extra practice - classzone 1 of 2 extra practice 941 solve the inequality. then graph your solution....

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Extra Practice

940 Student Resources

CHAPTER 1

Graph the numbers on a number line. Then write the numbers in increasingorder. (Lesson 1.1)

1. º3, �8�, �47�, º2.8, �

95� 2. 4, �

23�, º�6�, º�

23�, 0 3. 0.4, �

35�, º1.6, 0, �3�

4. º5, 0, º�137�, º�5�, 1 5. 3.4, 0.3, º�

25�, �5�, �

52� 6. �2�, 1.4, 1.5, 0.5, 1

Identify the property shown. (Lesson 1.1)

7. (3 + 7)5 = 5(3 + 7) 8. (19 • 4) • 4 = 19 • (4 • 4) 9. º6 + 6 = 0

10. 2(13 + 11) = 2 • 13 + 2 • 11 11. 150+11 = 11 + 150 12. (4 + 8) + 9 = 4 + (8 + 9)

Evaluate the expression. (Lesson 1.2)

13. 4 + 7 º 8 ÷ 4 14. 3 • 9 º (15 º 7) 15. 8 º (4 + 3)2 + 5

16. 2x º 8 when x = 6 17. x3 º 5x when x = 3 18. 3 + 12x º x2 when x = º2

Simplify the expression. (Lesson 1.2)

19. 5x2 º 3x + 7x2 º 10x 20. 7x º y + 9x º 2y 21. º3x2 + 2x º 6x2

22. 4(x º 5) º 3(2x + 7) 23. 2(x º 1) + 3(x + 2) 24. 6(x º y) + 3(y + 2x)

Solve the equation. Check your solution. (Lesson 1.3)

25. 3n º 4 = 17 26. m + 14 = 8 º 2m 27. 5x + 17 = 2x º 10

28. º5(2x º 1) = 3(x + 4) 29. 4.7a + 6.2 = º4.61 30. �13�(x º 6) = º�

25�x + �1

154�

Solve the equation for y. (Lesson 1.4)

31. 3x + 4y = 12 32. 3y º 5x = º13 33. º6y + 7x = º9

34. 3xy + x = 15 35. �45�x º 10y = º3 36. �

13�x º �

25�y = º10

POSTAGE In Exercises 37–39, the cost of sending an overnight package from SpeedyAir is $15.00 for the first pound and $3.00 for each additional pound. How much will itcost to send a 7 pound package? Use the following verbal model. (Lesson 1.5)

= + •

37. Assign labels to the parts of the verbal model.

38. Use the labels to translate the verbal model into an algebraic model.

39. Solve the algebraic model. Answer the question.

40. SCHOOL BAND The school band is planning a carnival to raise money. Theyplan to sell 500 tickets. Adult tickets will be $4.50 and student tickets will be$2.50. They need to collect $1650 in ticket sales to meet their goal. How manyadult and student tickets do they need to sell? (Lesson 1.5)

Number ofadditional pounds

Cost per pound ofadditional pounds

Cost of first pound

Total cost

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Extra Practice 941

Solve the inequality. Then graph your solution. (Lesson 1.6)

41. 3x + 7 > 28 42. ºm º 3 < 3m + 5 43. 2.3x º 5.9 > º1.3

44. º7(n + 3) ≥ 0 45. 4 ≤ x + 2 ≤ 12 46. º6 ≤ 3x + 2 ≤ 11

47. 6x + 4 < 22 or 5x º 8 ≥ 32 48. 5n + 16 ≤ 31 or 8 + 4n > 48 49. 3x º 7 ≤ 16 or 2x º 1 > 23

Solve the equation. (Lesson 1.7)

50. |x + 3| = 6 51. |2x º 6| = 50 52. |x º 7| = 3

53. |10x º 73| = 29 54. |9 º 3x| = 15 55. |20 º 7x| = 42

56. |�14�x + 5| = 21 57. |�

12�x º 1| = 0 58. |10 + �

13�x| = 16

Solve the inequality. Then graph the solution. (Lesson 1.7)

59. |x + 3| > 4 60. |4 º 8x| ≥ 100 61. |7x + 7| < 14

62. |y + 8| ≤ 15 63. |2y º 5| < 1 64. |2a º 6| > 0

65. |3x + 1| ≥ 16 66. |4a + 7| ≤ 13 67. |º2y + 3| > 5

CHAPTER 2

Use a mapping diagram to represent the relation. Then tell whether therelation is a function. (Lesson 2.1)

1. 2. 3.

Evaluate the function when x = º2. (Lesson 2.1)

4. ƒ(x) = x + 17 5. ƒ(x) = ºx + 3 6. ƒ(x) = º5 + 8x

7. ƒ(x) = ºx º 48 8. ƒ(x) = |x + 3| º 9 9. ƒ(x) = 2x3 º 7x2 + 8

Tell whether the lines are parallel, perpendicular, or neither. (Lesson 2.2)

10. Line 1: through (3, 4) and (1, 6) 11. Line 1: through (1, 5) and (º4, º5)Line 2: through (º1, 0) and (3, 5) Line 2: through (º1, º9) and (2, º3)

12. Line 1: through (º6, 7) and (º3, 6) 13. Line 1: through (0, 0) and (5, 2)Line 2: through (º1, º9) and (1, º3) Line 2: through (0, º4) and (º2, 1)

14. Line 1: through (1, 8) and (º3, º4) 15. Line 1: through (0, º2) and (2, º2.5)Line 2: through (º2, º5) and (3, 5) Line 2: through (º4, 6) and (0, 5)

Draw the line with the given slope and y-intercept. (Lesson 2.3)

16. m = 2, b = º4 17. m = 0, b = 4 18. m = º3, b = º2

19. m = º1, b = 0 20. m = �12�, b = 2 21. m = º�

45�, b = º1

Find the slope and y-intercept of the line. (Lesson 2.3)

22. y = 2x 23. x = º1 24. y = 5 25. y = 2x º 5

26. y = 3x + 7 27. º2x + y = 10 28. 5x º y = 12 29. x º 3y = º8

3

1y

x1

2y

x1

1

y

x





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Graph the equation. (Lesson 2.3)

30. y = 3x 31. y = º2x º 4 32. y = 5x º 5 33. y = ºx º 3

34. y = 2x º �14� 35. y = �

38�x 36. y = �

35�x + 2 37. y = º�

12�x + 1

Write an equation of a line that has the given properties. (Lesson 2.4)

38. slope: 2, y-intercept: º4 39. slope: 0, y-intercept: 2

40. slope: �45�, y-intercept: 5 41. slope: 2, passes through (1, º3)

42. slope: �12�, passes through (º1, º1) 43. slope: º�2

5�, passes through (3, º4)

44. passes through (1, º6) and (4, º3) 45. passes through (º3, 3) and (2, º7)

46. passes through (º5, 3) and (5, º3) 47. passes through (2, 6) and (º7, 6)

48. FLYING TIME The table below gives the distance (in miles) and flying time (in hours) to Atlanta, Georgia, from various U.S. cities. Draw a scatter plot of thedata and approximate an equation of the best-fitting line. Then predict the flyingtime for a city that is 900 miles from Atlanta. (Lesson 2.5)

Graph the inequality in a coordinate plane. (Lesson 2.6)

49. y ≥ 2 50. x < 3.6 51. x > º3

52. 3x > 12 53. º2y ≤ 8 54. y > 2.5

55. y < x º 2 56. y ≥ 3x + 4 57. y > 4x º 7

58. y ≤ 2x + 3 59. 6x + 12y ≤ º24 60. �12�x + �

34�y > 0

Evaluate the function for the given value of x. ƒ(x) = (Lesson 2.7)

61. ƒ(º2) 62. ƒ(1) 63. ƒ(5) 64. ƒ(º1) 65. ƒ(0)

Graph the function. (Lesson 2.7)

66. ƒ(x) = 67. ƒ(x) =

Graph the function. Then identify the vertex, tell whether the graph opens up ordown, and tell whether the graph is wider, narrower, or the same width as thegraph of y = |x|. (Lesson 2.8)

