C Challenge

48. Geometry Suppose the prism below has the same surface area as a cube with edges 8 in. long.

    

    1. Write an expression for the surface area of the prism shown.
    2. Write an equation that relates the surface area of the prism to the surface area of the 8-in. cube.
    3. Solve the equation you wrote in part (b). What are the dimensions of the prism?
49. 1. Solve the equation x 2 − 6 x + 4 = 0 , x squared , minus 6 . x plus 4 equals 0 comma  but leave the solutions in the form p ± q . p plus minus square root of q .
    2. Use the formula x = − b 2 a x equals . fraction negative b , over 2 eh end fraction  to find the coordinates of the vertex of the graph of y = x 2 − 6 x + 4 . y equals . x squared , minus 6 . x plus 4 .
    3. Reasoning Explain the relationship between your answers to parts (a) and (b).

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

50. The rectangular poster has an area 40  ft 2 . 40 , ft squared , .  What is the value of x to the nearest tenth of a foot?

    

51. The width of a notebook is 2.15 × 10 – 2 m . 2.15 , times , 10 super en dash 2 end super , m .  In decimal form, how many meters wide is the notebook?
52. What is the solution of the equation 19 + x = 35 ? 19 plus x equals 35 question mark
53. How many elements are in the intersection of the two sets M = { 2 , 3 , 4 , 5 } m equals left brace 2 comma 3 comma 4 comma 5 right brace  and N = { 1 , 3 , 5 , 9 } ? n equals left brace 1 comma 3 comma 5 comma 9 right brace question mark
54. A ribbon with straight edges has an area of 24  in. 2 . 24 , in. squared , .  Its width is x and its length is 2 x + 13 . 2 x plus 13 .  What is the width of the ribbon in inches?
55. What is the x-intercept of the graph of 2 x + 3 y = 9 ? 2 x plus 3 y equals 9 question mark
56. The sum of two numbers is 20. The difference between three times the larger number and twice the smaller number is 40. What is the larger number?

Mixed Review

See Lesson 9-4.

Solve by factoring.

57. n 2 + 11 n + 30 = 0 n squared , plus 11 . n plus 30 equals 0
58. 9 v 2 − 64 = 0 9 v squared , minus 64 equals 0
59. 12 w 2 = 28 w + 5 12 w squared , equals 28 w plus 5

See Lesson 7-4.

Simplify.

60. ( m 3 ) 4 open , m cubed , close to the fourth
61. − b 7 ( b 8 ) − 1 negative , b to the seventh . open , b to the eighth , close super negative 1 end super
62. t ( t 2 ) 6 t . open , t squared , close to the sixth
63. y 8 ( y − 7 ) − 3 y to the eighth . open , y super negative 7 end super , close super negative 3 end super

Get Ready! To prepare for Lesson 9-6, do Exercises 64–66.

See Lesson 1-2.

Evaluate b 2 − 4 a c b squared , minus 4 eh c  for the given values of a, b, and c.

64. a = 2 , b = 5 , c = − 7 eh equals 2 comma b equals 5 comma c equals negative 7
65. a = 2 , b = 4 , c = 2 eh equals 2 comma b equals 4 comma c equals 2
66. a = 1 , b = 3 , c = 6 eh equals 1 comma b equals 3 comma c equals 6

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