x2 x 1 Find all the zeros of each function. negative real zeros. CRAFTS Stephan has a set of plans to build a wooden box. 9x Practice Roots and Zeros Solve each equation. x3 6x 20 0 6. 1 i 21. 3i 18. Chapter 6 58 Glencoe Algebra 2 . f(x) 4x3 2x2 x 3 8. He wants to reduce the volume of the box to 105 cubic inches. 4. 15 0 2. h(x) x3 7x2 17x 15 14. q(x) 3x4 x3 3x2 7x 5 10. x4 x3 x2 x 2 0 State the possible number of positive real zeros. Write and solve a polynomial equation to find out how much Stephen should take from each dimension. a division of The McGraw-Hill Companies. g(x) x4 4x3 3x2 14x 8 16. State the number and type of roots. He would like to reduce the length of each dimension in the plan by the same amount. f(x) x4 6x3 6x2 24x 40 Write a polynomial function of least degree with integral coefficients that has the given zeros. Copyright © Glencoe/McGraw-Hill. x4 5x2 4 0 3. 7. 17. Inc. p(x) 2x4 2x3 2x2 x 1 9. 1. x5 81x 4. x3 x2 3x 3 0 5. 2. and imaginary zeros of each function. 5. q(x) x4 50x2 49 15. 3 i 19. 5. h(x) 2x3 3x2 65x 84 12. h(x) x6 8x3 24. 21. q(x) 9. s(x) 7x 14 3. The volume of the box is 1540 in3. 2x 12 2. n(x) 7x 6 20. g(x) 5x3 x2 x 8 6. g(x) x6 1 25. v(x) 10. q(x) x3 x4 x3 2x3 x4 x4 6x4 9x2 49x2 6x 3x2 3x3 2x3 29x3 27x 27 20 4x 5x2 3 40x2 7x 12 4 27x 36 15. GEOMETRY The height of a square pyramid is 3 meters shorter than the side of its base. how tall is it? Use the formula V Bh. a division of The McGraw-Hill Companies. h(x) 13.NAME ______________________________________________ DATE______________ PERIOD _____ 6-9 1. q(x) x4 4x3 x2 16x 20 23. x3 x3 x3 x3 2x3 x4 2x4 3x2 x2 7x2 6x2 7x2 x3 7x3 6x 8x 17x 4x 21x 16 4x2 8 12 15 24 54 8. 7. The length is 2 inches more than twice the width. p(x) 3x2 x 7 5. q(x) 6x5 x3 3 Find all of the rational zeros of each function. z(x) 18. f(x) 2x4 7x3 2x2 19x 12 22. Inc. g(x) 16. 3 Chapter 6 65 Glencoe Algebra 2 Lesson 6-9 . f(x) 12. b(x) 14. 1 If the volume of the pyramid is 432 m3. p(x) Find all of the zeros of each function. TRAVEL The height of a box that Joan is shipping is 3 inches less than the width of the box. h(x) 17. c(x) 11. h(x) x3 Practice Rational Zero Theorem 5x2 x4 8x3 List all of the possible rational zeros of each function. d(x) 19. f(x) Copyright © Glencoe/McGraw-Hill. What are the dimensions of the box? 26. f(x) 3x5 5x2 x 6 4. g 3. (3. MEASUREMENT The formula f converts inches n to feet f. ( f g)(x). 4. and m converts 12 5280 feet to miles m. and 2. 3). 3). 1)} Copyright © Glencoe/McGraw-Hill. g(x) h(x) 13. 24. g(x) h(x) 8x 2x 3 2x x2 3x 2 10. ( 3. g(x) h(x) 12. (0. g(x) h(x) 3x x 4 x 3 2x2 9. g[h( 2)] 18. 1)} 2)} 6. 4)} {(0. g(x) h(x) x 6 3x2 x 2 3x2 1 If f(x) x2. find f g and g f if they exist. ( 1. 1). Write a composition of functions that converts inches to miles. 0). a division of The McGraw-Hill Companies. 8. ( f 2x x 1 3 g)(x). f[ g(1)] 17. h[f(20)] 15. [f (h g)]( 1) 23. f(x) g(x) Practice Operations on Functions g)(x). 1)} 5. f(x) g(x) x2 x2 7x 9 12 For each set of ordered pairs. h[ g( 3)] 21. (1. 6)} {(6. f g {(0.NAME ______________________________________________ DATE______________ PERIOD _____ 7-1 7-1 Find ( f 1. (1. (3. 2). (4. n f Chapter 7 9 Glencoe Algebra 2 Lesson 7-1 . Find [ g h](x) and [h g](x). f(x) g(x) 8x2 1 x2 f (x) for each f(x) and g(x). 16. ( 5. 0). and h(x) x 4. g(x) h(x) 11. 5). f[h( 9)] 20. 2). Inc. 0). ( 3.01x2 models the manufacturing cost per item when x items are produced. 3). {( 2. g(x) 5x. (0. and g(x) 150 0. Write a function C(x) for the total manufacturing and service cost per item. BUSINESS The function f(x) 1000 0. 0). h[f(4)] 19. g[f(8)] 22.001x2 models the service cost per item. find each value. f g {( 9. (6. 8)} {(8. 3). 9). (3. (1. f g {( 4. 4)} 7. f g {( 4. 3). ( 1. 1). [f (g h)](4) 14. (0. (12. 1)} Find the inverse of each function. ( 5.99 per square yard. Then graph the function and its inverse. g(x) h(x) 15. 8)} 3. (3. f(x) g(x) x x 2x 2x 6 6 11. a division of The McGraw-Hill Companies. 2). 1). (1. f(x) g(x) 14. 6). ( 5. 165) give the weight in pounds as a function of height in inches for 5 students in a class. {( 5. 2). 4). 10. (10. What will the new flooring cost the Cleary’s? Chapter 7 17 Glencoe Algebra 2 Lesson 7-2 . 1). (7. (65. (71. y 3x 2 f (x ) g (x ) y O x O x O x Copyright © Glencoe/McGraw-Hill. 140). f(x) g(x) 13. (0. 121). g(x) h(x) 13x 1 x 13 13 1 8 4 2x 1 x 2 16. and (72. {( 3. 7. The Clearys are replacing the flooring in their 15 foot by 18 foot kitchen. 1. 108). 4). 17. 3). The formula f(x) 9x converts square yards to square feet. 4). MEASUREMENT The points (63. (5. Determine whether each pair of functions are inverse functions. The new flooring costs $17. (7. use the following information. 7). Give the points for these students that represent height as a function of weight. (5. g(x) 3 x 9. {(8. 0). (1. {( 5.NAME ______________________________________________ DATE______________ PERIOD _____ 7-2 7-2 Practice Inverse Functions and Relations Find the inverse of each relation. {(0. 8)} 6. 1). 6)} 2. Find the inverse f 1(x). Inc. ( 2. (14. 2). (67. 180). REMODELING For Exercises 17 and 18. 9). What is the significance of f 1(x) for the Clearys? 18. 5). (4. 9). 13)} 4. {( 3. f(x) g(x) 4x 1 (1 4 6 x 7 7 x 6 1 x) 12. 7)} 5. f(x) 3 x 4 8. If v 70 feet per second and v0 8 feet per second. find h. y 1 y 2x 3 O x O x O x Copyright © Glencoe/McGraw-Hill. y y O 6x x 8. y 2 x y 2 O x O O x x 4. y y x 5 3 9. y y 5x 2. Inc. State the domain and range of each function. ROLLER COASTERS The velocity of a roller coaster as it moves down a hill is v v02 64h.NAME ______________________________________________ DATE______________ PERIOD _____ 7-3 Practice Square Root Functions and Inequalities Graph each function. WEIGHT Use the formula d 39602 WE Ws 3960. how far from Earth is the astronaut? Chapter 7 24 Glencoe Algebra 2 . y y x 1 3. 7. where v0 is the initial velocity and h is the vertical drop in feet. 1. y 2 y O 3x 2 x O x 10. y y 3x 4 5. y x 7 4 y 6. 11. If an astronaut’s weight on Earth WE is 148 pounds and in space Ws is 115 pounds. which relates distance from Earth d in miles to weight. a division of The McGraw-Hill Companies. Graph each inequality. 4 (0.1 7. 3 27x9y12 29. 4 256 12. 0.8 2. x2 10x 25 37. 17 feet. and c are the lengths of the sides of the triangle and s is half the perimeter of the triangle. b. 4 1296 17. The variable e in the formula is a measure of how well the object radiates energy. Chapter 7 31 Glencoe Algebra 2 Lesson 7-4 . 0. HERO’S FORMULA Salvatore is buying fertilizer for his triangular garden. 49a10b16 34. Hero’s formula states that the area of a triangle is s(s a)(s b)(s c). If the lengths of the sides of Salvatore’s garden are 15 feet. 4 (x 5)8 35. where a. 3 25 4. and 20 feet.94. 324 11.94)2 Simplify. 6 5555 8.NAME ______________________________________________ DATE______________ PERIOD _____ 7-4 Practice nth Roots Use a calculator to approximate each value to three decimal places. 676x4 y6 28. 49m2t8 22. 5 243x10 19. a division of The McGraw-Hill Companies. what is the object’s radiant temperature to the nearest tenth of a degree? 38. 3 216p3q9 27. 5 243 16. which is the amount of energy radiated by the object. what is the area of the garden? Round your answer to the nearest whole number. 5 89 3. Copyright © Glencoe/McGraw-Hill. The formula Tr Tk e relates an object’s radiant temperature Tr to its kinetic temperature Tk. 6 (m 4)6 32. The internal temperature of an 4 object is called its kinetic temperature. 3 4 5. 1. If an object’s kinetic temperature is 30°C and e 0. (2x)8 25. 3 64 1024 243 14. 144m8n6 30.512 15. 3 0. 5 18. 3 64r6w15 24. Inc. so he is using Hero’s formula to find the area. 3 (2x 1)3 33. 9. 3 343d6 36. 5 32x5y10 31. 4 625s8 26. 1. 4 7. 16m2 25 23.81 10. (14a)2 20. RADIANT TEMPERATURE Thermal sensors measure an object’s radiant temperature. He knows the lengths of all three sides.1 6. 6 64 13. (14a)2 21. 22. 15. 14. (1 6 )(5 7) 26. 45x3y8 1 4 7 c d 128 11. 12.NAME ______________________________________________ DATE______________ PERIOD _____ 7-5 Simplify. ( 5 6 )( 5 2) 24. 3 5 6 2 1 6 24 30. 6 20 8 5 5 45 20. Then evaluate s to the nearest mile per hour. Use the Pythagorean Theorem to find a simplified expression for the measure of the hypotenuse. 5 1215 7. Use the formula to write a simplified expression for s if 85. 3 8g3k8 216 24 8 9a3 10. 33. (3 7 )2 23. (3 15 )( 4 45 ) 17. 32. 3 2 3 5 2 2 2 29. a division of The McGraw-Hill Companies. 4 16. 35. 3 13. 3 432 3. 8 48 6 75 7 80 21. BRAKING The formula s 2 5 estimates the speed s in miles per hour of a car when it leaves skid marks feet long. 3 405 5. Chapter 7 38 Glencoe Algebra 2 . PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. 3 128 4. ( 2 10 )( 2 10 ) 25. 3 5000 6. 810 240 250 19. 5 4 3 2 3 3 x x 31. (3 2 2 3 )2 Copyright © Glencoe/McGraw-Hill. ( 108 6 3 )2 28. 540 4 Practice Operations with Radical Expressions 2. (2 24 )(7 18 ) 18. 34. 1. 4 48v8z13 11 9 9a5 64b4 9. 125t6w2 8. Inc. ( 3 4 7 )2 27. y 1 2 22. 27 3 1 27 3 1 3 Copyright © Glencoe/McGraw-Hill. where P is the power in watts and R is the 500 watts and resistance in ohms. (n3) 5 2 Write each radical using rational exponents. What is the company’s cost to produce 150 DVDs per day? Round your answer to the nearest dollar. 3 27m6n4 8. 4 6 3 6 4 29. 125 15. Inc. 1 9. a 3b 30. 5 2a10b Evaluate each expression. m 7 4. 6 5 3. 1 31. 25 2 64 343 3 Simplify each expression. 79 6. 1024 1 5 11. 64 3 2 17. g 7 3 5 g7 19.NAME ______________________________________________ DATE______________ PERIOD _____ 7-6 1 Practice Rational Exponents 2 4 1. a division of The McGraw-Hill Companies. 5. How much current does an appliance use if P R 10 ohms? Round your answer to the nearest tenth. 4 153 7. 5 3 2. s 4 3 s4 20. 85 27. b 10 23. ELECTRICITY The amount of current in amperes I that an appliance uses can be calculated using the formula I P R 1 2 . Chapter 7 45 Glencoe Algebra 2 Lesson 7-6 Write each expression in radical form. 81 4 3 4 10. u 1 3 4 5 21. q5 2 2 1 3 4 24. 4 3 3 13 18. BUSINESS A company that produces DVDs uses the formula C 88n 3 330 to calculate the cost C in dollars of producing n DVDs per day. 2z 2 1 q5 5t 2 5 t z2 1 26. t3 1 25. 256 2 3 13. 216 16. 12 123 28. ( 64) 2 14. . 8 2 3 5 3 1 4 12. 5 7h 2 7 9 w y 4m 1 9. 4r 2x z 2a 3 2) 4 1 17. STATISTICS Statisticians use the formula v to calculate a standard deviation . 8 27. Find the variance when the standard deviation is 15. 30. where v is the variance of a data set. 6 11. 21. GRAVITATION Helena drops a ball from 25 feet above a lake. a division of The McGraw-Hill Companies. 4 4 2m 8n 2t 3 4t 1 16. The formula t 1 4 25 h describes the time t in seconds that the ball is h feet above the water. 12. 14. 1. 3 a 25. 13. 22. 4 3h x 2 1 3 0 12 1 4 1 2 8 12 2 r 2x 4 3 5 2 13 1 0 2 6 7 3 5. 3 6. How many feet above the water will the ball be after 1 second? Chapter 7 53 Glencoe Algebra 2 Lesson 7-7 . c 2 7. 9 16 1 3 6 d 2x 2 3 4 1 10 0 10. x 1 29. 2d 6x 1) 2 5 4 12 2q c 4 5) 3 6 5 5 23. 9 5 6 26. 4 10 4.NAME ______________________________________________ DATE______________ PERIOD _____ 7-7 Practice Solving Radical Equations and Inequalities Solve each equation or inequality. 