68. y = |x| º 4 69. y = 2|x| + 5 70. y = º|x| + 1

71. y = |x + 3| 72. y = º2|x| 73. y = 3|x| º 4

74. y = |1 º x| + 3 75. y = �12�|x| + 2 76. y = �

13�|x|

º1, if x < 01, if 0 ≤ x < 33, if x ≥ 3

�12�x º 5, if x < º2

5x + 4, if x ≥ º2

3x + 2, if x ≤ 1x + 4, if x > 1


Mobile Little Chicago Dallas Austin Colorado Denver LosRock Springs Angeles

Distance 302 459 585 717 817 1185 1204 1944

Time 2.23 2.5 2.82 3.03 3.2 4.83 4.92 7.33





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CHAPTER 3

Check whether the ordered pair is a solution of the system. (Lesson 3.1)

1. (2, 1) 2. (0, 5) 3. (º3, º2) 4. (º1, º8)3x º 2y = 4 5x + y = 5 º7x + 12y = º22 10x + 5y = º50º2x + 2y = 3 9x º 4y = º20 º4x + y = 10 3x º 7y = 53

Graph the linear system and tell how many solutions it has. If there is exactlyone solution, estimate the solution and check it algebraically. (Lesson 3.1)

5. y = 3 6. 3x + y = 10 7. y = 2x º 5 8. 2x º y = 4x + y = 7 y = 2x º 5 6x º 3y = 15 5x + 2y = 17

9. 5x º y = 7 10. y = �13�x º 4 11. �

12�x + 3y = 2 12. �

13�x + y = 0

y = 5x + 6y = �

13�x + 9 �

15�x º 2y = º4 �

16�x º 4y = 9

Solve the system using any algebraic method. (Lesson 3.2)

13. 3x º 2y = 4 14. 5x + y = 5 15. 12x º 7y = º22 16. 8x º y = 1º2x + 2y = 3 9x º 4y = º20 º4x + y = 10 ºx + 4y = 27

17. y = 2x º 4 18. x + 2y = 5 19. x º y = 1 20. º2x + 3y = 10º2y = x º 2 º2x + 3y = º3 9x º 8y = 0 5x + 6y = º16

Graph the system of linear inequalities. (Lesson 3.3)

21. x > º6 22. y ≥ 2x + 3 23. x + y ≥ º2 24. 2x º y > 1y < x + 4 y < º3x + 5 º4x + y ≤ º5 º5x + y ≤ 4

25. x > 3 26. 3x + y < º4 27. x < º10 28. x > 1y < º10 y ≥ 2x + 1 y < 3 y < 5x + y < 7 ºx + y < 4 y ≥ x + 5 y ≥ x + 2

y ≤ ºx º 8 y ≤ ºx + 5

Find the minimum and maximum values of the objective function subject tothe given constraints. (Lesson 3.4)

29. Objective function: 30. Objective function: 31. Objective Function:C = 4x + 5y C = x + 3y C = 5x º 3y

Constraints: Constraints: Constraints:x ≥ 0 x ≤ 0 x ≥ 0y ≤ 4 x ≥ º4 y ≥ 0x ≤ 7 y ≥ 3 y ≤ ºx + 9y ≥ º5 y ≤ º2x + 5 x ≤ 5

Sketch the graph of the equation. Label the points where the graph crosses thex-, y-, and z-axes. (Lesson 3.5)

32. x + y + z = 10 33. 3x + y + 2z = 12 34. 4x + 5y + 2z = 20

35. 5x + 5y + 3z = 15 36. 6x º 4y + 3z = 16 37. 3x + 5y + z = º9

Write the linear equation as a function of x and y. Then evaluate the functionfor the given values. (Lesson 3.5)

38. 3x + 2y + 4z = 12, ƒ(2, 3) 39. x + y + 3z = 9, ƒ(º3, 3) 40. 9x + 6y º 18z = 12, ƒ�º�13�, 2�

41. º2x + 5y º 2z = 10, ƒ(1, 4) 42. 8x º y º z = 16, ƒ�º�14�, º8� 43. ºx + 4y + 7z = º31, ƒ�5, �

12��

Extra Practice 943





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Solve the system using any algebraic method. (Lesson 3.6)

44. 3x + 2y = 12 45. 2x + y = º2 46. x + y + z = 32y º 5z = 1 ºx + 3y º 4z = º26 3x + 3y + 3z = 10x + y + z = 6 5x º 6y + z = 17 x º 3y + 4z = 6

47. º2x + 3y + z = 20 48. x + y + z = 3 49. 2x º 4y º z = º187x º 5y + 3z = º35 x + y º z = 3 º6x º 3y + 2z = 24x + 4y + 4z = 12 2x + 2y + z = 6 4x + y º 6z = º37

50. APPLES You have $20.75 to spend on picking 15 pounds of three different typesof apples in an orchard. The Red Rome apples cost $1.29 per pound, the GrannySmith apples cost $1.49 per pound, and the Empire apples cost $1.09 per pound.You want twice as many Granny Smith apples as the other two kinds combined.How many pounds of each type of apples should you buy? (Lesson 3.6)

CHAPTER 4

Perform the indicated operation. (Lesson 4.1)

1. � � + � � 2. � � + � � 3. � � + � �

4. � � º � � 5. � º � 6. º6� �

7. 2� � + 3� � 8. 5� � º � � 9. �12� � �

Find the product. If it is not defined, state the reason. (Lesson 4.2)

10. � � � � 11. 1.6 3 9� � � 12. � � � �

13. � � � � 14. � � � � 15. � � � �BEVERAGE MACHINE In Exercises 16–18, you refill the beverage machinesat work and you record the money received as income from each machine every day.There are three machines with four types of beverages. Juice is $.85, fruit punch is$.75, lemonade is $.65, and water is $.60. The matrix shows how many of each itemwere sold today. (Lesson 4.2)

16. Write the matrix that gives the price of each item.

17. Use matrix multiplication to determine how much money is in each machine.

18. Which machine has the most money?

12º3

0

5º2

2

6º4º8

56

11

10

º8

5º3º3

º1º1.8

00.5

10º40.3

º3.00

º2.0

84.3

0

96.15.1

3.87.5

4.51.7

º42

99

º36

48

57

06

º83

26.4º2

4º5

0º1

º61

23

9.88.4

7.46.8

5.24.6

80

76

73

14

07

º2º3

º27

º15

03

41

07

º14

2º3

�51

�

�23�

�31�

1

�25�

�13�

4

6

º354

9º2

0

º345

234

2º1

º4º6

03

5º3

36

º1º2

0º1

13

59

º67

º46

10

6º2

3º4


J FP L W

� �142233

18219

131516

12158

MACHINE 1

MACHINE 2

MACHINE 3





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Extra Practice 945

Evaluate the determinant of the matrix. (Lesson 4.3)

19. � � 20. � � 21. � �

22. � � 23. � � 24. � �Use Cramer’s rule to solve the linear system. (Lesson 4.3)

25. 3x + y = 3 26. 4x + 5y = 30 27. 8x º 10y = º84x + 5y = º7 º3x º 3y = º9 9x + 2y = º62

28. 2x + z = 6 29. x + y + 2z = 0 30. 3x + 4y + 2z = 123x º 2y + 4z = 13 2x º 6y + 5z = 6 º2x º 3y º 4z = º12ºy º 3z = º15 ºx + 3y º 7z = 6 5x + 5y + 6z = 8

Find the inverse of the matrix. (Lesson 4.4)

31. � � 32. � � 33. � � 34. � �35. � � 36. � � 37. � � 38. � �Use an inverse matrix to solve the linear system. (Lesson 4.5)

39. 2x + 3y = 13 40. º4x º 3y = º2 41. 6x º 3y = º3 42. 5x + 2y = 8x º 5y = 0 2x + y = 2 º4x + 7y = º3 º2x º 9y = 46

43. 3x º 8y = 16 44. º7x º 2y = º8 45. º5x º y = 2 46. º6x + 5y = º2º2x + 5y = º10 3x º 6y = 0 10x + 3y = 1 4x º 3y = 2

47. Use the given inverse of the coefficient matrix to solve the linear system. (Lesson 4.5)

x + 2z = 5º2x + 3y + 4z = º82x º y + 2z = 10

CHAPTER 5

Graph the quadratic function. Label the vertex and axis of symmetry. (Lesson 5.1)

