C Challenge

54. Industry The average hourly wage H(x) of workers in an industry is modeled by the function H ( x ) = 16.24 x 0.062 x + 39.42 , h , open x close , equals . fraction 16.24 , x , over 0.062 , x plus , 39.42 end fraction . comma  where x represents the number of years since 1970. In what year does the model predict that wages will be $25/h?
55. Open-Ended Write a rational equation that has the following.
    1. one solution
    2. two solutions
    3. no real solution
56. Sports An automatic pitching machine can pitch all its baseballs in 1 1 4 1 , and 1 fourth  hours. One attendant can retrieve all the baseballs pitched by one machine in 3 1 2 3 , and 1 half  hours. At least how many attendants working at the same rate should be hired so that the baseballs from 10 machines are all retrieved in less than 8 hours?

Standardized Test Prep

SAT/ACT

57. What is the solution of x + 1 x = − 2 ? x plus , 1 over x , equals negative 2 question mark
    1. 1, − 1 negative 1
    2. 0 only
    3. − 1 2 negative , 1 half  only
    4. − 1 negative 1  only
58. Which of the following is equivalent to 6 24 2 3 ? fraction 6 square root of 24 , over 2 square root of 3 end fraction . question mark
    6. 2 2 2 square root of 2
    7. 3 2 3 square root of 2
    8. 5 2 5 square root of 2
    9. 6 2 6 square root of 2
59. An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What is that interest rate?
    1. 2.00%
    2. 5.78%
    3. 6.93%
    4. 200%

Extended Response

60. A librarian orders 48 fiction and nonfiction books for the school library. A fiction book costs $15 and a nonfiction book costs $20. The total cost of the order was $900. How many nonfiction books did the librarian order? Show your work.

Mixed Review

See Lesson 8-5.

Simplify each difference.

61. 3 y + 1 4 y + 4 − 2 y + 7 2 y + 2 fraction 3 y plus 1 , over 4 y plus 4 end fraction . minus . fraction 2 y plus 7 , over 2 y plus 2 end fraction
62. 5 x 2 y + 4 − 6 y 2 + 2 y fraction 5 x , over 2 y plus 4 end fraction . minus . fraction 6 , over y squared , plus 2 y end fraction
63. x + 1 2 x − 2 − 2 x x 2 + 2 x − 3 fraction x plus 1 , over 2 x minus 2 end fraction . minus . fraction 2 x , over x squared , plus 2 x minus 3 end fraction

See Lesson 7-5.

Solve each equation.

64. log 10 0.001 = x log base 10 . 0.001 , equals x
65. log 3 27 = 3 x + 6 log base 3 , 27 equals 3 x plus 6
66. log 0.5 ( x + 1 ) = 3 log base 0.5 , open x plus 1 close equals 3

See Lesson 6-7.

Find the inverse of each function. Is the inverse a function?

67. y = 5 − 2 x y equals 5 minus 2 x
68. y = x 2 + 1 y equals , x squared , plus 1
69. y = x 3 − 4 y equals , x cubed , minus 4

Get Ready! To prepare for Lesson 9-1, do Exercises 70-75.

See Lesson 1-1.

Identify the pattern and find the next three terms.

70. 1, 3, 5, 7, …
71. − 2 , − 4 , − 6 , − 8 , … negative 2 comma negative 4 comma negative 6 comma negative 8 comma dot dot dot
72. 0.2, 1, 5, 25, 125, …
73. 50, 45, 40, 35, …
74. 16, 32, 64, …
75. − 3 , − 7 , − 11 , − 15 , … negative 3 comma negative 7 comma negative 11 comma negative 15 comma dot dot dot

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