1 x 2p 6 d 3 8 3 9 2 q 6 5 5 1 2. Copyright © Glencoe/McGraw-Hill. 15. (6u 20. 24. (7v 18. 3. (3g 19. Inc. 28. 18 7 8. x3 4 a n2 a 25x2 1 10x 25 8. w2 y 11. Write a rational expression to describe the 5x 6 volume of the rectangular pyramid. 23. 2. 17. Inc. 9. 14. 15 (2m3n2)3 18m5n4 3. 16.NAME ______________________________________________ DATE______________ PERIOD _____ 8-1 9a2b3 27a4b4c 2k2 k2 x4 x3 x4 a 6 a w y n y y k 9 Practice Multiplying and Dividing Rational Expressions Simplify each expression. 12. 24x2 w5 6x2 4x 12x 12 15. 7s 15 (s 4)2 1 10s 25 s 4 2x 18. GEOMETRY A rectangular pyramid has a base area of and a height of x2 x2 x2 3x 2x 10 square centimeters 3x centimeters. 9 a2 a2 5a 6 2a 5a 6 10 19. 4 x x x x3 x2 (x 23 2x 2)3 4x 4 x2 9 4 x 8 20. Chapter 8 9 Glencoe Algebra 2 Lesson 8-1 6. Copyright © Glencoe/McGraw-Hill. 3 21. x 5 10x 2 2xy 3 w2 3x x2 6 9 x2 13. a division of The McGraw-Hill Companies. 10. 25 3v2 2u3y 15xz5 n5 n x2 6x a5y3 wy7 x 6 2s2 y 6 5x v2 13v 10 25x3 14u2y2 n2 n8 24 2x2 a3w2 w5y2 x2 3 s2 y2 5x2 8 x 6n 10y2 35y2 15y 5y 4. Determine the length of the other leg of the triangle. 1. 5. GEOMETRY A right triangle with an area of x2 4 square units has a leg that measures 2x 4 units. 2x2 7. x2 22. . 2r 8. x 4 4 5. 5 6ab 7 8a 11. 4w2 6d 9. x 3 2. Mai kayaks 2 miles downstream and then back to her starting point. Chapter 8 16 Glencoe Algebra 2 . 1 6c2d 3 4cd3 13.NAME ______________________________________________ DATE______________ PERIOD _____ 8-2 1. 2. x 1. 4w 9. d2 6. where d is the distance. g 7. to r write a simplified expression for the total time it takes Mai to complete the trip. 5 2x 12 x2 20 4x 12 20. 2x 5 x x 8 4 15. x 24. abc4 3g 8. GEOMETRY The expressions 5x 20 10 . . 2p p2 5p 3 6 p2 5 9 21. t d . r2 x r. x2 2. x2 1. and represent the lengths of the sides of a 2 x 4 x 4 triangle. x2y. a division of The McGraw-Hill Companies. 4m 3mn 2 14. y y2 3y 5 10 y2 y y 2 Copyright © Glencoe/McGraw-Hill. xy3 4. 1 5n 3 4 7 10n 2 1 y 1 x y x y r 6 r r2 r2 r 4r 2r 1 2 3 22. 16 x2 16 x 2 4 17. 2 5m m 9 4m 5 9 m 18. g2 2x Practice Adding and Subtracting Rational Expressions Find the LCM of each set of polynomials. 4 a 3 a 9 5 16. a2b3c. If r represents her rate in calm water. 19. x2 Simplify each expression. r 1 6x 8 3. 25. 3. 26. 2a a 3 a 2a 3 36 a2 9 23. then r 2 represents her rate with the current. Inc. and r 2 represents her rate against the current. 2(d2 1 9) 6. 5 12x4y 1 5x2y3 12. Use the formula for time. 10. KAYAKING Mai is kayaking on a river that has a current of 2 miles per hour. Write a simplified expression for the perimeter of the triangle. f (x ) shed a coat of paint. Inc. f(x) x2 x 7 10x 21 3. Graph f (x) 6 6x x 6 6x x describes the 0. f(x) x2 x 9x 5 20 Graph each rational function. f(x) x f (x ) 4 2 8. y 0. PAINTING Working alone. f(x) x x2 2 4x 4 4. What is the illumination in foot-candles that the object receives at a distance of 20 feet from the light source? What domain and range values are meaningful in the context of the problem? O d Chapter 8 23 Glencoe Algebra 2 Lesson 8-3 . The equation f (x) complete in 1 hour. It takes her father x hours working alone to give the Copyright © Glencoe/McGraw-Hill.NAME ______________________________________________ DATE______________ PERIOD _____ 8-3 Practice Graphing Rational Functions Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of each rational function. f(x) x2 x 100 10 5. what portion of the job can they complete together in 1 hour? What domain and range values are meaningful in the context of the problem? x 11. 7. f(x) (x 3x 3)2 f (x ) O O x x O x 10. f(x) x2 x 2x 6 24 6. 1. f(x) x x f (x ) 3 2 9. a division of The McGraw-Hill Companies. f(x) x2 6 3x 10 2. If Tawa’s O portion of the job Tawa and her father working together can for x father can complete the job in 4 hours alone. LIGHT The relationship between the illumination an object receives from a light source of I foot-candles and the square of the distance d in feet of the object from the source can be modeled by I(d) 4500 . Tawa can give the shed a coat of paint in 6 hours. Graph the function I(d) d2 4500 for d2 I 0 I 80 and 0 d 80. u 5. If y varies directly as x and y 10.5 3 4x Find each value. find x when y 6. find V when P 320 millimeters of mercury. or inverse variation. If y varies jointly as x and z and y and z 1. 14. If V 80 cubic centimeters when P 2000 millimeters of mercury. 33. Copyright © Glencoe/McGraw-Hill. If a spring stretches 20 inches with 25 pounds attached. 1. If y varies inversely as x and y 19. 21. Then name the constant of variation. joint. find y when x 3. 5. what is the area of a trapezoid when its height is 8 meters and its bases are 10 meters and 15 meters? Chapter 8 31 Glencoe Algebra 2 Lesson 8-4 . If y varies jointly as x and z and y and z 2. If y varies directly as x and y 12 when x 2 and z 3. 1. xy h 8. C d 8wz 2. find y when x 6 15. 2d 4s mn 3. If y varies directly as x and y 12.5. If y varies inversely as x and y 18. If the area is 480 square meters when the height is 20 meters and the bases are 28 meters and 20 meters. find y when x 6. If y varies inversely as x and y 17. L 7. 24 when x 1. 16. find y when x 2 and z 6. GEOMETRY The area A of a trapezoid varies jointly as its height and the sum of its bases. 4. find y when x 4 16 when x 3 when x 18 when x 5 when x 4.NAME ______________________________________________ DATE______________ PERIOD _____ 8-4 Practice Direct. 12 13. 4. y 4. If y varies jointly as x and z and y and z 8.4. find x when y 11. Joint.5. 37. SPRINGS The length S that a spring will stretch varies directly with the weight F that is attached to the spring. find y when x 5. find y when x 1.25 g 5 k 4. 2. GASES The volume V of a gas varies inversely as its pressure P. 0. and Inverse Variation State whether each equation represents a direct. a division of The McGraw-Hill Companies. If y varies directly as x and y 11. p 6. how far will it stretch with 15 pounds attached? 22. If y varies directly as x and y 8 when x 16 when x 132 when x 7 when x 2. 9. find x when y 20. find y when x 60 when x 3 and z 4. Inc.5. Identify the type of function represented by each equation. y x2 x 5x 6 2 y O x O x O x 10. | 2x 1| y B. BUSINESS A startup company uses the function P 1. a division of The McGraw-Hill Companies. y O x O x O x Match each graph with an equation below. y 3 y 8. PARKING A parking lot charges $10 to park for the first day or part of a day. y 3. After that.NAME ______________________________________________ DATE______________ PERIOD _____ 8-5 Practice Classes of Functions Identify the type of function represented by each graph. 1 C. 2 Chapter 8 39 Glencoe Algebra 2 Lesson 8-5 . x y O x O x O x Copyright © Glencoe/McGraw-Hill. A. Inc. it charges an additional $8 per day or part of a day. 1. y y x 2 3 D. 7. Describe the graph and find the cost of parking for 6 1 days. y 6. y 2x2 y 1 9. y 2.3x2 3x 7 to predict its profit or loss during its first 7 years of operation. Describe the shape of the graph of the function. 11. y 2x 5. y 4. Then graph the equation. g 17. 3 27. 5. x x s s 1 3x 1 2h 3 a 3 y 6 x 1 2b b 1 3 4v v x2 x2 1 4 4 6a 2a 2 5 h 2 1 1 s 5 x x 2 5s s 8 2 p 10 p2 2 5 y 5 t 0 3 h 1 10. 19. 22. Chapter 8 46 Glencoe Algebra 2 . 8 14. Her goal is to make 60% of her free throws.NAME ______________________________________________ DATE______________ PERIOD _____ 8-6 Practice Solving Rational Equations and Inequalities Solve each equation or inequality. the function f(x) 9 19 x represents Kiana’s new ratio of free throws made. 21. Inc. the distance q of the image of the object from the lens. How many successful free x throws in a row will raise Kiana’s percent made to 60%? Is this a reasonable answer? Explain. Check your solutions. 1. 7. BASKETBALL Kiana has made 9 of 19 free throws so far this season. What is the distance of an object from a lens if the image of the object is 5 centimeters from the lens and the focal length of the lens is 4 centimeters? Is this a reasonable answer? Explain. 5 12. 16. a division of The McGraw-Hill Companies. 20. 3. and the focal length f of the lens. 4. 7 a 19 y 4 x 1 2 x b b 12 2c v2 2 x 22 a 5 x 2 2 1 3 1 3 2 3v Copyright © Glencoe/McGraw-Hill. c c 1 4 5v v x 2 1 7 c2 2 2 24. 13. b 18. 11. 8. If Kiana makes her next x free throws in a row. 15. 1 6. OPTICS The lens equation lens. 9. 1 p 1 q 1 relates the distance p of an object from a f 28. 23. 12 x 3 4 3 2 4 p y 5 9 2t 4 w 4 5x 4 p 2 1 10 1 3p g g 1 n 3 k y y r r 4 r 2 y 4 4 3 k 7 5 y2 r2 r2 2 n 4 4 k2 2 1 2 n2 g w 1 1 3 3 2x 1 5 2 2 3 4 25 7k 14 3y 16 16 12 10 y 5 2. 8 ) Simplify each expression. 36n 24. (n 24 3 ) n 75 15. 2. 33x 22.4) and (2. Check your solution.6) 11. 76x 23. 0. 4. 13. Write an exponential function to model the population y of bacteria after x days. 125 5 11 Solve each equation or inequality. y 5(0. 164n 5 94n 1 3 1 1 n 8 1282n 1 BIOLOGY For Exercises 25 and 26.8) and (1.5(2)x y Sketch the graph of each function. (0. 3) and (1. (2 16. y 6 y5 11 6 6 13 17. use the following information. y 3(0. 13 2 ) 8 14. ) and (3. 4) 8. 19. The initial number of bacteria in a culture is 12. 1.5)x y O x O x O x Determine whether each function represents exponential growth or decay. Then state the function’s domain and range. (0. (0. 0. 26.5) Copyright © Glencoe/McGraw-Hill.6) x 5. a division of The McGraw-Hill Companies. 10. 92x 5 81 27x 4 20. 23n 72x 1 20 21. (0. n3 18. (0. EDUCATION A college with a graduating class of 4000 students in the year 2005 predicts that it will have a graduating class of 4862 in 4 years. 25. The number after 3 days is 96. 1. y Practice Exponential Functions 1. 7. y 4(3)x y 3. How many bacteria are there after 6 days? 27. Chapter 9 9 Glencoe Algebra 2 Lesson 9-1 . y 0.1(2) x 6. 10) 12. 1) and ( 1. Inc. (0. 10) 9.000. y 5 4 x Write an exponential function whose graph passes through the given points.NAME ______________________________________________ DATE______________ PERIOD _____ 9-1 1. Write an exponential function to model the number of students y in the graduating class t years after 2005.000. 2) and (1. Sounds that reach levels of 120 decibels or more are painful to humans. log7 1 16 1 49 1) 16. 125 1 81 2. The value of the account A at the end of five years can be determined from the equation log A log[1000(1 0. 1 3 4 1 1 64 3. log10 0. log6 (2y 3 2 8) 5 2) 2 33. log3 81 17. logy 16 34. log9 9(n Solve each equation or inequality. 53 4. 2log2 32 21. where R is the relative intensity of the sound. Chapter 9 17 Glencoe Algebra 2 Lesson 9-2 . Inc. log10 0. log4 x 30. log 1 27 3 20. 25. Find the value of A to the nearest dollar.04)5]. log7 q 32. log2 19. log3 (x2 4) 35. log3 1 81 3 5 4 10. log4 1 256 15. log 1 x 5 31. is L 10 log10 R. logn 1 8 3 0 3 20) log7 (x 27. log8 4 22. log10 n 28. log25 5 6 1 2 9. log2 64 11. log4 x 29. INVESTING Maria invests $1000 in a savings account that pays 4% interest compounded annually. 7776 5 6 Write each equation in exponential form. log6 64 24.0001 18. 14. 3 4 Practice Logarithms and Logarithmic Functions Write each equation in logarithmic form. log3 1 3 23. log8 (3x 3 3 4 7) log8 (7x 26. 