1. y = x2 + 3x º 4 2. y = º2x2 + x + 5 3. y = (x + 3)2 º 4 4. y = (x + 1)(x º 4)

5. y = �12�(x º 4)2 + 2 6. y = 3(x + 4)(x º 1) 7. y = (x + 8)(x º 3) 8. y = º�

13�(x + 2)(x º 1)

9. SWIMMING The drag force F (in pounds) of water on a swimmer can bemodeled by F = 1.35s2 where s is the swimmer’s speed (in miles per hour). At what speed is the force minimized? (Lesson 5.1)

Factor the trinomial. If the trinomial cannot be factored, say so. (Lesson 5.2)

10. x2 + 8x + 15 11. m2 º 9m + 20 12. 3x2 + 11x º 4 13. 6x2 + 5x º 6

14. 9a2 º 56a + 12 15. 4u2 º 4u º 35 16. n2 º 49 17. x2 º 10x + 25

18. 16m2 º 24m + 9 19. 4x2 º 2x º 20 20. 3p2 + 15p º 42 21. 6x2 + 13x º 25

º19

3º2

7º3

º94

21

6º8

2º8

14

7º5

º12

62

º31

6º4

01

36

47

º6104

53

17

º90

º10

293

7100

21º6

1

1º112

309

60

13

52

º39

6º4

01

º32

47

� �º3º41.5

º1º10.5

56

º2A–1 =





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22. x2 + 10x + 21 = 0 23. 2x2 º 13x º 7 = 0 24. 3x2 º 24x º 27 = 0 25. 25m2 º 20m + 4 = 0

26. x2 º 8x = º15 27. 8k2 + 5k = 2k2 + 4 28. 10x2 º 3x = º2x2 + 36 29. 2(q2 º 20) + 17q = º10q2

Write the quadratic function in intercept form and give the function’s zeros.(Lesson 5.2)

30. y = x2 + 10x + 9 31. y = x2 º 5x 32. y = 2x2 + 3x º 2 33. y = 6x2 º 24

34. y = 4x2 º 12x + 8 35. y = 5x2 º 13x + 6 36. y = 4x2 + 22x + 24 37. y = 7x2 º 63


38. �3�2� 39. �1�2�5� 40. 3�2�7� • �3� 41. �2�4�3�

42. �1�5� • �3� 43. � 44. 6�5� • �5� 45. ��12 6

5� Solve the equation. (Lesson 5.3)

46. x2 = 144 47. x2 = 160 48. 2x2 = 400 49. º4(x + 2)2 = º20

50. �x9

2� º 1 = 5 51. 7x2 = 175 52. x2 º 100 = º82 53. �

13�(x º 4)2 = 3


54. x2 = º16 55. x2 = º10 56. 3x2 = º27 57. 5x2 = º125

58. (y º 3)2 = º49 59. 6x2 = º216 60. 4(x + 5)2 = º8 61. º�14�(r + 1)2 = 5

Write the expression as a complex number in standard form. (Lesson 5.4)

62. (3 + 5i) + (2 + i) 63. (º6 + 4i) + (2 º 7i) 64. (4 + 3i)2 65. (15 º 7i) º (15 º 7i)

66. i(5 + i) 67. º2i(3 º 2i) 68. (9 º 2i)(9 + 2i) 69. (9 º 5i) º (º2 + 6i)

70. (10 º 7i)2 71. �5 +3

i� 72. �42ºi

i� 73. �11

º+

ii�

Solve the equation by completing the square. (Lesson 5.5)

74. x2 º 6x = 7 75. x2 º 4x + 8 = 0 76. x2 º 10x = 1 77. m2 + 2.6m º 3 = 0

78. 2n2 º 5n = 7 79. 3n2 º 4n = 4 80. 3y2 + 2y = 5 º 4y 81. 5n2 + 6n = 8

82. VEGETABLE GARDEN You are planning to create a vegetable garden behindyour house. Your house will be one side of the rectangular garden, and the gardenwill have a fence on its other sides. You bought 40 feet of fencing and enoughmulch to cover 140 square feet. If the back of the house is 30 feet wide, whatshould the garden’s dimensions be? (Lesson 5.5)

Use the quadratic formula to solve the equation. (Lesson 5.6)

83. 4x2 + x = 3 84. x2 + 10x + 25 = 0 85. x2 + 3x º 8 = 0

86. x2 º 4x + 5 = 0 87. 7m2 º 6m + 10 = 0 88. 2(m + 1)2 = 3m + 7

Find the discriminant of the quadratic equation and give the number and typeof solutions of the equation. (Lesson 5.6)

89. x2 + 7x + 12 = 0 90. x2 º 8x + 16 = 0 91. 5m2 + 3m + 10 = 0

92. x2 + 5x º 6 = 0 93. 2x2 º 4x + 7 = 0 94. 4x2 + 3x º 15 = 0

81�125






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Graph the inequality or system of inequalities. (Lesson 5.7)

95. y ≤ 2x2 96. y > x2 º 4 97. y < º3x2 + 2x + 4

98. y ≤ x2 + 1 99. y > x2 º 4x + 4 100. y > x2 + 3x º 5y ≥ x2 y < ºx2 + 5x º 3 y < º2x2 + 1

Write a quadratic function in vertex form for the parabola whose graph has thegiven vertex and passes through the given point. (Lesson 5.8)

101. 102. 103.

104. vertex: (3, 0) 105. vertex: (º3, º5) 106. vertex: (º1, º4)point: (2, 1) point: (1, 27) point: (º2, º6)

Write a quadratic function in intercept form whose graph has the given x-intercepts and passes through the given point. (Lesson 5.8)

107. x-intercepts: 2, 6 108. x-intercepts: º1, 3 109. x-intercepts: 4, 0 110. x-intercepts: º2, 3point: (5, º3) point: (2, 3) point: (1, º6) point: (2, 1)

111. x-intercepts: 1, 2 112. x-intercepts: º1, 4 113. x-intercepts: 5, º2 114. x-intercepts: º3, º3point: (5, 9) point: (0, º1) point: (2, 2) point: (1, 48)

CHAPTER 6

Evaluate the expression. Tell which properties of exponents you used. (Lesson 6.1)

1. 52 • 52 2. (º4)3(º4) 3. (23)3 4. 6º2

5. ��45��2

6. ��37��º2

7. 80 • 8º3 8. �33

º

º

2

4�

9. ��16��3��

16��3

10. ��13��2�º3

11. �40

6•

3

62� 12. 55 • 50 • 5º3

Simplify the expression. Tell which properties of exponents you used. (Lesson 6.1)

13. (32x2)4 14. (x2y2)º3 15. �xx

8

5� 16. �8

4

x

x5

4

y

y3

7

�

17. (6x3y4)º2 18. º4(xº5y2)2 19. (º3x9y3)º7 20. (6xº3yº1)º8

21. (8(x3y4)2)º2 22. �2

3

x

x

º

º

3

6

y

y

º

º

5

3� 23. �3xy

10

4� • �9

x

x4

2

y

y3

2

� 24. �1

8

5

x

x3y

y0

4

� • �16

5

x

y

5

4

y2

�

Use synthetic division to evaluate the polynomial function for the given valueof x. (Lesson 6.2)

25. ƒ(x) = 2x3 + 3x2 º 5x + 1; x = 2 26. ƒ(x) = 10x3 º 5x2 + 4; x = º1

27. ƒ(x) = x5 º 3x3 º 2x; x = º2 28. ƒ(x) = ºx4 + 7x º 12; x = 3

Graph the polynomial function. (Lesson 6.2)

29. ƒ(x) = x3 30. ƒ(x) = x4 + 1 31. ƒ(x) = 3 º x3

32. ƒ(x) = x4 º 3x 33. ƒ(x) = ºx5 º 2 34. ƒ(x) = x5 + 2x3 + 3

1

1

y

x

(5, 2)

(2, 1)1

1

y

x

(2, 4)

(1, 2)

1

1

y

x

(2, 2)

(1, 1)

Extra Practice 947





of 2

Find the sum or difference. (Lesson 6.3)

35. (2x2 + 6x + 3) + (3x2 + 4x + 4) 36. (4x º 3) + (3 º 8x)

