Reasoning Determine whether each statement is always, sometimes, or never true for real numbers a and b Explain.

51. 2 b b = 2 fraction 2 b , over b end fraction , equals 2
52. a b 3 b 4 = a b fraction eh , b cubed , over b to the fourth end fraction . equals eh b
53. a 2 + 6 a + 5 2 a + 2 = a + 5 2 fraction eh squared , plus 6 eh plus 5 , over 2 eh plus 2 end fraction . equals . fraction eh plus 5 , over 2 end fraction

Standardized Test Prep

SAT/ACT

54. Which expression simplifies to − 1 negative 1 ?
    1. x + 1 x − 1 , x ≠ 1 fraction x plus 1 , over x minus 1 end fraction . comma x not equal to 1
    2. r + 3 3 − r , r ≠ 3 fraction r plus 3 , over 3 minus r end fraction . comma r not equal to 3
    3. n − 2 2 − n , n ≠ 2 fraction n minus 2 , over 2 minus n end fraction . comma n not equal to 2
    4. 4 − p 4 + p , p ≠ − 4 fraction 4 minus p , over 4 plus p end fraction . comma p not equal to negative 4
55. Which inequality represents the graph below?

    

    6. y > 1 3 x + 1 y greater than , 1 third , x plus 1
    7. y < 1 3 x + 1 y less than , 1 third , x plus 1
    8. y ≥ 1 3 x + 1 y greater than or equal to , 1 third , x plus 1
    9. y ≤ 1 3 x + 1 y less than or equal to , 1 third , x plus 1
56. What is 6 96 fraction square root of 6 , over square root of 96 end fraction  in simplified form?
    1. 16
    2. 4
    3. 1 4 1 fourth
    4. 1 16 1 sixteenth

    Short Response

57. You are painting a wall for a display. You want to have a blue border of uniform width around a white rectangle, as shown. The areas of the blue border and the white rectangle should be the same. What should be the approximate width x of the blue border? Show your work.

    

Mixed Review

See Lesson 10-6.

Use Δ A B C cap delta eh b c  below. Find the value of each expression.

58. cos B cosine b
59. sin A sine eh
60. tan B tangent b

See Lesson 10-2.

Simplify each radical expression.

61. 20 ⋅ 10 square root of 20 dot square root of 10
62. a 4 b 7 c 8 square root of eh to the fourth , b to the seventh , c to the eighth end root
63. 9 x ⋅ 11 x square root of 9 x end root , dot , square root of 11 x end root
64. 2 m 25 m 5 square root of fraction 2 m , over 25 , m to the fifth end fraction end root
65. 80 10 fraction square root of 80 , over square root of 10 end fraction
66. 28 y 5 7 y 2 square root of fraction 28 , y to the fifth , over 7 , y squared end fraction end root

Get Ready! To prepare for Lesson 11-2, do Exercises 67–72.

See Lesson 8-6.

Factor each expression.

67. 2 c 2 + 15 c + 7 2 , c squared , plus 15 c plus 7
68. 15 t 2 − 26 t + 11 15 , t squared , minus 26 t plus 11
69. 9 q 2 + 12 q + 4 9 , q squared , plus 12 q plus 4
70. 4 c 2 − 12 c + 5 4 , c squared , minus 12 c plus 5
71. 24 t 2 − 14 t − 3 24 , t squared , minus 14 t minus 3
72. 3 q 2 − q − 14 3 , q squared , minus q minus 14

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