70 5. logb 1024 6) 36. log6 216 3 5 8. 13. 34 81 1 6. 7. What is the relative intensity of 120 decibels? 38. log32 8 Evaluate each expression.00001 12. Check your solutions.NAME ______________________________________________ DATE______________ PERIOD _____ 9-2 1. log9 1 Copyright © Glencoe/McGraw-Hill. SOUND An equation for loudness. log7 (8x log3 x 37. in decibels. a division of The McGraw-Hill Companies. 5 may cause local damage. How many times greater is the amplitude of an earthquake that measures 4. log2 (5y 30.NAME ______________________________________________ DATE______________ PERIOD _____ 9-3 Use log10 5 expression. log10 245 Practice Properties of Logarithms 0. 9. where x represents the amplitude of the seismic wave causing ground motion. log10 175 0. log3 16 5) 1 log3 64 3 log10 m log8 (t log10 r 2 6 1 2 1) log10 2 log8 12 1) log10 b log3 (a log4 (x log8 (n log10 (r log4 1 1 1) 2y) log7 72 1 2 log10 w 9) 5) 1) log16 (x2 1 log2 (1 log7 3 2 log7 x 31. 4 log2 x 16. If the intensity of a certain sound is tripled. log10 (c2 10) 4) 2 log7 8 3 10. log10 8. a division of The McGraw-Hill Companies. log3 y 17. The Richter scale magnitude reading m is given by m log10 x.5 on the Richter scale is felt by many people. log10 4 25. log10 0. Inc. Check your solutions. SOUND Recall that the loudness L of a sound in decibels is given by L 10 log10 R.5 on the Richter scale than one that measures 3.5? Chapter 9 24 Glencoe Algebra 2 . log4 (x2 24. log8 48 14. by how many decibels does the sound increase? 32. 1. log16 (9x 28. log3 (a 22. where R is the sound’s relative intensity. log2 d 18. and an earthquake rated at 4. log9 (3u 15. log8 (n 0 log6 (7x log10 (c 10) 1) 26.6990 and log10 7 2. log10 25 6. log7 x 3 log10 4 2 log6 9 14) log8 w log2 5 5 log2 2 3) 3) 4) 3) 5) 2) log8 4 log2 405 log2 8 log10 4 2) 2) 4) log3 6 Copyright © Glencoe/McGraw-Hill. EARTHQUAKES An earthquake rated at 3. log6 x 13.2 Solve each equation. log10 35 5. log10 (b 20. log10 u log6 54 log9 5 log9 2u 12. log10 (3m 19. 3 log5 (x2 27. log7 n 11. log6 (2x 29. log10 7 5 5 7 25 7 4. log8 (t 21. log10 7.8451 to approximate the value of each 3. log10 (r 23. log2 18 24. log8 32 27. 6z 13. a division of The McGraw-Hill Companies. 25 100 1 2 2 9.9 27 3 10.NAME ______________________________________________ DATE______________ PERIOD _____ 9-4 1.51 1.58 10 8 mole per liter.05 Use the formula pH log[H ] to find the pH of each substance given its concentration of hydrogen ions. 42x 120 47. 4. log 101 Practice Common Logarithms Use a calculator to evaluate each expression to four decimal places. ACIDITY The pH of vinegar is 2.2 y 16. How many times greater is the relative intensity of the air-raid siren than that of the jet engine noise? Chapter 9 31 Glencoe Algebra 2 Lesson 9-4 . 9m 14.5x 15. How long will it take the culture to increase to 50. milk of magnesia: [H ] mole per liter Solve each equation or inequality. log 2.0 7 mole per liter 6 5. 30x 22. log11 9 28. SOUND An equation for loudness L in decibels is given by L 10 log R. where R is the sound’s relative intensity. log9 6 25. 2b 17. 5w 21.6 64. 5x 3 1 52n 1 Express each logarithm in terms of common logarithms.31 38 72 82. Then approximate its value to four decimal places. 5a 12. HORTICULTURE Siberian irises flourish when the concentration of hydrogen ions [H ] in the soil is not less than 1. 8.000 bacteria? 32. The number of bacteria N present after t hours is N 1000(2) t. 42x 18.51 10 2. An air-raid siren can reach 150 decibels and jet engine noise can reach 120 decibels.5 4 2 7.6. 2a 45. Round to four decimal places.9 and the pH of milk is 6. What is the pH of the soil in which these irises will flourish? 30. 3. 2n 20.16 mole per liter 10 11 7. log 0. 8. 2x 11. acid rain: [H ] 6. black coffee: [H ] 10 mole per liter 5 10 3.2 3. log7 8 29. BIOLOGY There are initially 1000 bacteria in a culture. 9z Copyright © Glencoe/McGraw-Hill. 23. log5 12 26. How many times greater is the hydrogen ion concentration of vinegar than of milk? 31. 2. Inc. milk: [H ] 2.1 50 17 9x 1 19. The number of bacteria doubles each hour. and k 0. A Pert. 4 ex 19 28. e x 31 23.5 5. ln (x 3) 5 43. ln ( 2x) 7 39.8 25. what is the balance in the account after 5 years? 46. ln 3. e4. ln 4x 3 38. ln 5x ln x 7 INVESTING For Exercises 45 and 46. 5ex 1 7 27.5x 6 32. ln 50 x 10. ln 9. ln 6 1. 17. 2ex 3 1 26.2 7. ln 2. 9. ln e 2y Solve each equation or inequality.2 Practice Base e and Natural Logarithms 0. e 8.NAME ______________________________________________ DATE______________ PERIOD _____ 9-5 1. ln (x 6) 1 41. 2e5x 24 Copyright © Glencoe/McGraw-Hill. find t. e5 10x 15. Chapter 9 38 Glencoe Algebra 2 .6 Use a calculator to evaluate each expression to four decimal places. 9 e2x 10 36.035.037 Write an equivalent exponential or logarithmic equation. ln (x 2) 3 42.7918 12. 45. e2 x 1 Evaluate each expression. e 4x 5 31. 2. e 3x 7 15 37. e0. and t is the time in years. a division of The McGraw-Hill Companies. ex 9 22. ex 8 14. 21. r is the annual interest rate.1 24. How long will it take the balance in Sarita’s account to reach $2000? 47. ln 0.2300 13. where P is the principal. ln 8 6.5x 10 40. eln 12 18.3 2.5 4. e3x 5 32 35. ex 5. If a 100. ln 3x ln 2x 9 44. e2x 1 55 34. Inc. ln e 1 20. y 50. eln 3x 19. ex 1. If Sarita deposits $1000 in an account paying 3. 33. 3ex 10 8 29. where a is the initial amount present and k is the decay constant for the radioactive substance.4% annual interest compounded continuously. e 2. use the formula for continuously compounded interest. e1. RADIOACTIVE DECAY The amount of a radioactive substance y that remains after t years is given by the equation y aekt. ln 1 3. ln 36 2x 11. e3x 8 30. e x 4 16. NAME ______________________________________________ DATE______________ PERIOD _____ 9-6 Practice Exponential Growth and Decay P1 1. If Dave originally paid $8400 for the car. a division of The McGraw-Hill Companies. in how many months is it worth $7350? 10.26t. Find the constant k in the decay formula for the substance. One of these.000? 5. BACTERIA How many hours will it take a culture of bacteria to increase from 20 to 2000 if the growth rate per hour is 85%? 3. Since Dave bought the car. After how many years will the value have depreciated to $100. INFLATION For Dave to buy a new car comparably equipped to the one he bought 8 years ago would cost $12. What is the value of k for Cobalt-60? 7. How long ago did the whale die? Use k 0. How long will it take for the population to reach 25. has several isotopes.000. POPULATION The population of rabbits in an area is modeled by the growth equation P(t) 8e0.7 years.000 depreciates at a fixed rate of 12% per year. where P is in thousands and t is in years. RADIOACTIVE DECAY Cobalt. WHALES Modern whales appeared 5 10 million years ago. Cobalt-60 is used to trace the path of nonradioactive substances in a system. The vertebrae of a whale discovered by paleontologists contain roughly 0. how long ago did he buy it? 6.25% as much carbon-14 as they would have contained when the whale was alive.000? 9. INVESTING The formula A an account that earns an annual interest rate r compounded twice a year. DEPRECIATION A computer system depreciates at an average rate of 4% per month.500.00012. 4. BIOLOGY In a laboratory. Suppose $500 is invested at 6% annual interest compounded twice a year. Inc. the inflation rate for cars like his has been at an average annual rate of 5. an element used to make alloys. DEPRECIATION A piece of machinery valued at $250. a culture increases from 30 to 195 organisms in 5 hours. is radioactive and has a half-life of 5. 8. If the value of the computer system was originally $12. RADIOACTIVE DECAY A radioactive substance has a half-life of 32 years. In how many years will the investment be worth $1000? 2. Chapter 9 45 Glencoe Algebra 2 Lesson 9-6 r 2t gives the value of an investment after t years in 2 .1%. cobalt-60. What is the hourly growth rate in the growth formula y a(1 r) t ? Copyright © Glencoe/McGraw-Hill. 5. 1.5) 4. 21. (4. 2). 4) 10. 30. 14. 6). 2) 7) 11. ( 14. (8. 11) 2) 1) 7) 2. 27. 5). 1). (9. 8 1 2 Find the distance between each pair of points with the given coordinates. (2. ( 6.2) 1 2 . 2). 26. 3) 2) 8) 22. 12. 8). 8) 7). ( 0. 3. 17.NAME ______________________________________________ DATE______________ PERIOD _____ 10-1 Practice Midpoint and Distance Formulas Find the midpoint of each line segment with endpoints at the given coordinates. 29. (12.2). 2) 5) 18. 9. ( 3. 24. ( 2. 13. (0. ( 4. (0. ( 6. 7. 3). 32. 0) 5). ( 2. 6) 23. 3). . ( 2. ( 6. ( 1. find the 25. (4. (4. 2). (10. 6) 4. (8. and ( 2. center of the circle and the length of its diameter. 4). (8. 1). 3). GEOMETRY Find the perimeter of a triangle with vertices at (1.6. (9. (5. 9).5. (8.5. 4). ( 2. Inc.5. (6. ( 5 2.1. ( 5. . (1. 6) 6). (5. 2). 3) 2). 3). (9. (10. 5). 20. 9) 8. 7). 16. 4 5) 2) and B is at ( 3. 28. 8) 6. ( 9. ( 7. (9. (9. (8. Copyright © Glencoe/McGraw-Hill. (4. 4. a division of The McGraw-Hill Companies. (3. (3. If A is at ( 6. Chapter 10 9 Glencoe Algebra 2 Lesson 10-1 . 4). (3. 5 5 5 31. 1. ( 5. ( 9. 15. ( 1. (1. 8).7). ( 4 2. ( 4. (1. GEOMETRY Circle O has a diameter AB. 6).4. 2. . 3). 7) 8). 3). ( 8. 2 3 7 .6 . 3). 4. ( 3. (8. 8 2 5 . (2.4 3 3 1 1 . 4) 6) 3) 19. ( 7. Write an equation for each parabola described below. a division of The McGraw-Hill Companies. 3). 7. 4). vertex ( 2. y 3x2 12x 7 Identify the coordinates of the vertex and focus. Chapter 10 16 Glencoe Algebra 2 .NAME ______________________________________________ DATE______________ PERIOD _____ 10-2 Practice Parabolas Write each equation in standard form. vertex (0. y (x y 4)2 3 5. y 2x2 12x 19 2. Then find the length of the latus rectum and graph the parabola. Assume that the bottom of the upward-facing dish passes through (0. 0) and that the distance from the bottom to the focus point is 8 inches. 1. 4. 1). Then draw the graph. Inc. axis of symmetry x 1. y 1 2 x 2 3x 1 2 3. TELEVISION Write the equation in the form y ax2 for a satellite dish. the equations of the axis of symmetry and directrix. vertex (1. a 0 y y y O x O O x x 10. x 3(y 1)2 y 3 O x O x O x Copyright © Glencoe/McGraw-Hill. and the direction of opening of the parabola with the given equation. latus rectum: 2 units. focus 0. 7 3 8 8. directrix x 3 9. x 1 2 y 3 1 y 6. passes through ( 4.9 unit 5. (x 1)2 y y2 4y 12 12. 5). endpoints of a diameter at ( 2. Write an equation to represent a possible boundary of the area affected by gale winds. (x 3)2 y2 16 y 9. Hurricane Katrina devastated southern Louisiana. Chapter 10 24 Glencoe Algebra 2 . 9) and (0.5. 15. tangent to x-axis Find the center and radius of the circle with the given equation. x2 y2 2x y 4 6y 26 –8 O –4 O –4 –8 4 8x x O x Copyright © Glencoe/McGraw-Hill. center 3 . radius 0. a division of The McGraw-Hill Companies. x2 y2 2x y O 6y 1 x O x O x WEATHER For Exercises 14 and 15. 0). 7. center at ( 9. center at ( 6. Gale winds can affect an area up to 300 miles from the storm’s center.NAME ______________________________________________ DATE______________ PERIOD _____ 10-3 Practice Circles Write an equation for the circle that satisfies each set of conditions. radius 8 units 1 . 