37. (5x3 º 2x2 + 7) º (8x2 º 11) 38. (9x3 º 7x2 + 8) + (º8x3 + 5x2 º 15)

39. (29x º 8) + (15x3 + 9x2 º 8) 40. (6x3 º 7x4 + 10x) º (4x3 º 6x2)Find the product of the polynomials. (Lesson 6.3)

41. (x + 7)(x º 5) 42. (x º 3)2 43. (5 º 3x)(x + 1)(x + 6)

44. (ºx3 º 3)(x2 º 5x + 4) 45. 6x(2x3 º 4x2 + 7) 46. (x + 12)(2x2 º 3x + 5)

47. (2x + 8)3 48. (x + 1)(3x + 3)(2x + 3) 49. (x + y)3

Factor the polynomial. (Lesson 6.4)

50. x3 º 27 51. 2x3 + 250 52. 256x5 º 81x3

53. x3 + 7x2 + 15x + 9 54. x3 º x2 º 14x + 24 55. 3x3 º 24

56. x3 + 5x2 + 8x + 40 57. 2x3 + 18x2 º 5x º 45 58. 3x5 + 6x3 º 45x

59. PACKAGING A factory needs a box that has a volume of 6 cubic inches. Thewidth should be 1 inch less than the height and the length should be 3 inchesgreater than the height. What should the dimensions of the box be? (Lesson 6.4)

Divide. Use synthetic division when possible. (Lesson 6.5)

60. (x3 º 2x2 º 8x + 5) ÷ (x º 1) 61. (x3 º 10x2 + 27x º 12) ÷ (x º 4)

62. (5x2 º 6) ÷ (x º 2) 63. (3x4 º 17x3 + 13x2 º 24x + 16) ÷ (x + 4)

64. (x4 + x3 º 3x º 3) ÷ (x + 1) 65. (4x4 º 5x3 + 2x2 º x + 5) ÷ (x º 2)

Find all the real zeros of the polynomial function. (Lesson 6.6)

66. ƒ(x) = x3 º 2x2 º 11x + 12 67. ƒ(x) = x4 + 5x3 + 10x2 + 20x + 24

68. ƒ(x) = 2x3 º 3x2 º 23x + 12 69. ƒ(x) = x5 + x4 + 3x3 º 8x2 º 8x º 24

70. ƒ(x) = 3x4 º 5x3 º 5x2 + 5x + 2 71. ƒ(x) = 16x3 + 80x2 + x + 5

Find all the zeros of the polynomial function. (Lesson 6.7)

72. ƒ(x) = x3 º x2 + 4x º 4 73. ƒ(x) = x4 º 7x3 + 17x2 º 17x + 6

74. ƒ(x) = x3 + x2 + 9x + 9 75. ƒ(x) = x4 + 2x3 º 12x2 º 40x º 32

76. ƒ(x) = x3 º 7x2 º x + 7 77. ƒ(x) = x4 º 6x2 + 5

Write a polynomial function of least degree that has real coefficients, the givenzeros, and a leading coefficient of 1. (Lesson 6.7)

78. 3, 1, 5 79. º1, º2, º2 80. 4, 6, º7 81. i, ºi, 3

82. i, º4i, 4i 83. 2, 1 + i 84. 6i, 6i 85. 3, º2, º1 + i

86. 4 º i, 5 º i, 2 87. 2 + i, 6i 88. 2, 2, 3 º i 89. 5, º5, º6i, 5i


90. ƒ(x) = (x + 3)(x º 4)(x + 1) 91. ƒ(x) = 3(x º 3)(x + 1)3 92. ƒ(x) = º(x º 1)(x + 1)(x º 5)

93. ƒ(x) = 2(x º 1)(x + 4)2 94. ƒ(x) = 2(x º 3)(x + 2)2 95. ƒ(x) = º3(x + 1)(x º 1)(x º 2)

96. ƒ(x) = 2(x º 1)(x + 2)3 97. ƒ(x) = 5(x + 3)(x º 2)2 98. ƒ(x) = 2(x º 1)(x º 2)(x + 3)






of 2

Find a polynomial that fits the data. (Lesson 6.9)

99. 100.

101. 102.

CHAPTER 7

Evaluate the expression without using a calculator. (Lesson 7.1)

1. �3 2�7� 2. �3 º�1�2�5� 3. 16º1/2 4. 642/3

5. º(253/2) 6. º(2433/5) 7. (�4 8�1�)º2 8. �5 3�2�

9. 81/3 10. (º216)º1/3 11. (�3 6�4�)1/2 12. (�3 7�2�9�)1/2


13. 51/4 • 53/4 14. (31/3)2/5 15. 21/4 • 81/4 16.

17. �81

06

1

1

/

/

2

2� 18. �2�5� • �3 2�5� 19. (�3 7� • �4 7�)2 20.

Simplify the expression. Assume all variables are positive. (Lesson 7.2)

21. x1/2 • x1/5 22. (x3)1/2 23. �4 8�1�x6�y8� 24. � 25. 26. 27. �3 28. �6 9�xy�6� • �6 6�x1�2�

Let ƒ(x) = x2 º 4x + 5 and g(x) = x2 º 9. Perform the indicated operation and state the domain. (Lesson 7.3)

29. ƒ(x) + g(x) 30. ƒ(x) º g(x) 31. g(x) + ƒ(x) 32. g(x) º ƒ(x)

33. ƒ(x) + ƒ(x) 34. ƒ(x) º ƒ(x) 35. g(x) + g(x) 36. g(x) º g(x)

Let ƒ(x) = 3x1/3 and g(x) = x1/2. Perform the indicated operation andstate the domain. (Lesson 7.3)

37. ƒ(x) • g(x) 38. �ƒ

g

(

(

x

x

)

)� 39. g(x) • ƒ(x) 40. �

ƒ

g

(

(

x

x

)

)�

41. ƒ(g(x)) 42. g(ƒ(x)) 43. ƒ(ƒ(x)) 44. g(g(x))

Find the inverse function. (Lesson 7.4)

45. ƒ(x) = 3x + 1 46. ƒ(x) = º2x º 1 47. ƒ(x) = ºx º 4 48. ƒ(x) = 5x º 7

49. ƒ(x) = 2x + 3 50. ƒ(x) = º4x º 5 51. ƒ(x) = �12�x º 4 52. ƒ(x) = 3x3 + 2

53. ƒ(x) = º�13�x + 5 54. ƒ(x) = 2x4; x ≥ 0 55. ƒ(x) = x4 º �

18�; x ≥ 0 56. ƒ(x) = �

12�x2 º 5; x ≥ 0

57. AREA The area A of a circular object is A = πr2 where r is the radius of theobject. Find r in terms of A. (Lesson 7.4)

8x6y12

�27�5 x4��8 x3�

�3 x� • �x3��1�6�x1�2�

16x4y5�

25z4

�1�0��4 1�0�

123/5�121/5

Extra Practice 949

x 1 2 3 4 5 6

ƒ(x) 3 15 55 141 291 523

x 1 2 3 4 5 6

ƒ(x) 2 5 9 14 20 27

x 1 2 3 4 5 6

ƒ(x) 5 16 43 92 169 280

x 1 2 3 4 5 6

ƒ(x) 3 3 9 27 63 123





of 2

Graph the function. Then state the domain and range. (Lesson 7.5)

58. y = 2�x� 59. y = �14��x� 60. y = �x�º� 4� 61. y = (x + 5)1/2

62. y = 6�x�+� 5� 63. y = �3 x� + 1 64. y = 3�3 x�+� 1� 65. y = 4�3 x�º� 1�2� + 3

66. y = �12��x�+� 2� 67. y = �3 x�º� 5� + 1 68. y = �

13��3 x�º� 8� º 5 69. y = º2(x + 2)1/3 º 4

Solve the equation. Check for extraneous solutions. (Lesson 7.6)

70. x1/4 = �2156� 71. x1/4 º 81 = 0 72. 2(x + 1)2/3 = 6 73. �x� + 1= �1

16�

74. x2/3 = 16 75. �3 x� + 4 = 2 76. �1�1�x�+� 3� = 2x 77. �x�º� 1�3� = 2�x�+� 7�

78. �5�x�+� 1� = x º 4 79. �x�+� 3� = �2�x�º� 7� 80. 2�x�º� 2� = �x� 81. 4�3�x�º� 7� = 2�º�x�+� 7�3�

Find the mean, median, mode, range, and standard deviation of the data set.(Lesson 7.7)

82. 8, 9, 9, 10, 11, 10, 12, 8, 9, 11 83. 52, 56, 57, 58, 58, 73, 55, 58, 57, 58

84. 2.3, 2.7, 2.8, 2.8, 2.8, 4.7, 4.9, 5.2 85. 21.4, 18.6, 15.3, 62, 21.9, 18.6, 21.3

CHAPTER 8

Graph the function. State the domain and range. (Lesson 8.1)

1. y = 3x 2. y = 3 • 4x 3. y = 5(1.5)x 4. y = 4(2)x

5. y = 2 • 7x º 1 6. y = º�12�(2.5)x 7. y = 3x º 1 8. y = 3x º 2 + 1

9. y = 2x º 2 + 4 10. y = 4 • 5x º 1 º 2 11. y = 3 • 2x + 2 12. y = 5 • 2x º 3


13. y = ��12��x

14. y = 2��13��x

15. y = º3��14��x

16. y = º��15��x

17. y = (0.25)x 18. y = º2��14��x

º 1 19. y = ��23��x

+ 3 20. y = º5��12��x


21. e4 • e3 22. eº6 • e7 23. 4e3x • 4e3x 24. (7eºx)º2

25. �1e03ex

x� 26. �3 64�e6�x� 27. e2x • e4x º 1 28. �5

ee

x�

29. �20

5ee

4x� 30. (6eº2x)3 31. �1�6�e8�x� 32. ��

13�eº3�º3


33. y = e0.5x 34. y = eº0.75x 35. y = 2eº(x º 1) 36. y = 0.5eºx

37. y = �12�ex º 3 + 1 38. y = 3ex º 2 º 4 39. y = �

13�eº2(x º 1) º 2 40. y = 0.1e2x º 3

41. MOUNT FUJI The relationship between air pressure and altitude can be modeled byP = 14.7eº0.00004h where P is the air pressure (in pounds per square inch) and h isthe altitude (in feet above sea level). Mount Fuji in Japan rises to a height of 12,388feet above sea level. What is the air pressure at the peak of Mount Fuji? (Lesson 8.3)






of 2

Evaluate the expression without using a calculator. (Lesson 8.4)

42. log2 16 43. log5 25 44. log11 1 45. log1/4 2

46. log3 3º2.16 47. log7 343 48. log29 29 49. log9 9

3

Find the inverse of the function. (Lesson 8.4)

50. y = log4 x 51. y = log1/3 x 52. y = log6 36x

53. y = ln 3x 54. y = ln (x + 1) 55. y = ln (x º 3)


56. y = log3 x 57. y = ln x º 2 58. y = log x + 4 59. y = ln (x º 3)

60. y = log5 (x + 2) 61. y = ln x + 7 62. y = log1/2 x + 1 63. y = log5 x + 2

Use a property of logarithms to evaluate the expression. (Lesson 8.5)

64. log2 (4 • 8) 65. ln e3 66. log2 82 67. log6 216

68. log �1100� 69. ln �

e15� 70. log 0.001 71. log3 272

Expand the expression. (Lesson 8.5)

72. log3 9x 73. log 3x4 74. log6 x5 75. ln 15x

76. log7 49x2 77. log �9�x� 78. ln x1/3y4 79. log x2y3z4

Condense the expression. (Lesson 8.5)

80. log4 7 + log4 10 º log4 2 81. 4 ln x + 6 ln y + 3 ln z 82. 5 log4 3 + 6 log4 x + 7 log4 y

83. �14�(ln 9 º ln x) + �

14� ln 3 84. 6(ln 3 + ln x) + �

14� ln 3 85. 3(log5 10 º log5 2) + �

12� log5 �10

10�

Solve the equation. Check for extraneous solutions. (Lesson 8.6)

86. 3x = 10 87. 4x º 3 = 11 88. 3x + 2 = 9x + 1 89. 10x + 4 = 10

90. ln 8x = 4 91. ln (5 º x) = 12 92. log3 x = 4 93. log5 (2x + 10) = log5 4x

Write an exponential function of the form y = abx whose graph passes throughthe given points. (Lesson 8.7)

94. (2, 18), (1, 6) 95. (0, 0.5), (3, 4) 96. (º1, 6), (1, 0.5) 97. (º2, 0.01), (1, 1.25)

98. (3, 9), �8, �245�� 99. �º1, �

14��, �2, �

38�� 100. (2, 27), �º2, �

13�� 101. (1, º8), (0, º2)

102. EXPANDING BUSINESS The table below shows the number s of stores ownedby a company from 1987 to 1998 where t represents the number of years since1987. Find an exponential model for the data. Then use the model to predicthow many more stores there will be in 2006. (Lesson 8.7)

Write a power function of the form y = axb whose graph passes through thegiven points. (Lesson 8.7)

103. (º2, º8), (3, 27) 104. (1, 5), (4, 10) 105. (1, 2), (4, 4) 106. (2, 4), (3, 37)

107. (º1, º3), (3, 81) 108. (2, 1), (6, 9) 109. (º1, 0.5), (4, 8) 110. (º5, º8), (º10, º32)

Extra Practice 951

t 0 1 2 3 4 5 6 7 8 9 10 11

s 17 33 55 84 116 165 272 425 676 1015 1412 1900





of 2

Evaluate the function ƒ(x) = �1 +

64eºx� for the given value of x. (Lesson 8.8)

111. ƒ(1) 112. ƒ(2) 113. ƒ(º2) 114. ƒ(3)

115. ƒ(0) 116. ƒ(4.1) 117. ƒ(º0.6) 118. ƒ��14��

Graph the function. Identify the asymptotes, y-intercept, and the point ofmaximum growth. (Lesson 8.8)

119. y = �1 +

13eº2x� 120. y = �

1 + 21eº0.5x� 121. y = �

1 +2eºx� 122. y = �

1 +5eº2x�

123. y = �1 +

32eº4x� 124. y = �

1 + e4º1.04x� 125. y = �

1 + 65eº2.5x� 126. y = �

1 + 28eº0.4x�

CHAPTER 9

The variables x and y vary inversely. Use the given values to write an equationrelating x and y. Then find y when x = 4. (Lesson 9.1)

1. x = 3, y = 6 2. x = 2, y = 8 3. x = º1, y = 4 4. x = 2, y = 6

5. x = º�13�, y = 9 6. x = �

12�, y = 6 7. x = �

12�, y = �

18� 8. x = �

25�, y = �1

10�

The variable z varies jointly with x and y. Use the given values to write anequation relating x, y, and z. Then find z when x = 4 and y = 7. (Lesson 9.1)

9. x = 2, y = 3, z = 6 10. x = º3, y = 6, z = 18 11. x = 10, y = º15, z = 5

12. x = º1, y = 2, z = 4 13. x = �34�, y = �

12�, z = 8 14. x = �

15�, y = �

78�, z = �2

1�


15. y = �3x� 16. y = �x º

23� + 1 17. y = �2x

5+ 1� º 4 18. y = �x

x++

61

�

19. y = �xxº+

21� 20. y = �x

x++

43

� 21. y = �2xxº 5� 22. y = �ºx

4ºx

3�

FUNDRAISER In Exercises 23–25, your school is publishing a calendar to raisemoney for a local charity. The total cost of using the photos in the calendar is $710.In addition to this “one-time” charge, the unit cost of printing each calendar is $4.50.(Lesson 9.2)

23. Write a model that gives the average cost per calendar as a function of thenumber of calendars printed.

24. Graph the model and use the graph to estimate the number of calendars youneed to print before the average cost decreases to $6 per calendar.