11. 6. radius 5 2 units 4. center (2. x2 6x y y2 0 13. Write an equation to represent a possible boundary of Katrina’s eye. 2). radius 4 units 3. Then graph the circle. 26). 8. center (0. In 2005. Inc. use the following information. 3x2 3y2 y 12 10.2). the circular eye of a hurricane is about 15 miles in diameter. 4 2. 14. 5) 5) 12). center ( 4. A satellite photo of Katrina’s landfall showed the center of its eye on one coordinate system could be approximated by the point (80. 4. On average. 1. NAME ______________________________________________ DATE______________ PERIOD _____ 10-4 Practice Ellipses Write an equation for each ellipse. Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with the given equation. 3) 6. major axis 20 units long and parallel to x-axis. endpoints of minor axis at (0. major axis 10 units long. 0) Copyright © Glencoe/McGraw-Hill. SPORTS An ice skater traces two congruent ellipses to form a figure eight. (0. foci at ( 4. (y 36 1)2 (x 1 3)2 1 12. 0) and (4. minor axis 10 units long. 3) 5. 3) and (0. 2 15 ) 9. center at (2. 2). with the second loop to its right. 3) (3. 5) 3. 0). 2 5) y (0. 2) and (4. 2) and (0. (–6. a division of The McGraw-Hill Companies. (x 4)2 49 (y 25 3)2 1 y 8 4 y 4 –8 4 8x –4 O –4 –8 –12 y 4 x O x –8 –4 O –4 –8 13. 1. 8). 0) 12 x O 2. foci at (0. endpoints of minor axis at (0. Write an equation to model the first loop if its major axis (along the x-axis) is 12 feet long and its minor axis is 6 feet long. 3) y (4. (0. 3) (–5. center at (0. 0) and (9. endpoints of major axis at ( 9. 2 15 ) and (0. 3) and (7. y2 16 x2 9 1 11. 4. Write another equation to model the second loop. Inc. 0). endpoints of minor axis at (1. Chapter 10 32 Glencoe Algebra 2 . –3) (0. 4) 8. 2 5) 6 (11. Assume that the center of the first loop is at the origin. endpoints of major axis at (4. 1) 7. major axis 16 units long. Then graph the ellipse. 0) –6 O –2 (0. 3) y 2 –12 (–11. minor axis 6 units long and parallel to x-axis. 3) x (0. –1) O x Write an equation for the ellipse that satisfies each set of conditions. 10. center at (2. (–3. 0) and (3. vertices (0. 3) –8 –4 O 4 8x (–3. 1. 7). Suppose the vertices of such a mirror are located at ( 3. –2) (3. (y 1 2)2 (x 4 1)2 1 10. –3 5 ) –8 x (1. Copyright © Glencoe/McGraw-Hill. 0). 1) and (1. ASTRONOMY Astronomers use special X-ray telescopes to observe the sources of celestial X rays. 2 34 ) 8 y 3. which reflects the X rays to a focus. 8 4 (0. 0) and (5. ( 26.NAME ______________________________________________ DATE______________ PERIOD _____ 10-5 Practice Hyperbolas Write an equation for each hyperbola. 3 5 ) 2. conjugate axis of length 6 units 6. 1) and (1. Find the coordinates of the vertices and foci and the equations of the asymptotes for the hyperbola with the given equation. foci (1. 2 34 ) –4 (–1. 5. –2) Write an equation for the hyperbola that satisfies each set of conditions. y2 16 x2 4 1 9. 8. conjugate axis of length 18 units 9). 5) 4 (–3. 4. a division of The McGraw-Hill Companies. 0). O y x –4 (0. Write an equation that models the hyperbola formed by the mirror. 0). vertices ( 5. and one focus is located at (5. (y 4 2)2 (x 4 3)2 1 8 4 –8 –4 O –4 –8 y y y O 4 8x O x x 11. Chapter 10 39 Glencoe Algebra 2 Lesson 10-5 . Some X-ray telescopes are fitted with a metal mirror in the shape of a hyperbola. 7) and (0. vertices (1. vertices (1. foci 7. –2) 4 y (0. 0) 1 5) 3). Inc. –3) (0. –1) O –8 –4 (–3. Then graph the hyperbola. 7. circle. state whether the graph of each equation is a parabola. or hyperbola. ellipse. 4x2 y2 16 9. 5x2 5y2 45 0 11. State whether the graph of the equation is a parabola. O x O x O x Without writing the equation in standard form. Chapter 10 46 Glencoe Algebra 2 . 0) and then travels along a path that gets closer and closer to the line y 2 x. 0). Then graph the equation. 5 Write an equation that describes the path of the satellite if the center of its hyperbolic orbit is at (0. 1.NAME ______________________________________________ DATE______________ PERIOD _____ 10-6 Practice Conic Sections Write each equation in standard form. ASTRONOMY A satellite travels in an hyperbolic orbit. It reaches the vertex of its orbit at (5. 3x2 9 3y2 6y 6. x2 y2 6x 7 3. 9x2 y2 54x 6y 81 y y y Copyright © Glencoe/McGraw-Hill. 9x2 16y2 64y 80 0 10. 4y2 36x2 4x 144 0 13. ellipse. x2 2x y 12. 5x2 6y2 30x 12y 9 y y y O O x x O x 4. or hyperbola. 196y2 1225 100x2 5. 6x2 6y2 36 8. Inc. y2 3x 2. circle. a division of The McGraw-Hill Companies. Copyright © Glencoe/McGraw-Hill. 1. x x ( y 3)2 2 12. y y x2 x 2 y 20. 25x2 x 5 2 4y2 100 14. x x 2( y 1)2 y 3 6 3. If the ellipse can be modeled by the equation x2 4y2 4 for y 0 and the two congruent segments can be modeled by y 3 x and y 2 3 x. Inc. Assume that the center of the ellipse is at (0. a division of The McGraw-Hill Companies. x2 x2 y2 y2 64 8 Solve each system of inequalities by graphing. 9 ( y 3)2 3 x2 x2 y2 16 1 9 y2 13. GEOMETRY The top of an iron gate is shaped like half an ellipse with two congruent segments from the center of the ellipse to the ellipse as shown. x2 4y y2 3x 25 8. 4x2 2x2 9y2 9y2 36 18 11. x2 y2 y2 x2 3 3 16. x2 x2 4 y2 y2 8 4 1 15. x2 y 2y2 1 x 1 5. (x x 2)2 y2 y 1 5 2. 19.NAME ______________________________________________ DATE______________ PERIOD _____ 10-7 Practice Solving Quadratic Systems Find the exact solution(s) of each system of equations. 4y2 4x2 9x2 9y2 36 36 6. y2 y 3x2 6 2x 1 4. x2 7 y2 7 1 9 3x2 y2 17. y2 10 6x2 4y2 40 2x2 9. x2 x y2 3y 25 5 10. 0). x2 x2 y2 y2 8 4 36 16 y 21. 0) what are the coordinates of points A and B? Chapter 10 53 Glencoe Algebra 2 Lesson 10-7 . (y 16 3)2 (x 4 2)2 1 4 (x 1)2 (y 2)2 y –8 –4 O –4 4 8x O x –8 O x 22. y x2 x2 y2 3 9 7. 2 A B (0. x x2 2y y2 3 9 18. 7 17 . 18. 11. ? . d 0. 38. a1 7. 19.4. 10 14. a1 1 . Inc.15. 24. … . d 3. . 7. 100. in how many weeks will he have 101 students? 28. 3. 8. … 20.8. 11 26. n 7.2. … 19. a18 for 17. d 4 10. 6. a37 for 124.d 5 3 . a1 10. a1 Copyright © Glencoe/McGraw-Hill. Japan. 21. 6. d 2 9. 34. 6. a division of The McGraw-Hill Companies. … 3. 5. 1. … Find the arithmetic means in each sequence.8 Find the indicated term of each arithmetic sequence. He began with 26 students. 24. 1. 19.25. 114. … 2 2 2. 4. … 5. 11. ? . 4. … 5 5 Write an equation for the nth term of each arithmetic sequence. 3. 5. 8. . 1.n 5 Complete the statement for each arithmetic sequence. 4. SALARIES Yolanda interviewed for a job that promised her a starting salary of $32. … 22. 5. … 14. ? . EDUCATION Trevor Koba has opened an English Language School in Isehara. 5. ? . 1. a1 8. n 31 9 . a1 9. a1 16. 13. 5. 1.NAME ______________________________________________ DATE______________ PERIOD _____ 11-1 Practice Arithmetic Sequences Find the next four terms of each arithmetic sequence. 119. n 29 15. 1. a1 12. 17. 10 8. d 7 8. 166 is the ? th term of 30. 3. … 23. … 3. 2 is the ? th term of 3 4 .000 with a $1250 raise at the end of each year.d 6 1 3 12. 25. a1 5 . 86. 11. 11. 4. d 5. 93. 5. 3. ? . ? . 18 27. … Find the first five terms of each arithmetic sequence described. What will her salary be during her sixth year if she accepts the job? Chapter 11 9 Glencoe Algebra 2 Lesson 11-1 . 8. … . 82. If he enrolls 3 new students each week.d 2 1 2 11. d 6.1. a1 14. 14. 23. 5 15. an 85. a1 4. n 26. an 19. n 13.NAME ______________________________________________ DATE______________ PERIOD _____ 11-2 Practice Arithmetic Series Find Sn for each arithmetic series described. how many towels are stacked on the shelf? 28. n 15. 13 4 7 20 (1 9 11 27 … … 27 272 6 14. 13. a1 8.4. If the first person to win the jackpot wins $496. d 16. Each day the merchant adds an amount equal to the day of the month. 10 2n) 1) (5 j 1 3n) 10) 19. 1. n 20. d 3. a1 5. a1 7. an 13 8 22 21 33 3. BUSINESS A merchant places $1 in a jackpot on August 1. a1 10. n 11 3. a1 14. n 2. 4 1 86 6 83 11 80 5 … … (9 n 1 101 91 20 4n) Copyright © Glencoe/McGraw-Hill. 16. an 16. a1 1. Each layer of towels has one less towel than the layer below it. an 5. a1 12. an 4. an 15. 89 18. d 36. (2k k 4 21. an 6. he or she wins the $1 in the jackpot. (5n n 3 (4 n 1 4n) Find the first three terms of each arithmetic series described. an 5 44 12 13 148 121. a division of The McGraw-Hill Companies. a1 3. If there are 20 towels on the bottom layer and one towel on the top layer. STACKING A health club rolls its towels and stacks them in layers on a shelf. Sn 120 26. d 0. 8 17. an 6.n 3 Find the sum of each arithmetic series. the merchant adds $2 to the jackpot on August 2 and draws another name. If the customer is present. a1 9. an 5 . n 5. Sn 1207 24. n 98. a1 6. Sn 4 5 100 25. an 25. on what day of the month was her or his name drawn? Chapter 11 16 Glencoe Algebra 2 . n 15. n 10. If the customer is not present.8 2. d 5. n 16. Sn 45 27. d 2 . then draws the name of a regular customer. Inc. a1 11. n 1 20. an 10. 22. an 5. r 4. a8 for 16. 3.n 10 9 8 Copyright © Glencoe/McGraw-Hill. 4. 20. 96. … 17. … 5. ? . n 1 . If the number of bacteria doubles every 2 hours. 162.NAME ______________________________________________ DATE______________ PERIOD _____ 11-3 Practice Geometric Sequences Find the next two terms of each geometric sequence. LIGHT If each foot of water in a lake screens out 60% of the light above. 5. Write an equation for the nth term of each geometric sequence. r 1 . what percent of the light passes through 5 feet of water? 31. a1 10. 24. a1 9. … 180. 144. 25. 28. a1 15. ? . how many bacteria will be in the culture at the end of 12 hours? 30. 40. … 4. … 21.r 3 3 2 8. … Find the geometric means in each sequence. r 1 . r 3. 486. 19. 5. a1 5. 9 26. a12 for 96. ? . 90. 1 1 . ? . ? . . … Find the first five terms of each geometric sequence described. 1. 25. 15. a division of The McGraw-Hill Companies. 144. 16. a1 20. 30. 3. 30. 250 3.… 2 4 20. 80. . 7. INVESTING Raul invests $1000 in a savings account that earns 5% interest compounded annually. … 3. … 14. 37. … 12. a1 13. n 6 10 12. 12 29. 768 27. ? .… 10 2. ? .500.… 4 8 16 6. 5. n 14. a1 7. ? . 22. ? . 7. a1 1. r 1 . r 4 2 3 Find the indicated term of each geometric sequence. 1. r 1 . ? . 1280 28.n 2 1 . 50 6 1 . a1 9 18. 216. 11.n 5 8. How much money will he have in the account at the end of 5 years? Chapter 11 24 Glencoe Algebra 2 . r 12. Inc. ? . 1 3 9 . 6. 10. a1 3125. 48. r 3. 1. 30. … 2. BIOLOGY A culture initially contains 200 bacteria. 1458. 60. 1. 24. 23. . ? . ? . how many people will have heard the joke by the end of Saturday. a1 7. Sn 665. a1 9. Assuming no duplication. r 2 2 4 2. a1 4. r 6. 9 n 1 2 n 3 1 Find the indicated term for each geometric series described. 25. 2 16. r 16. not including Hugh? Chapter 11 31 Glencoe Algebra 2 Lesson 11-4 23.r 3 64. a1 12. r 2. r 5. 64 Copyright © Glencoe/McGraw-Hill. n 1 2560 1 n 2 1 22. an 3. CONSTRUCTION A pile driver drives a post 27 inches into the ground on its first hit. n 2 . 54 96 18 144 1 … to 6 terms … to 7 terms 9 14. r 2. a division of The McGraw-Hill Companies. COMMUNICATIONS Hugh Moore e-mails a joke to 5 friends on Sunday morning. Each of these friends e-mails the joke to 5 of her or his friends on Monday morning. n 6. n 10 1.5. r 1 2 2 3 192. 5( 2) n n 1 10 4 1 3 8 1 … to 8 terms … to 6 terms 5 1 9 8 17. 162 15.n 3 21 4 6 3. an 54. 28.NAME ______________________________________________ DATE______________ PERIOD _____ 11-4 Practice Geometric Series Find Sn for each geometric series described. 13.r 9 1 3 1. a1 . a1 5. 1 19. an 768. a1 2. a5 81. Sn 1365.160. a1 7 10. a1 6. n 9 16. r 3072.5. r 2 . and so on. n Find the sum of each geometric series. Sn 10. n 3. 6 ( 3) n n 1 18. a6 6. a1 26. a1 24. Sn 1023. 1. an 5. Inc. an 5120. a1 27. a1 3. a6 3. Find the total distance 3 the post has been driven after 5 hits. r 9. a1 11. r 1 . Each additional hit drives the post 2 the distance of the prior hit. r 4. n 1 1(4) n 4 1 20. r 3. a1 8. n 1 1 n 2 1 21. r 1. a1 160. n 12. r 6 2 5 2 7 3 4 3 5 1 2 2. a1 5. r 135. PENDULUMS On its first swing. 0.25 0. 0.3 22.1 135 13. On each successive swing.43 33. 0. 2 11. 0. a1 4. 0.150 35. 18 10. 0. 100 15. the ball continues to reach 9 of its previous height. … … 16.5 17. 26. a1 8. 10 traveled by the pendulum when it stops swinging? 36. 0. 24. 1. 0. 0. a1 6. 18. a1 9.84 29. ELASTICITY A ball dropped from a height of 10 feet bounces back With each successive bounce. n 0. if it exists. 6 12. n 1 5( 0.125 0. the pendulum travels 4 the distance of its previous swing.08 9 7 27 49 270 7 10 1 12 … … 7 100 1 6 … 0.5 7 1000 1 3 18 1 4 … … … 0. What is the total distance 5 9 of that distance.6 31. 25.243 28. r 500. a1 7. 3 21.1)n 1 Write each repeating decimal as a fraction. a1 3.06 23. 0.09 32. r 112. Inc.27 34. 4 25 35. a pendulum travels 8 feet.0006 … 0.990 30. 0. 10 14.00003 … 1 20.NAME ______________________________________________ DATE______________ PERIOD _____ 11-5 Practice Infinite Geometric Series Find the sum of each infinite geometric series. 0. What is 10 the total vertical distance (both up and down) traveled by the ball when it stops bouncing? (Hint: Add the total distance the ball falls to the total distance it rises. 27. 0. a division of The McGraw-Hill Companies. 3 n 1 20 0. r 6 4 1 2 8 3 1 2 6 5 1 5 … … … 67. r 98.8 19.003 2 6 3 n 4 … Copyright © Glencoe/McGraw-Hill.006 1 n 4 2 n 3 1 2 3 2 3 1 18 n 1 1 26.) Chapter 11 38 Glencoe Algebra 2 .008 … 0. r 42. a division of The McGraw-Hill Companies. 25. 1 in. f(x) Copyright © Glencoe/McGraw-Hill. a1 9. 1 in. x0 x. x0 5. x0 23. f(x) 15. x0 1 5 3 1 17. What is the perimeter of the new shape? 1 in. a1 7. 3x 8 4x 8x x2 4. 26. 13. f(x) 22. f(x) 1 1 18. a1 3. 24. an 1 1 5. a1 6. x0 1. use the following information. a1 5. a1 3. an 1 1 1 8an 1 1 1 Find the first three iterates of each function for the given initial value. f(x) 19. x0 3x. f(x) 20. f(x) 2 4x2. x0 2x2. Inc. INFLATION Iterating the function c(x) 1. a1 11. an 3. f(x) 10x 8 5(x 2. x0 3 1 1 14. What function f(x) can you iterate to find the perimeter of each successive shape if you continue this process? Chapter 11 45 Glencoe Algebra 2 Lesson 11-6 Find the first five terms of each sequence. a1 10. an 1. x0 3). a1 4. a1 12. an 3. an 4. Find the cost of a $2000 ring in five years at 5% inflation. an 8. a2 2. x0 9. f(x) 21. 1 in. a1 4 an 5an an 8. an 3. what will the perimeter of the third shape be? 27. a1 7. What is the perimeter of the original square? 1 in. a2 1 an 3an n 5 2 2. an 2. a2 1 an 10 3an 4an 8 an 1 1 1 an 3an 1 1 1 5 4an 2an an 6an 1.NAME ______________________________________________ DATE______________ PERIOD _____ 11-6 Practice Recursion and Special Sequences 1. f(x) 16. 3 in. FRACTALS For Exercises 24–27. a2 2. an 1.05x gives the future cost of an item at a constant 5% inflation rate. an 3. Replacing each side of the square shown with the combination of segments below it gives the figure to its right. . If you repeat the process by replacing each side of the new shape by a proportional combination of 5 segments. an 4. (3x 16. (5x Find the indicated term of each expansion.NAME ______________________________________________ DATE______________ PERIOD _____ 11-7 Practice The Binomial Theorem Evaluate each expression. (m 14. (x 15. (x 20. 9! 5! 12! 7. (a 22. 11! 6. 7! 5. GEOMETRY How many line segments can be drawn between ten points. 6!6! 4. 8! 5!3! 3. (r 13. if you use exactly two of the ten points to draw each segment? 32. 1. sixth term of (m 28. PROBABILITY If you toss a coin 4 times. (n 10. a division of The McGraw-Hill Companies. 8! 6!2! 2. how many different sequences of tosses will give exactly 3 heads and 1 tail or exactly 1 head and 3 tails? Chapter 11 53 Glencoe Algebra 2 Lesson 11-7 . 9. fourth term of (x b)10 s)14 3y)6 26. Inc. no three of which are collinear. seventh term of (a 27. v)5 y)4 y)6 3)5 5)5 4)4 y)4 y)4 3z)3 3)6 2y)5 y)5 3b)4 2z)4 4n)3 2y)4 19. (3m 24. 25. 3!38! Expand each power. tenth term of (2x 30. (2m 17. (w 18. (x 12. ninth term of (r 29. (3 23. fifth term of (2x n)10 y)12 1)9 31. 20! 18! 41! 8. (2x 21. (2d Copyright © Glencoe/McGraw-Hill. (x 11. 1 3 5 … (2n 1) 7. 1 2 4 8 … 2n 1 2n 1 2. 1 4 7 … (3n 2) n3 n2 n2 3n 2 1 2 5. 18n 1 is a multiple of 17.NAME ______________________________________________ DATE______________ PERIOD _____ 11-8 Practice Proof and Mathematical Induction Prove that each statement is true for all positive integers. Find a counterexample for each statement. Inc. 13 23 33 … n3 n4 n3 1 Chapter 11 60 Glencoe Algebra 2 . 1 4 9 … n2 n(n 1)(2n 6 1) Copyright © Glencoe/McGraw-Hill. a division of The McGraw-Hill Companies. 1. 4. 5n 2n 3 is divisible by 3. 6. 3. second. 1. and third place winners. 5.NAME ______________________________________________ DATE______________ PERIOD _____ 12-1 Practice The Counting Principle State whether the events are independent or dependent. and 2 different club head materials. 3 different grips. From 15 entries in an art contest. In how many ways can the four call letters of a radio station be arranged if the first letter must be W or K and no letters repeat? 9. How many 7-digit phone numbers can be formed if the first digit cannot be 0 or 1. How many 7-digit phone numbers can be formed if the first digit cannot be 0. There are five different routes that a commuter can take from her home to the office. choosing an offensive player of the game and a defensive player of the game in a professional football game 3. How many 7-digit phone numbers can be formed if the first digit cannot be 0 or 1. and any digit can be repeated? 11. In how many ways can she make a round trip if she uses a different route coming than going? 8. How many 6-character passwords can be formed if the first and last characters are digits and the remaining characters are letters? Assume that any character can be repeated. Solve each problem. She must select one of three morning history classes and one of two afternoon math classes. each containing 10 digits. How many different combinations are offered? 7. and any digit can be repeated? 10. Chapter 12 Copyright © Glencoe/McGraw-Hill. Inc. How many numerical codes are possible? 6. 4. Jillian is selecting two more courses for her block schedule next semester. 5 different lies. choosing an ice cream flavor and choosing a topping for the ice cream 2. 9 Glencoe Algebra 2 Lesson 12-1 . and no digit can be repeated? 12. and no digit can be repeated? 13. a camp counselor chooses first. a division of The McGraw-Hill Companies. A briefcase lock has 3 rotating cylinders. How many 7-digit phone numbers can be formed if the first digit cannot be 0. How many 6-character passwords can be formed if the first character is a digit and the remaining 5 characters are letters that can be repeated? 14. A golf club manufacturer makes irons with 7 different shaft lengths. 1. 3) C(6. C(11. a front. and a back 16. selecting 3 desserts from 10 desserts that are displayed on a dessert cart in a restaurant 17. making 5-sided polygons by choosing any 5 of 11 points located on a circle to be the vertices 20. 7) 5. If 8 people apply for the job. selecting a 4-person bobsled team from a group of 9 athletes 14. 18) 12. will allow her to buy only 4 new subscriptions. 3) 6. P(9. however. 13. Inc. Then find the number of possibilities. a division of The McGraw-Hill Companies. beginning with a woman 21. forming a 2-person sales team from a group of 12 salespeople 19. 2) 9. C(8. P(3. 3) 11. arranging 4 charms on a bracelet that has a clasp. If she takes photographs of 3 people in a group. C(3. P(4. How many different groups of students can be chosen from a class of 16 students? 22. 9) 2. STUDENT GROUPS Farmington High is planning its academic festival. 18. Her budget. SUBSCRIPTIONS A school librarian would like to buy subscriptions to 7 new magazines. P(8. P(7. 2) 10. 3) 7. 1) 3. 6) 4. 1) 8. C(9. an arrangement of the letters in the word annually Copyright © Glencoe/McGraw-Hill. an arrangement of the letters in the word Canada 15. how many different groups of 5 attendants can the airline hire? 24. How many different groups of 4 magazines can she choose from the 7 magazines? Chapter 12 16 Glencoe Algebra 2 . 2) Determine whether each situation involves a permutation or a combination. how many different groups can she photograph? 23. seating 5 men and 5 women alternately in a row. PHOTOGRAPHY A photographer is taking pictures of a bride and groom and their 6 attendants. C(20. P(4. AIRLINES An airline is hiring 5 flight attendants. C(9.NAME ______________________________________________ DATE______________ PERIOD _____ 12-2 Practice Permutations and Combinations Evaluate each expression. All math classes will send 2 representatives to compete in the math bowl. 28. P(1 red and 1 yellow) 5. Find the probability of each selection. The store has 28 books of wallpaper samples. 4 11 5 16 21. 5 99 9 70 23. P(1 quarter and 1 nickel) 12. a division of The McGraw-Hill Companies. and 5 yellow balls. P(550–559) 19. 24. 12 13 3 95 22. P(1 red and 1 green) A bank contains 3 pennies. P(1 WallPride and 3 Deluxe) 14. 16. The store will allow Henrico to bring 4 books home for a few days so he can decide which wallpapers he wants to buy. 26. use the Range 400–449 450–499 500–549 550–559 600–649 650 table that shows the range Number of 129 275 438 602 620 412 of verbal SAT scores for Students freshmen at a small liberal arts college. 8 nickels. P(4 WallPride) 15. P(1 nickel and 1 dime) 10. 15:1 34. 7. Two balls are selected at random. P(2 red) 4. 17. P(2 dimes) 9. P(1 quarter and 1 penny) 11. 1000:1 30. and 10 quarters. 9:7 35. P(2 red and 1 yellow) 3. Inc. find the probability of each selection. 2:5 33. 1. 4 dimes. P(3 WallPride and 1 Deluxe) For Exercises 17–20. If a freshman student is chosen at random. P(at least 650) Find the odds of an event occurring. Express as decimals rounded to the nearest thousandth. 12:17 31. 25. P(2 pennies) 8. 20. given the odds of the event. 1 1000 8 15 Find the probability of an event occurring. 2:23 32. 8:13 Glencoe Algebra 2 24 . P(400–449) 18. 27. 13.NAME ______________________________________________ DATE______________ PERIOD _____ 12-3 Practice Probability A bag contains 1 green. 4 red. Two coins are selected at random. 