25. Describe what happens to the average cost as the number of calendars printedincreases.


26. y = �2xx2

++

31

� 27. y = �x2 +

75

� 28. y = �xx

2

2++

92

� 29. y = �x2 º

x º5x

6º 6

�

30. y = �3x2 º

5 º2x

x+ 1

� 31. y = �x2 + 8

2xx

+ 15� 32. y = �

xº2 º

3x2

9� 33. y = �x

2 º 32xx

º 10�






of 2

Perform the indicated operation. Simplify the result. (Lesson 9.4)

34. �3

x

x2y

y3

5

� • �6yx

2

� 35. �20

y2x5� • �

1

x

0

2y

x

2

3� 36. �xx

2

ºº

34

� • �8xx

º+

126�

37. �x3 +

2x3x2� • �

x2 +55xx

3

+ 6� 38. �7x2 º

x314x

� ÷ �5x º

x510

� 39. �x2 º

x +x º

420

� • �x2 º

x2ºx º

315

�

40. (x2 + 5x º 36) ÷ �5x

x

2 +º

465x

� 41. (x3 + 8) • �36xx

3

3

ºº

192xx

2� 42. �

xx

2

2

º+

72xx

+º 3

152

� ÷ �x2

3ºx2

1º3x

1+2x

40�

Perform the indicated operation and simplify. (Lesson 9.5)

43. �53x� + �5

9x� 44. �

61x52� º �

68x2� 45. �3

4x� + �5

2x� 46. �2(x

3º 1)� +

47. �2xx2 º

+41

� + �x º5

2� 48. �4x

º+

95x

� + �2x1º 1� 49. º �x +

35� 50. �

x28+x º

x º1

6� º �x º

42�

Simplify the complex fraction. (Lesson 9.5)

51. 52. 53. 54.

55. 56. 57. 58.

Solve the equation using any method. Check each solution. (Lesson 9.6)

59. �7x� + �

12� = 4 60. �4

x� + �

12� = 5 61. �

4x� + �

13� = 10 62. �2

1x� + �3

x� = 7

63. �xº+

23� = �x +

11� 64. �x +

42� = �x

ºº

33� 65. �x

º+

41� = �x º

21� 66. �x +

34� = �x º

92�

67. �x4ºx

1� = �x2 º

x1

� 68. �105ºx

x� = �x ºx2

10� 69. �x2 º

39

� = �x +6

3� 70. �x2 º

34

� = �x +2

2� + �x ºx

2�

CHAPTER 10

Find the distance between the two points. Then find the midpoint of the linesegment joining the two points. (Lesson 10.1)

1. (0, 0), (6, 8) 2. (0, 5), (º2, 0) 3. (º4, º2), (1, º5) 4. (3, 3), (3, 6)

5. (4.5, 2), (1.5, 6) 6. (º3, 5), ��12�, 6� 7. (º5, 2.3), (º3, 4.7) 8. �º�

14�, 6�, �8, º�

34��

Graph the equation. Identify the focus and directrix of the parabola. (Lesson 10.2)

9. y2 = 10x 10. x2 = º4y 11. y2 = º6x 12. y2 = 11x

13. x2 º 16y = 0 14. 6x2 = 5y 15. x º �18�y2 = 0 16. x + �1

10�y2 = 0

Write the standard form of the equation of the parabola with the given focus ordirectrix and vertex at (0, 0). (Lesson 10.2)

17. (3, 0) 18. (0, º4) 19. ��12�, 0� 20. �0, º�

18��

21. y = 6 22. x = º2 23. y = �34� 24. x = º�

78�

�3x2 + 6

2x + 12�+ �

x3 ºx

8�

��2x2

3+x

4� º �

4xx2

º+

28

�

�x2 º

849

�

��3x2 º

521x

� º �x º6

7�

�x2 º

24

� + �x º1

2�

��x º

52� + �x +

32�

�3x2º 1� º �4(3x

5+ 1)�

��9x2

xº 1�

�3x2

2º 3�

��x +

11� + �

x2 º32xx º 3�

�5x7+ 2� º �2(5x

3+ 2)�

��5x

x+

2

2�

�x +9

1��

�13� º �x +

61�

�4x� º 4�2 + �

1x�

7��x2 + 8x + 15

x + 1�4

Extra Practice 953





of 2

Graph the equation. (Lesson 10.3)

25. x2 + y2 = 4 26. x2 + y2 = 36 27. x2 + y2 = 12 28. 2x2 + 2y2 = 98

29. 6x2 + 6y2 = 54 30. 5x2 + 5y2 = 120 31. 9x2 + 9y2 = 126 32. 15x2 + 15y2 = 300

Write the standard form of the equation of the circle that has the given radiusor passes through the given point and whose center is the origin. (Lesson 10.3)

33. r = 4 34. r = 8 35. r = �1�3� 36. r = 2�5�

37. (0, 6) 38. (º4, 1) 39. (2, 5) 40. (º6, º2)

OCEAN NAVIGATION In Exercises 41 and 42, the beam of a lighthouse can be seenfor up to 10 miles. You are on a ship that is 5 miles east and 7 miles north of thelighthouse. (Lesson 10.3)

41. Write an inequality to describe the region lit by the lighthouse beam.

42. Can you see the lighthouse beam from the ship?

Graph the equation. Then identify the vertices, co-vertices, and foci of theellipse. (Lesson 10.4)

43. �x9

2� + �1

y6

2

� = 1 44. �8x1

2� + �3

y6

2

� = 1 45. �2x5

2� + �4

y9

2

� = 1 46. �2x5

2� + �1

y4

2

4� = 1

47. �1x6

2

9� + �2y2

2

5� = 1 48. x2 + �y4

2

� = 1 49. �1x6

2� + y2 = 4 50. �

x4

2� + y2 = 81

Write an equation of the ellipse with the given characteristics and centerat (0, 0). (Lesson 10.4)

51. Vertex: (0, 8) 52. Vertex: (5, 0) 53. Vertex: (º7, 0) 54. Vertex: (º2, 0)Co-vertex: (4, 0) Co-vertex: (0, º3) Co-vertex: (0, º2) Focus: (º�3�, 0)

55. Vertex: (16, 0) 56. Vertex: (0, 13) 57. Co-vertex: (º2, 0) 58. Co-vertex: (0, º3)Focus: (2�3�9�, 0) Focus: (0, 12) Focus: (0, 2�9�9�) Focus: (º�7�, 0)

Graph the equation. Identify the foci and asymptotes. (Lesson 10.5)

59. �4x9

2� º �6

y4

2

� = 1 60. �2x5

2� º y2 = 1 61. �1

x0

2� º �

y6

2

� = 1 62. �8x1

2� º �2

y5

2

� = 1

63. �3y6

2

� º x2 = 1 64. y2 º 25x2 = 25 65. x2 º 16y2 = 144 66. 100x2 º 49y2 = 4900

Write an equation for the conic section. (Lesson 10.6)

67. Circle with center at (3, 4) and radius 5 68. Parabola with vertex at (2, º1) and focus at (2, 1)

69. Circle with center at (2, º5) and radius 7 70. Parabola with vertex at (º2, 5) and focus at (3, 5)

71. Ellipse with vertices at (º2, 3) and (8, 3) and foci at (º1, 3) and (7, 3)

72. Ellipse with vertices at (º9, 1) and (5, 1) and co-vertices at (º2, 6) and (º2, º4)

73. Hyperbola with vertices at (5, 6) and (º1, 6) and foci at (º2, 6) and (6, 6)

74. Hyperbola with vertices at (4, º2) and (4, º6) and foci at (4, 1) and (4, º9)

Classify the conic section. (Lesson 10.6)

75. x2 º 3y + 10 = 0 76. 8x2 + 8y2 + 64x + 32y º 160 = 0

77. 16x2 º 9y2 + 96x + 18y º 135 = 0 78. 25x2 + 16y2 + 100x º 128y º 44 = 0






of 2

Find the points of intersection, if any, of the graphs in the system. (Lesson 10.7)

79. x2 + y2 = 20 80. x2 º y = 3 81. x2 + y2 = 6 82. 4x2 + y2 = 16x º y = º2 2x º y = º12 x º y = 5 y = x º 2

83. x2 º y2 = 9 84. 2x2 + y2 = 10 85. x2 + y2 = 8 86. 5x2 + 4y2 = 12y = 2x º 6 y = x º 3 x + y = y = x + 1

CHAPTER 11

Write the next term in the sequence. Then write a rule for the nth term. (Lesson 11.1)

1. 2, 5, 8, 11, . . . 2. 5, 10, 20, 40, . . . 3. 3, º1, º5, º9, . . . 4. �13�, 1, �

53�, �

73�, . . .