11:14 Chapter 12 29. P(2 WallPride and 2 Deluxe) Copyright © Glencoe/McGraw-Hill. given the probability of the event. If Henrico randomly chooses 4 books to bring home. P(2 dimes and 1 quarter) Henrico visits a home decorating store to choose wallpapers for his new house. including 10 books of WallPride samples and 18 books of Deluxe Wall Coverings samples. Find the probability of each selection. find each probability. P(2 green) 2. P(1 green and 1 yellow) 6. what is the probability that there is no rain on the first two days. Find the probability. Kershel’s mother is shopping at a bakery. She assigns each job a number from 1 to 20. use the following information. 2 dimes. 4 shades of yellow. P(no 4s) 4. then 5) 2. then 1) 5. Inc. Kershel selects one. P(three 4s) 3. Assuming that the daily probabilities of rain are independent. RANDOM NUMBERS For Exercises 15 and 16. determine whether the events are independent or dependent. then 1 quarter). Serena is creating a painting. Of the jobs. a division of The McGraw-Hill Companies. 12. 16. if no replacement occurs 10. What is the probability that neither selection was a chocolate chip cookie? 14. Without looking. and 6 shades of blue. She chooses randomly from 6 shades of red. The owner offers Kershel a cookie from a jar containing 22 chocolate chip cookies. Anita has a list of 20 jobs around the house to do. P(even number. and sets her calculator to generate random numbers from 1 to 20. 15. if replacement occurs 11. 3 are outside.NAME ______________________________________________ DATE______________ PERIOD _____ 12-4 Practice Multiplying Probabilities A die is rolled three times. 10 shades of green. and 15 oatmeal cookies. P(2. then dime. and the rest are inside. if replacement occurs 9. P(3 dimes). P(2 nickels. Use it to find the probability that the first two numbers correspond to inside jobs. 7. METEOROLOGY The Fadeeva’s are planning a 3-day vacation to the mountains. then 3. and the third to an outside job. 18 sugar cookies. Then find each probability. then quarter). She wants to use 2 more colors. P(three different even numbers) 6. and 5 quarters in a purse. then 5. P(nickel. then dime. if no replacement occurs 8. P(3 dimes). and plans to do 3 of them today. which can reoccur. drops it back in. A long-range forecast reports that the probability of rain each day is 10%. What is the probability that she chooses 2 shades of green? 13. 1. and then randomly selects another. Three coins are selected in succession at random. then odd number. then 1) There are 3 nickels. Sketch a tree diagram showing all of the possibilities that the first three numbers generated correspond to inside jobs or outside jobs. if no replacement occurs For Exercises 12 and 13. What is the probability that the number generated corresponds to an outside job three times in a row? Chapter 12 31 Glencoe Algebra 2 Lesson 12-4 . Find each probability. 4 shades of purple. P(any number. but that it rains on the third day? Copyright © Glencoe/McGraw-Hill. then quarter). P(nickel. a division of The McGraw-Hill Companies. What is the probability of selecting a senior or a female? 15. P(fewer than 3 white) 2. P(one 5) 9. and 3 pieces of blueberry pie. Find each probability. 7. there are 20 school superintendents. Six of the 12 seniors are females and 12 of the juniors are males. An airline has one bank of 13 telephones at a reservations office. 8 take reservations for domestic flights and 5 take reservations for international flights. If one of these people is chosen at random. A clerk chooses 4 CD players at random for floor displays from a shipment of 24 CD players. 13 principals. MUSIC Forty senior citizens were surveyed about their music preferences. 1. A department store employs 28 high school students. P(two 5s) 10. what is the probability that the person chosen takes domestic reservations or is a male? Copyright © Glencoe/McGraw-Hill. If an operator is chosen at random. what is the probability that he or she likes only country and western music? What is the probability that he or she likes classical and/or country. but not 1940’s pop? Classical 3 7 6 5 Country and Western 4 6 1940’s Pop 9 Chapter 12 38 Glencoe Algebra 2 . P(4 white or 4 blue) 4. 18. P(no 5s) 8. Then find the probability. P(at least 3 white) 6. P(one 5 or two 5s) Determine whether the events are mutually exclusive or inclusive.NAME ______________________________________________ DATE______________ PERIOD _____ 12-5 Practice Adding Probabilities An urn contains 7 white marbles and 5 blue marbles. P(three 5s) 11. The results are displayed in the Venn diagram. Inc. and 6 assistant principals. 4 pieces of chocolate cream pie. At a statewide meeting. P(at least two 5s) 12. what is the probability that he or she is either a principal or an assistant principal? 17. P(3 white or 3 blue) 3. Seven of the operators taking domestic reservations and 3 of the operators taking international reservations are female. P(no white or no blue) Jason and Maria are playing a board game in which three dice are tossed to determine a player’s move. If a senior citizen from the survey group is selected at random. what is the probability of choosing 4 players with a blue case or 4 players with a red case? 14. 13. Of the 13 operators who work there. If Janine selects a piece of pie at random for dessert. If 15 of the players have a blue case and the rest have a red case. all juniors and seniors. what is the probability that she selects either apple or chocolate cream? 16. P(exactly 3 white) 5. One student employee is chosen at random. A restaurant has 5 pieces of apple pie. Find each probability. Four marbles are selected without replacement. 335. 6.3. 8. 3.7. 850. median. Find the mean. Which measure would you quote as the “average?” Explain. 9. {10. 2001.4. As a hospital administrator. 3. 2. and standard deviation of the number of games played to the nearest tenth. 725. 18} 3. 8. 5. 1. 91. 82. {47. 0. S. 5} 4. use the frequency table that shows the percent of public school teachers in the U. Inc. 1.7. 4. Find the mean. 2. 11. Suppose you believe teachers use computers or the Internet too often. 1. a division of The McGraw-Hill Companies. 5. The 22 nurses on the same floor see the patients an average of 3 hours a day.5.3. in 1999 who used computers or the Internet at school for various administrative and teaching activities. HEALTH CARE Eight physicians with 15 patients on a hospital floor see these patients an average of 18 minutes a day. median. Activity Create instructional materials Administrative record keeping Communicate with colleagues Gather information for planning lessons Multimedia classroom presentations Access research and best practices for teaching Communicate with parents or students Access model lesson plans Source: National Assessment of Educational Progress Percent Using Computer or Internet 39 34 Copyright © Glencoe/McGraw-Hill. 22.5} 7. 12. 2. 96. 2001 and September 8. 9. of Games Frequency 141 140 139 138 137 136 135 Source: Major League Baseball 4 3 4 5 2 3 3 46 Glencoe Algebra 2 .9. 800. 54. 0. 23 16 8 8 8 6 10. 93. 1. {1100. or mode as an indicator of the amount of daily medical attention the patients on this floor receive? Explain. 91. 37} 2. 5. 3. 8. would you quote the mean. For how many players is the number of games within one standard deviation of the mean? Chapter 12 No.8. 61. use the frequency table that shows the number of games played by 24 American League baseball players between opening day. 3.4.6. 0. For Exercises 11 and 12. {3. 7.NAME ______________________________________________ DATE______________ PERIOD _____ 12-6 Practice Statistical Measures Find the variance and standard deviation of each set of data to the nearest tenth. and mode of the data. 4.1. 22.1. {1.5. 2.5. 3. 4. 4. median. {2. 4.8.9. For Exercises 8–10. 950} 5. 700. mode.6} 6. Suppose you believe teachers use computers or the Internet too infrequently. 5.9. 39. 5. 10. Which measure would you quote as the “average?” Explain. The scores on a test administered to prospective employees are normally distributed with a mean of 100 and a standard deviation of 15. About what percent of the scores are over 115? 8. about what percent of the days does the temperature meet your preference? Chapter 12 53 Glencoe Algebra 2 Lesson 12-7 15 . negatively skewed. 4. Inc. Do the data appear to be positively skewed. 3. About what percent of the scores are between 70 and 130? 6. 0–8 9–17 18–25 26 Hours TESTING For Exercises 5–10. or normally distributed. 5. how many would you expect to score lower than 85? 11. Make a histogram of the data.NAME ______________________________________________ DATE______________ PERIOD _____ 12-7 Practice The Normal Distribution Determine whether the data in each table appear to be positively skewed. About what percent of the scores are lower than 85 or higher than 115? 9.2 . or normally distributed? Explain.8 . TEMPERATURE The daily July surface temperature of a lake at a resort has a mean of 82 and a standard deviation of 4. use the frequency table that shows the number of hours worked per week by 100 high school seniors. If 80 people take the test. If you prefer to swim when the temperature is at least 77. a division of The McGraw-Hill Companies. Frequency 60 50 40 30 20 10 Weekly Work Hours Hours 0–8 9–17 18–25 26 Number of Students 30 45 20 5 Copyright © Glencoe/McGraw-Hill. how many would you expect to score higher than 130? 10. Time Spent at a Museum Exhibit Minutes 0–25 26–50 51–75 75–100 100 Frequency 27 46 89 57 24 2. About what percent of the scores are between 85 and 130? 7. 1. use the following information. negatively skewed. Average Age of High School Principals Age in Years 31–35 36–40 41–45 46–50 51–55 56–60 60 Number 3 8 32 40 38 4 For Exercises 3 and 4. If 75 people take the test. NAME ______________________________________________ DATE______________ PERIOD _____ 12-8 Practice Exponential and Binomial Distribution For Exercises 1–4, use the following information. The exponential distribution shown at the right has a mean of 0.25. Use the graph or function equation to find each probability. Round to the nearest hundredth. f(x ) 1 0.9 0.8 0.7 0.6 1. x 3. x 0.6 0.75 2. x 4. x 1 0.5 0.5 0.4 0.3 For Exercises 5–9, use the following information. A binomial distribution has a 25% rate of success. There are 41 trials. 5. What is the probability that there will be 11 successes? 6. What is the probability that there will be 26 failures? 0.2 0.1 0.25 0.5 0.75 1 1.25 1.5 1.75 2 3 4 x 7. What is the probability that there will be at least 3 successes? 8. What is the probability that there will be 38 or more failures? 9. What is the expected number of failures? HYGIENE For Exercises 10–13, use the following information. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. The mean amount of time a person spends brushing his or her teeth is 45 seconds. 10. What is the probability that a randomly selected person spends more than 2 minutes brushing his or her teeth? 11. What is the probability that a randomly selected person spends less than 1.5 minutes brushing his or her teeth? 12. 75% of people spend less than how long brushing their teeth? 13. 10% of people spend more than how long brushing their teeth? PROJECTS For Exercises 14–17, use the following information. Your science teacher is drawing names from a hat to assign groups of 4 for a project. Half of the people in your class are girls. 14. What is the expected number of girls in a group? 15. What is the probability that there will be 3 boys in a group? 16. What is the probability that there will be 2 or less girls in a group? 17. What is the probability that all four members of a group will be boys? Chapter 12 60 Glencoe Algebra 2 NAME ______________________________________________ DATE______________ PERIOD _____ 12-9 Practice Binomial Experiments Find each probability if a coin is tossed 6 times. 1. P(exactly 3 tails) 3. P(0 tails) 5. P(at least 4 tails) 2. P(exactly 5 tails) 4. P(at least 4 heads) 6. P(at most 2 tails) 2 The probability of Chris making a free throw is . If she shoots 5 times, find each 3 probability. 7. P(all missed) 9. P(exactly 2 made) 11. P(at least 3 made) 8. P(all made) 10. P(exactly 1 missed) 12. P(at most 2 made) When Tarin and Sam play a certain board game, the probability that Tarin will win 3 a game is . If they play 5 games, find each probability. 4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 15. P(Sam wins exactly 3 games) 17. P(Tarin wins at least 3 games) 16. P(Sam wins at least 1 game) 18. P(Tarin wins at most 2 games) 19. SAFETY In August 2001, the American Automobile Association reported that 73% of Americans use seat belts. In a random selection of 10 Americans in 2001, what is the probability that exactly half of them use seat belts? HEALTH For Exercises 20 and 21, use the following information. In 2001, the American Heart Association reported that 50 percent of the Americans who receive heart transplants are ages 50–64 and 20 percent are ages 35–49. 20. In a randomly selected group of 10 heart transplant recipients, what is the probability that at least 8 of them are ages 50–64? 21. In a randomly selected group of 5 heart transplant recipients, what is the probability that 2 of them are ages 35–49? Chapter 12 67 Glencoe Algebra 2 Lesson 12-9 13. P(Sam wins only once) 14. P(Tarin wins exactly twice) NAME ______________________________________________ DATE______________ PERIOD _____ 12-10 Practice Sampling and Error Determine whether each situation would produce a random sample. Write yes or no and explain your answer. 1. calling every twentieth registered voter to determine whether people own or rent their homes in your community 2. predicting local election results by polling people in every twentieth residence in all the different neighborhoods of your community 3. to find out why not many students are using the library, a school’s librarian gives a questionnaire to every tenth student entering the library 4. testing overall performance of tires on interstate highways only 5. selecting every 50th hamburger from a fast-food restaurant chain and determining its fat content to assess the fat content of hamburgers served in fast-food restaurant chains throughout the country Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 6. assigning all shift workers in a manufacturing plant a unique identification number, and then placing the numbers in a hat and drawing 30 at random to determine the annual average salary of the workers Find the margin of sampling error to the nearest percent. 7. p 10. p 13. p 26%, n 14%, n 34%, n 100 500 1000 8. p 11. p 14. p 55%, n 96%, n 49%, n 100 1000 1500 9. p 12. p 15. p 75%, n 21%, n 65%, n 500 1000 1500 16. COMPUTING According to a poll of 500 teenagers, 43% said that they use a personal computer at home. What is the margin of sampling error? 17. TRUST A survey of 605 people, ages 13–33, shows that 68% trust their parents more than their best friends to tell them the truth. What is the margin of sampling error? 18. PRODUCTIVITY A study by the University of Illinois in 1995 showed an increase in productivity by 10% of the employees who wore headsets and listened to music of their choice while they were working. The margin of sampling error for the study was about 7%. How many employees participated in the study? Chapter 12 74 Glencoe Algebra 2 NAME ______________________________________________ DATE______________ PERIOD _____ 13-1 Practice Right Triangle Trigonometry Find the values of the six trigonometric functions for angle . A 35 . 10. 4. 7 x 17 15. x 41 28 8. A 17 . Inc.2 15. SURVEYING John stands 150 meters from a water tower and sights the top at an angle of elevation of 36 . b 25 A b c C a B 12. x 17 30 7 Copyright © Glencoe/McGraw-Hill. B 71 . b 7 14. 5.2 9. c 8 13. c 95 16. 3 3 3 Write an equation involving sin. b 52. How tall is the tower? Round to the nearest meter. a division of The McGraw-Hill Companies. a 4. B 36 . Then solve the equation. x 49 32 20 7. 5 3. 1. a 12 11. or tan that can be used to find x. cos.3 x Solve ABC by using the given measurements. 45 11 24 2. 19. c 3. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. Chapter 13 9 Glencoe Algebra 2 Lesson 13-1 . x 6. M. 72 Find one angle with positive measure and one angle with negative measure coterminal with each angle. 20. 870 13. Round to the nearest degree and nearest radian. 820 5 2 7 12 9. 18 11. 22. ROTATION A truck with 16-inch radius wheels is driven at 77 feet per second (52. a division of The McGraw-Hill Companies. 33. 347 14. 210 y 2. 580 y O x O x O x 4.NAME ______________________________________________ DATE______________ PERIOD _____ 13-2 Practice Angles and Angle Measure Draw an angle with the given measure in standard position. 17. 2 5 3 2 24. 6 12. 31. 32.5 miles per hour). Inc. 285 28. 34. TIME Find both the degree and radian measures of the angle through which the hour hand on a clock rotates from 5 A. 80 27. 36. 9 2 8. 110 29. 250 13 5 3 8 10. 21. 4 19. 18.M. 65 26. 560 y O x O x O x Rewrite each degree measure in radians and each radian measure in degrees. 15. 16. 30. 37 5 6 4 25. 165 13 30 3 16 Copyright © Glencoe/McGraw-Hill. Chapter 13 16 Glencoe Algebra 2 . 93 17 6 5 12 35. 450 y 6. Find the measure of the angle through which a point on the outside of the wheel travels each second. 7. to 10 A. 23. 305 y 3. 135 y 5. 1. Inc. if the terminal side of 5) Find the reference angle for the angle with the given measure. some of the light rays are bent or refracted as they pass from the air through the material. 8. 16. 7 4 Find the exact value of each trigonometric function. 21) 3. find the exact values of the remaining five trigonometric functions of . The angles of reflection 1 and of refraction 2 in the diagram at the right are related by the equation sin 1 n sin 2. sin 2 . find the measure of 2. Quadrant IV 5 17. cot ( 90 ) 14. tan 12 . 8) 2. For each function. 1. 4. tan 13 6 Copyright © Glencoe/McGraw-Hill. FORCE A cable running from the top of a utility pole to the ground exerts a horizontal pull of 800 Newtons and a vertical pull of 800 3 Newtons. LIGHT Light rays that “bounce off” a surface are reflected by the surface. air 1 1 surface 2 19. csc 3 4 10. cot 210 13.NAME ______________________________________________ DATE______________ PERIOD _____ 13-3 Practice Trigonometric Functions of General Angles Find the exact values of the six trigonometric functions of in standard position contains the given point. If the surface is partially transparent. What is the sine of the angle between the cable and the ground? What is the measure of this angle? 800 N 800 3N Chapter 13 23 Glencoe Algebra 2 Lesson 13-3 Suppose is an angle in standard position whose terminal side is in the given quadrant. ( 20. 13 8 6. cot 2 11. (6. 210 7. . ( 2. 236 5. a division of The McGraw-Hill Companies. Quadrant III 3 18. If 1 60 and n 3. tan 5 3 9. cos 405 15. tan 135 12. NAME ______________________________________________ DATE______________ PERIOD _____ 13-4 Practice Law of Sines Find the area of 1. B 13. b 4 3. C 32 . 2. B 9 cm 40 9 cm C 46 11 yd A C A C A 4. a 14. She leaves a dock and heads due north in her boat to the first nesting site. A 20. A 56 . a 30 . checks boaters on a lake to make sure they do not disturb two osprey nesting sites. A 16. b 15.6 ft Solve each triangle. A 70 .4 ft.6 cm 6. A 19. A 11. b 107 . an officer for the Department of Fisheries and Wildlife.9 cm. b 8. A 34 . a 6. Then solve each triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. a 113 . C 25 . or two solutions. c 14 km 7. A 10. From here. one solution. B 80 .6 m.9 m 5. WILDLIFE Sarah Phillips. a 25. C 72 . C 38 . a 12. 9 yd ABC to the nearest tenth. c 8. c 6 9 40 9. A 21. She then travels 6. a division of The McGraw-Hill Companies. b 13 25 7 18 15. Inc. b 8 8 20 8 22.4 . A 17. a 110 . a 60 . b 12 13 12 Copyright © Glencoe/McGraw-Hill. b 20. a 8. 12 m 58 B B 15 m 3. A 17. she turns 5 north of due west and travels an additional 2. c 18. b 12. a 66 . a 112 . b 21.7 miles directly back to the dock. A 12. a 45 . 8. c 14 . A 18. b 19. Determine whether each triangle has no solution. Chapter 13 30 Glencoe Algebra 2 . How far from the dock is the first osprey nesting site? Round to the nearest tenth.14 miles to the second nesting site. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. 14. b 5. a 54 . A 29 . b 12 km. B 27 . B 47 . A 50 . 5 14.2 inches long from point A to point B. c 18. B 12 80 2. b 18 7. b 6. c 6. Inc. a 18. b 7. The straight-line distance between Station A and the plane is 7. C A 3 C 4 6 3. DRAFTING Marion is using a computer-aided drafting program to produce a drawing for a client.9 miles. 1. 4. b 30 13.1.5 . c 9 9. a 20.3 . C 112 .4 miles. how long is the segment from C to A? Chapter 13 37 Glencoe Algebra 2 Lesson 13-5 . A 23 .4 mi B 17. Then solve each triangle. A 37 . she moves 42 degrees counterclockwise from the segment connecting A and B and draws a second segment that is 6. From B. C 35 .6 . a 11 6. A 46. b 13 12. She begins a triangle by drawing a segment 4. C 40 80 A 7 B 30 B A 4. a 8.4 mi 6. To the nearest tenth. b 8. a 35. b 5.4 inches long. c 8 11.9 mi A 2. C 43. ending at point C. What is the angle of elevation from Station A to the plane? Round to the nearest degree. c 11 16. SATELLITES Two radar stations 2. c 6 15. A 78. The straight-line distance between Station B and the plane is 6. b 21. B 46. a 16. C 54 5. b 10.4 miles apart are tracking an airplane.4. c 12 10. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. B 71 . b 20. a Copyright © Glencoe/McGraw-Hill. b 24 8. a 16.NAME ______________________________________________ DATE______________ PERIOD _____ 13-5 Practice Law of Cosines Determine whether each triangle should be solved by beginning with the Law of Sines or Law of Cosines.3 . a division of The McGraw-Hill Companies. 7. a division of The McGraw-Hill Companies. P 2 .5 revolutions per minute. P(0.6) 2. cos ( 330 ) 11 4 11. FERRIS WHEELS A Ferris wheel with a diameter of 100 feet completes 2. sin 585 17. 7. 2 2 2 6. cos 18.8. P 3 1 . sin 13. cos 600 12. Inc. cos 7 10 3 14. 2 2 and cos . cos 7 4 8. What is the period of the function that describes the height of a seat on the outside edge of the Ferris Wheel as a function of time? Chapter 13 44 Glencoe Algebra 2 . 1 O 1 2 y 2 3 4 5 6 21. P 3 1 . sin ( 30 ) 9 2 9. 