5. º1, 4, º16, 64, . . . 6. �23�, �

36�, �

49�, �1

52�, . . . 7. �

14�, �1

16�, �6

14�, �2

156�, . . . 8. �

13�, 3, 27, 243, . . .

Find the sum of the series. (Lesson 11.1)

9. ∑8

i = 12i 10. ∑

4

i = 1(6i + 1) 11. ∑

5

i = 0i2 12. ∑

7

k = 13k2

13. ∑6

n = 2n3 14. ∑

3

n = 1�n +

n1� 15. ∑

6

k = 1�k +

k1

� 16. ∑8

k = 4k(k º 1)

Write a rule for the nth term of the arithmetic sequence. Then find a10.(Lesson 11.2)

17. 1, 4, 7, 10, 13, . . . 18. º3, 2, 7, 12, 17, . . . 19. 8, º2, º12, º22, º32, . . .

20. 2.4, 3.5, 4.6, 5.7, . . . 21. �94�, �

74�, �

54�, �

34�, �

14�, . . . 22. d = 3, a1 = 3.5

23. d = º2, a4 = 0 24. d = 1.75, a6 = 10.75 25. a1 = º5, a8 = 23

SEATING CAPACITY In Exercises 26 and 27, the first row of a concert hall has 20 seats, and each row after the first has one more seat than the row before it. There are 30 rows of seats. (Lesson 11.2)

26. Write a rule for the number of seats in the nth row.

27. Forty students from a class want to sit in the same row. How close to the front canthey sit?

Write a rule for the nth term of the geometric sequence. Then find a8. (Lesson 11.3)

28. 3, 6, 12, 24, . . . 29. º1, º�12�, º�

14�, º�

18�, . . . 30. 6, 42, 294, 2058, . . .

31. º10, 1, º�110�, �1

100�, . . . 32. r = 3, a1 = 3 33. r = 6, a2 = º18

34. r = 9, a1 = º27 35. a1 = 150, a3 = 6 36. a2 = 20, a6 = 5120

Find the sum of the first n terms of the geometric series. (Lesson 11.3)

37. 1 + 5 + 25 + 125 + . . . 38. 5 + 10 + 20 + 40 + . . . 39. 4 + (º12) + 36 + (º108) + . . .

n = 12 n = 10 n = 6

40. 100 + 50 + 25 + �225� + . . . 41. 60 + 10 + �

160� + �

13

06� + . . . 42. 6 + (º12) + 24 + (º48) + . . .

n = 8 n = 10 n = 7

1�3

1�2

1�2

1�4

Extra Practice 955





of 2

Find the sum of the infinite geometric series if it has one. (Lesson 11.4)

43. ∑‡

n = 0��

13��n

44. ∑‡

n = 12��

12��n

45. ∑‡

n = 0�45�(3)n 46. ∑

‡

n = 12��

15��n

47. ∑‡

n = 03��

76��n

48. ∑‡

n = 0��

18��n º 1

49. ∑‡

n = 1�13��º�

15��n

50. ∑‡

n = 0�º�

14��n º 1

Write a recursive rule for the sequence. The sequence may be arithmetic,geometric, or neither. (Lesson 11.5)

51. 2, 6, 10, 14, . . . 52. 77, 11, �171�, �14

19�, . . . 53. 2, 7, 22, 67, 202, . . .

54. 11.6, 10.1, 8.6, 7.1, . . . 55. º6, º9, 54, º486, . . . 56. 8, 8�3�, 24, 24�3�, . . .

CHAPTER 12

Each event can occur in the given number of ways. Find the number of ways allof the events can occur. (Lesson 12.1)

1. Event 1: 2 ways, Event 2: 1 way 2. Event 1: 2 ways, Event 2: 3 ways, Event 3: 4 ways

3. Event 1: 3 ways, Event 2: 4 ways 4. Event 1: 3 ways, Event 2: 3 ways, Event 3: 6 ways, Event 4: 5 ways

5. FOOD At your school cafeteria you can order a taco with one meat filling andone cheese filling. You have a choice of 3 meats and 4 cheeses. How many wayscan you order a taco with meat and cheese? (Lesson 12.1)

Find the number of distinguishable permutations of the letters in the word.(Lesson 12.1)

6. MATH 7. DOG 8. HELLO 9. MAINE

10. SCHOOL 11. STATISTICS 12. GEOMETRY 13. SISTERS

Find the number of combinations. (Lesson 12.2)

14. 10C3 15. 6C2 16. 11C5 17. 8C8

18. 15C4 19. 1C1 20. 9C8 21. 20C3

Expand the binomial. (Lesson 12.2)

22. (x + 3)4 23. (x + y)7 24. (2x º y)5 25. (x2 + 2y)6

26. (x4 + 4)3 27. (3x2 º 5)5 28. (3x º y2)4 29. (x3 + y3)3

A card is drawn randomly from a standard 52-card deck. Find the probability ofdrawing the given card. (Lesson 12.3)

30. ace of diamonds 31. any king 32. a club

33. a red card 34. a card other than 7 35. a face card (king, queen, jack)

The results of rolling a six-sided die 200 times are shown in the table below.Use the table to find the experimental probability of each event. (Lesson 12.3)

36. rolling a 1 37. rolling an even number 38. rolling a number greater than 1

39. rolling an odd number 40. rolling a 5 or a 6 41. rolling a number other than 2 or 3


Roll on die 1 2 3 4 5 6

Number of occurrences 20 40 33 37 34 36





of 2

Find the probability that the spinner will stop on a given region. (Lesson 12.3)

42. 1 43. 3

44. even 45. odd

46. blue 47. yellow

Find the indicated probability. State whether A and B are mutually exclusive.(Lesson 12.4)

48. P(A) = 0.3 49. P(A) = 0.4 50. P(A) = �185�

P(B) = 0.55 P(B) = 0.2 P(B) = ��?

P(A or B) = 0.85 P(A or B) = ��? P(A or B) = �112

5�

P(A and B) = ��? P(A and B) = 0.1 P(A and B) = 0

51. P(A) = 6% 52. P(A) = 40% 53. P(A) = 38%P(B) = 37% P(B) = ��? P(B) = 6%P(A or B) = ��? P(A or B) = 12% P(A or B) = 40%P(A and B) = 0% P(A and B) = 60% P(A and B) = ��?

Find P(A§). (Lesson 12.4)

54. P(A) = �12� 55. P(A) = 0 56. P(A) = 1 57. P(A) = �4

3�

58. P(A) = 0.6 59. P(A) = 0.2 60. P(A) = �112� 61. P(A) = �1

165�

You are drawing marbles from a bag. There are 6 green, 4 yellow, and 5 bluemarbles. Find the probability for the event if you replace the marble after eachdraw. (Lesson 12.5)

62. blue, then blue 63. green, then yellow 64. blue, then green 65. yellow, then blue

66. green, then green 67. yellow, then green 68. blue, then yellow 69. green, then blue

Calculate the probability of rolling a six-sided die 10 times and getting thegiven result. (Lesson 12.6)

70. exactly 3 sixes 71. exactly 4 ones 72. all odd numbers 73. exactly 3 evens

74. no odd numbers 75. exactly 6 threes 76. exactly 7 fives 77. 8 rolls greater than four

A normal distribution has a mean of 36 and a standard deviation of 5. Find theprobability that a randomly selected x-value is in the given interval. (Lesson 12.7)

78. between 31 and 41 79. between 21 and 36 80. between 31 and 46 81. less than 41

82. greater than 26 83. less than 51 84. between 21 and 46 85. greater than 36

CHAPTER 13

Evaluate the six trigonometric functions of the angle †. (Lesson 13.1)

1. 2. 3. 4.3

4

†

5 9†

2

3

†

7

7†

Extra Practice 957

8 12

345

6

7





of 2

Find one positive angle and one negative angle coterminal with the givenangle. (Lesson 13.2)

5. 35° 6. º70° 7. 125° 8. 2°

9. º45° 10. 315° 11. 585° 12. 600°

13. �23π� 14. �

112π� 15. �

165π� 16. �

71π3�

Find the arc length and area of a sector with the given radius r and centralangle †. (Lesson 13.2)

17. r = 4 in., † = 60° 18. r = 7 ft, † = 37° 19. r = 14 cm, † = 135°

20. r = 120 m, † = 167° 21. r = 9 cm, † = 4° 22. r = 28 in., † = 210°

Use the given point on the terminal side of an angle † in standard position.Evaluate the six trigonometric functions of †. (Lesson 13.3)

23. (4, 5) 24. (4, º1) 25. (º2, º6) 26. (º12, �3�)27. (6, 3) 28. (5, º12) 29. (3�7�, º2) 30. (�2�, �2�)31. (3, º5) 32. (7, º8) 33. (º3, 6) 34. (�5�, 3)

Evaluate the function without using a calculator. (Lesson 13.3)

35. sin (º390°) 36. sec 120° 37. cos 315° 38. tan (º150°)

39. cos �74π� 40. tan �76

π� 41. sin �º�

23π�� 42. csc �13

4π�

Evaluate the expression without using a calculator. Give your answer in bothradians and degrees. (Lesson 13.4)

43. tanº1 (º1) 44. cosº1 0 45. sinº1�º�12�� 46. cosº1 �º �

47. tanº1 48. sinº1 �12� 49. tanº1 �3� 50. sinº1

51. PLAYGROUND EQUIPMENT Two slides 12 feet long will be installed at the localplayground. At what angle to the ground should the first slide be set if the top ofthe slide is 8 feet off the ground? At what angle should the top of the second slidebe set if the slide must fit into a space that is only 6 feet wide? (Lesson 13.4)

Solve ¤ABC. (Lesson 13.5)

52. 53. 54. 55.

Find the area of the triangle with the given side lengths and included angle.(Lesson 13.5)

56. C = 120°, a = 12, b = 20 57. A = 55°, b = 7, c = 12

58. B = 30°, a = 18, c = 13 59. A = 80°, b = 120, c = 70

60. C = 20°, a = 10, b = 16 61. B = 35°, a = 50, c = 120

665�

50�

B

C

A

86�11

13

B

CA

41�

546�

B

C

A

7

6

34�B C

A

�3��2

�3��3

�2��2






of 2

Find the area of ¤ABC. (Lesson 13.6)

62. 63. 64. 65.

Write an xy-equation for the parametric equations. State the domain. (Lesson 13.7)

66. x = 12t º 5 and y = 10t º 3 for 0 ≤ t ≤ 60

67. x = 42t º 7 and y = 21t º 7 for 0 ≤ t ≤ 128

68. x = (17.54 sin 20°)t and y = 3t for 0 ≤ t ≤ 24

69. x = (10 cos 1°)t and y = (10 cos 1°)t for 0 ≤ t ≤ 50

CHAPTER 14

Find the amplitude and period of the graph of the function. (Lesson 14.1)

1. y = 6 sin �12�x 2. y = 2 sin �

18�x 3. y = �

17� cos πx 4. y = �

12� cos 2πx

5. y = sin 2πx 6. y = �13� cos �1

12�x 7. y = �

25� cos �

14�x 8. y = �

13� sin �

12�πx

Draw one cycle of the function’s graph. (Lesson 14.1)

9. y = 3 sin 2x 10. y = �12� cos 5x 11. y = 2 cos πx 12. y = 3 sin 2πx

13. y = 5 tan 2x 14. y = 5 tan �16�x 15. y = 7 cos 2πx 16. y = �

13� sin 3πx

Describe how the graph of y = sin x or y = cos x can be transformed toproduce the graph of the given function. (Lesson 14.2)

17. y = 3 + cos x 18. y = 7 + cos x 19. y = 4 º cos x 20. y = sin (x º π)

21. y = cos (x º π) 22. y = sin �x + �π4�� 23. y = cos �x º �

π2�� 24. y = º1 º sin �x + �

34π��


25. y = 2 + cos (x + π) 26. y = 1 º tan �x + �π2�� 27. y = 1 + sin (x + π) 28. y = 1 + sin ��2

1�x + �

34π��

29. y = º2 + tan x 30. y = º2 sin �12�x 31. y = cos �x º �

32π�� 32. y = 2 º tan (x º π)


33. csc x tan x 34. sin ��π2� º x� tan (ºx) 35. 1 º sin ��

π2� º x� cos x

36. �s

s

e

i

c

n2

2

x

(º

º

x)

1� º �

tan2 x1

+ 1� 37. �

sºin

ta(ºn

xx)

� 38.

39. �1 +sin

coxs x� + �1 +

sinco

xs x

� 40. �sec xta

ºn2

cxos x

� 41.cos x sin2 x º cos x��

cos x cot x

cos4 x + sin2 x cos2 x + sin2 x��

cos2 x

25

27 57�

B

C

A6

11

9B

A C

11

14

75�

B

A C

763�

8

A

C

B

Extra Practice 959





of 2

Find the general solution of the equation. (Lesson 14.4)

42. 2 sin x º �3� = 0 43. º1 º 2 sin x = 0 44. 10 cos x = 9 cos x + 1

45. 4 cos2 x º 1 = 0 46. cos x = 2 cos x + 1 47. 2 cos x sin x + sin x = 0

48. cos2 x = tan x º sin2 x 49. 6 cos2 x º 3 = 0 50. tan2 x º 2 tan x + 1 = 0

Solve the equation in the interval 0 ≤ x < 2π. Check your solutions. (Lesson 14.4)

51. 2 tan2 x º 1 = 0 52. sec2 x º 4 = 0 53. 2 sin x = sin x º 1

54. sin3 x = sin x 55. 4 cos x º 2 = 0 56. 6 cos x = 3 sec x

57. 2 tan2 x = sin x sec x 58. 1 º sin x = �2� cos x 59. cos2 x sin x = 3 sin x

Write a trigonometric function for the sinusoid with maximum at A andminimum at B. (Lesson 14.5)

60. A(0, 10), B(2π, 2) 61. A(ºπ, 2), B(π, 1) 62. A(º2, 7), B(0, 1)

63. A��π3�, 0�, B(0, º8) 64. A(0, 0), B(π, º1) 65. A(1, 23), B(2, 21)

66. CARNIVAL RIDE You and your friend are riding on a Ferris wheel with adiameter of 30 feet. When t = 0, your chair starts at the lowest point on thewheel, which is 6 feet above the ground. If the Ferris wheel is rotating at a rateof 4 revolutions per minute, write a model for the height h (in feet) of the chairas a function of the time t (in seconds). (Lesson 14.5)

Find the exact value of the expression. (Lesson 14.6)

67. sin 225° 68. cos (º15°) 69. cos 195° 70. sin 555°

71. tan �º�1π2�� 72. sin �19

2π� 73. tan �76

π� 74. sin �1

π2�

Evaluate the expression given sin u = �23� with 0 < u < �

π2� and cos v = º�

27�

with π < v < �32π�. (Lesson 14.6)

75. sin (u + v) 76. cos (u + v) 77. tan (u + v) 78. sin (u º v)

79. cos (u º v) 80. tan (u º v) 81. sin (v º u) 82. cos (v º u)

Find the exact value of the expression. (Lesson 14.7)

83. tan 105° 84. sin (º22.5°) 85. cos (º112.5°) 86. cos 165°

87. sin �78π� 88. cos �º�

π8�� 89. tan (º75°) 90. cos �º�

78π��

91. sin 67.5° 92. tan 22.5° 93. cos 105° 94. sin (º112.5°)

Find the exact values of sin 2x, cos 2x, and tan 2x. (Lesson 14.7)

95. cos x = �190�, 0 < x < �

π2� 96. sin x = �

45�, �

π2� < x < π 97. sin x = �

35�, 0 < x < �

π2�

98. sin x = �58�, �

π2� < x < π 99. cos x = �

11

12�, 0 < x < �

π2� 100. cos x = �

45�, �32

π� < x < 2π

101. sin x = º�45�, ��

32π� < x < 2π 102. cos x = �

34�, 0 < x < �

π2� 103. sin x = �

23�, �32

π� < x < 2π







extra practice - classzone 1 of 2 extra practice 941 solve the inequality. then graph your solution....

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