29 21 29 4. sin 840 Copyright © Glencoe/McGraw-Hill. P(0. cos 15. 2 2 Find the exact value of each function. 1 O 1 2 1 2 3 4 5 6 7 8 9 10 y 20. 1) 5. sin ( 225 ) 16. 0. Find sin 1. 19.NAME ______________________________________________ DATE______________ PERIOD _____ 13-6 Practice Circular Functions The given point P is located on the unit circle. P 20 . sin 2 3 10. 3. Determine the period of each function. Cos 1 tan 3 4 22. 1. 7. Arctan 3 3 16. Cos 1 3 2 x 9.NAME ______________________________________________ DATE______________ PERIOD _____ 13-7 Practice Inverse Trigonometric Functions Write each equation in the form of an inverse function. Which pulley moves through a greater angle? 26. and y cos 1 0. Both angles are greater than 270 and less than 360 . 1 3 2 14.17 describes the angle through which pulley B moves. cos 2. tan Cos 1 1 2 17. tan sin 1 12 13 20. cos [Arctan ( 1)] 19. sin 2 Cos 1 15 17 24. Arcsin 1 x 2 8. Round to the nearest hundredth. tan 3. Through how many degrees has the flywheel rotated after 25 milliseconds? Chapter 13 51 Glencoe Algebra 2 Lesson 13-7 . cos 3 1 2 Solve each equation by finding the value of x to the nearest degree. Sin 1 1 2 x Find each value. x Arctan ( 12. x 3) tan 1 3 3 10. Sin 1 cos 3 23. y tan 120 4. Sin 1 2 2 15. PULLEYS The equation x cos 1 0. Inc. cos 2 Sin 1 3 2 25. Write angle measures in radians. 1 2 cos x 5.95 describes the angle through which pulley A moves. sin 2 3 3 2 6. a division of The McGraw-Hill Companies. cos Sin 1 3 5 18. Cos Copyright © Glencoe/McGraw-Hill. 13. x Arccos 2 11. FLYWHEELS The equation y Arctan 1 describes the counterclockwise angle through which a flywheel rotates in 1 millisecond. sin Arctan 3 3 21. The function Fx 500 cos describes the relationship between the angle and the horizontal force. Then graph each function. Inc. a division of The McGraw-Hill Companies. An anchoring cable exerts a force of 500 Newtons on a pole.0 120 240 360 480 180 360 540 720 90 180 270 360 Copyright © Glencoe/McGraw-Hill. The force has the horizontal and vertical components Fx and Fy. use the following information. The function y 60 25 sin t.5 1. 9. What is the maximum high temperature and when does this occur? Chapter 14 9 Glencoe Algebra 2 Lesson 14-1 . What does this period represent? 10. y cot y 1 2 3. (A force of one Newton (N). y csc y 4 2 O 2 3 4 5. 2y sin y 1. use the following information. The function Fy 500 sin describes the relationship between the angle vertical force.NAME ______________________________________________ DATE______________ PERIOD _____ 14-1 Practice Graphing Trigonometric Functions Find the amplitude. if it exists. y 4 sin y 4 2 O 2 4 4 2 O 2 4 1 O 2. 6 models the average high temperature in degrees Fahrenheit in Centerville. is the force that gives an acceleration of 1 m/sec2 to a mass of 1 kg.) 7.0 0. 1. Determine the period of this function. What are the amplitude and period of this function? 8. where t is in months and t 0 corresponds to April 15. y cos 5 y 1 90 180 270 360 90 180 270 360 45 90 135 180 4. 4 FORCE For Exercises 7 and 8. What are the amplitude and period of this function? 500 N Fy Fx and the WEATHER For Exercises 9 and 10. y 2 tan y 4 2 O 2 4 1 2 6.5 O 0. and period of each function. The function that represents Jason’s blood pressure P can be modeled using a sine function with no phase shift. Jason’s heart rate is 45 beats per minute. 7. where t is the number of years since the stand was first cut in November. and period in seconds of the function. y 2 cos ( 30 ) 3 3. How often does the insect population reach its maximum level? Copyright © Glencoe/McGraw-Hill. The population of an insect species in a stand of trees follows the growth cycle of a particular tree species. Chapter 14 16 Glencoe Algebra 2 . Inc. and phase shift for each function. Find the amplitude. Write a function that represents Jason’s blood pressure P after t seconds. y 1 tan 2 2 2. period. Graph the function. When did the population last reach its maximum? 6. What condition in the stand do you think corresponds with a minimum insect population? BLOOD PRESSURE For Exercises 7–9. The insect population can be modeled by the function y 40 30 sin 6t. 4. 8. Then graph the function. a division of The McGraw-Hill Companies. 1. 1920. Jason’s blood pressure is 110 over 70. meaning that the pressure oscillates between a maximum of 110 and a minimum of 70. amplitude. midline.5 y 4 2 O 2 4 2 y 6 4 2 3 2 y 4 O 4 8 180 360 540 720 12 90 180 270 360 2 O 2 ECOLOGY For Exercises 4–6.NAME ______________________________________________ DATE______________ PERIOD _____ 14-2 Practice Translations of Trigonometric Graphs State the vertical shift. use the following information. use the following information. 5. y 3 csc (2 60 ) 2. P Jason’s Blood Pressure 120 Pressure 100 80 60 40 20 0 1 2 3 4 5 6 Time 7 8 9 t 9. sec . sin . sin . cot . if cos 1 and 270 3 360 Simplify each expression. For any point B not directly below the plane. a division of The McGraw-Hill Companies. if tan 1 and 270 2 360 9. AERIAL PHOTOGRAPHY The illustration shows a plane taking an aerial photograph of point A.NAME ______________________________________________ DATE______________ PERIOD _____ 14-3 Practice Trigonometric Identities Find the value of each expression. however. 1 cos sin 1 19. Express (sin )(csc sin ) in terms of cos only. 14. csc2 1 cot2 cos2 cos sin 16. sin . sin2 cot2 . there is no distortion in the image. cot2 1 15. Chapter 14 23 Glencoe Algebra 2 Lesson 14-3 11. csc cos sin 17. if csc 3 and 180 2 270 6. csc tan 12. 1. cot . the increase in distance creates distortion in the photograph. if cos 5 and 0 13 90 2. sin2 tan2 13. the exposure of the film reduces by (sin )(csc sin ). cot . sec2 cos2 tan2 20. if cot 1 and 0 2 90 5. if sin 15 and 180 17 270 3. Inc. Express a in terms of csc t. sin cos cot 18. TSUNAMIS The equation y a sin t represents the height of the waves passing a buoy at a time t in seconds. if tan 2 and 0 5 90 10. Copyright © Glencoe/McGraw-Hill. sec . This is because as the distance from the camera to the point being photographed increases. if tan 4 and 180 270 8. A B 21. cot . Because the point is directly below the plane. sec . if csc 8 and 270 360 7. if cos 3 and 270 10 360 4. 7. where E is the illuminance in foot candles on a surface. Verify the identity 8. tan4 2 tan2 1 sec4 5. sin2 cos2 cos2 sec2 2. where sin2 2gh sec2 . Chapter 14 30 Glencoe Algebra 2 . (sin2 )(csc2 sec2 ) sec2 Copyright © Glencoe/McGraw-Hill. (1 sin )(1 sin ) cos2 4. sec2 1 is the angle between the ground and the initial path.NAME ______________________________________________ DATE______________ PERIOD _____ 14-4 Practice Verifying Trigonometric Identities Verify that each of the following is an identity. and is the angle between the light beam and a line perpendicular to the surface. Verify the identity ER2(1 tan2 ) cos ER2 sec . and g is the acceleration due to gravity. 1. Inc. a division of The McGraw-Hill Companies. LIGHT The intensity of a light source measured in candles is given by I ER2 sec . R is the distance in feet from the light source. h is the maximum height reached. cos2 cot2 cot2 cos2 6. cos2 1 sin2 1 3. PROJECTILES The square of the initial velocity of an object launched from the ground is v2 2gh sin2 2gh . SOLAR ENERGY On March 21. 15. for a location that has a latitude of . use the following information. cos x 6 sin x 3 sin x 14. in terms of cos . In a certain circuit carrying alternating current. 16. cos 375 5. cos (180 ) cos 11. sin 150 8. Inc. sin ( 165 ) 6. Use the difference of angles formula to find the amount of solar energy. sin 225 2. Glencoe Algebra 2 37 Lesson 14-5 . 1. 13. Rewrite the formula using the sum of two angles. the maximum amount of solar energy that falls on a square foot of ground at a certain location is given by E sin (90 ). where is the latitude of the location and E is a constant. a division of The McGraw-Hill Companies.NAME ______________________________________________ DATE______________ PERIOD _____ 14-5 Practice Sum and Difference of Angles Formulas Find the exact value of each expression. cos 240 9. sin (360 ) sin 12. sin ( 75 ) 3. sin 195 Verify that each of the following is an identity. 10. the formula i find the current i in amperes after t seconds. sin ( 105 ) 7. sin (45 ) sin (45 ) 2 sin Copyright © Glencoe/McGraw-Hill. cos 75 4. Use the sum of angles formula to find the exact current at t Chapter 14 2 sin (120t) can be used to 1 second. ELECTRICITY In Exercises 15 and 16. The reduction E is given by E E0 cos4 . IMAGING A scanner takes thermal images from altitudes of 300 to 12. tan 15 7.000 meters. sin 8 Verify that each of the following is an identity. Using the identity 2 sin2 1 cos 2 . sin 4 4 cos 2 sin cos 11. 5. Inc. where H is the height and is half the scanner’s field of view. there is a reduction in film exposure for any point X not directly below the camera. cos 1 . verify that E0 cos4 E0 1 2 cos 2 2 2 . and cos 90 2. Verify that 2H sin 2 1 cos 2 2H tan . sin 2 . 270 4 360 4.0 13 2 . and E0 is the exposure for the point directly below the camera. Chapter 14 44 Glencoe Algebra 2 . AERIAL PHOTOGRAPHY In aerial photography.5 8. cos 2 . 90 17 for each of the following. cos 67. a division of The McGraw-Hill Companies. 180 3 270 Find the exact value of each expression by using the half-angle formulas.NAME ______________________________________________ DATE______________ PERIOD _____ 14-6 Practice Double-Angle and Half-Angle Formulas Find the exact values of sin 2 . sin 1. where is the angle between the perpendicular line from the camera to the ground and the line from the camera to point X. 9. sin2 2 tan sin 2 tan Copyright © Glencoe/McGraw-Hill. sin 2 8 . cos 5 . 10. tan 105 6. The width W of the swath covered by the image is given by W 2H tan . 180 3. 12. 0 360 3. 2 cos2 cos2 Solve each equation for all values of . 2 cos 2 sin2 . sec2 2 Solve each equation for all values of Copyright © Glencoe/McGraw-Hill. cot cot3 9. Chapter 14 51 Glencoe Algebra 2 Lesson 14-7 5. 2 . 2 cos sin 2 . if is measured in degrees. Write an expression that describes the times at which there is no current. 2 cos 2 1 2 sin2 12. csc2 3 csc 2 0 13. 22. 0 2 Solve each equation for all values of 7. 180 360 3 2 4. Inc. where i is the current in amperes and t is the time in seconds. 4 sin2 3 18. sin2 cos cos 15. cos2 sin sin 11. cos 4 cos 2 . 2 sin2 3 sin 1 20. cos2 sin2 if is measured in radians. WAVES Waves are causing a buoy to float in a regular pattern in the water. Write an expression that describes the position of the buoy when its height is at its midline. 2 sin3 sin2 10. 8. 4 sin2 1 0 19. The vertical position of the buoy can be described by the equation h 2 sin x.NAME ______________________________________________ DATE______________ PERIOD _____ 14-7 Practice Solving Trigonometric Equations Find all solutions of each equation for the given interval. 17. tan2 sec 1. 1. cos cos (90 ) 0. 90 180 2. 14. cos 2 sin 1 0 21. a division of The McGraw-Hill Companies. 6. 1 3 cos 4(1 cos ) 16. sin 2 cos . ELECTRICITY The electric current in a certain circuit with an alternating current can be described by the formula i 3 sin 240t.