41. Reasoning The GCF of two numbers p and q is 7. What is the GCF of p 2 p squared  and q 2 ? q squared , question mark  Justify your answer.

C Challenge

42. Manufacturing The diagram shows a cube of metal with a cylinder cut out of it. The formula for the volume of a cylinder is V = π r 2 h , v equals pi , r squared , h comma  where r is the radius and h is the height.

    

    1. Write a formula for the volume of the cube in terms of s.
    2. Write a formula for the volume of the cylinder in terms of s.
    3. Write a formula in terms of s for the volume V of the metal left after the cylinder has been removed.
    4. Factor your formula from part (c).
    5. Find V in cubic inches for s = 15 s equals 15  in. Use π = 3.14 . pi equals , 3.14 , .
43. 1. Geometry How many sides does the polygon have? How many of its diagonals come from one vertex?
    2. A polygon has n sides. How many diagonals will it have from one vertex?
    3. The number of diagonals from all the vertices is n 2 ( n − 3 ) . n over 2 . open , n minus 3 , close . .  Write this polynomial in standard form.
    4. A polygon has 8 sides. How many diagonals does it have?

       

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

44. Simplify the product 4 x ( 5 x 2 + 3 x + 7 ) . 4 x open , 5 x squared , plus 3 x plus 7 close .  What is the coefficient of the x 2 x squared -term?
45. What is the slope of the line that passes through C D ¯ ? c d bar , question mark
46. What is the solution of the equation 7 x − 11 = 3 ? 7 x minus 11 equals 3 question mark
47. Simplify the product 8 x 3 ( 2 x 2 ) . 8 , x cubed , open 2 , x squared , close .  What is the exponent?

48. The expression 9 x 3 − 15 x 9 , x cubed , minus 15 x  can be factored as a x ( 3 x 2 − 5 ) . eh x open 3 , x squared , minus 5 close .

    What is the value of a?

    

Mixed Review

See Lesson 8-1.

Simplify each sum or difference.

49. ( 5 x 2 + 4 x − 2 ) + ( 3 x 2 + 7 ) open 5 , x squared , plus 4 x minus 2 close plus open 3 , x squared , plus 7 close
50. ( 4 x 4 − 3 x 2 − 1 ) + ( 3 x 4 + 6 x 2 ) open 4 , x to the fourth , minus 3 , x squared , minus 1 close plus open 3 , x to the fourth , plus 6 , x squared , close
51. ( 3 x 3 − 2 x ) − ( 8 x 3 + 4 x ) open 3 , x cubed , minus 2 x close minus open 8 , x cubed , plus 4 x close
52. ( 7 x 4 + 3 x 3 − 5 x + 1 ) − ( x 3 + 8 x 2 − 5 x − 3 ) open 7 , x to the fourth , plus 3 , x cubed , minus 5 x plus 1 close minus open , x cubed , plus 8 , x squared , minus 5 x minus 3 close

See Lesson 6-5.

Solve each inequality for y. Then graph the inequality.

53. 4 x − 5 y ≥ 10 4 x minus 5 y greater than or equal to 10
54. 7 x − 2 y ≤ 8 7 x minus 2 y less than or equal to 8
55. − 3 y − x > 9 negative 3 y minus x greater than 9

Get Ready! To prepare for Lesson 8-3, do Exercises 56–58.

See Lesson 1-7.

Use the Distributive Property to simplify each expression.

56. 8 ( x − 5 ) 8 open x minus 5 close
57. − 3 ( w + 4 ) negative 3 open w plus 4 close
58. 0.25 ( 6 c + 16 ) 0.25 , open 6 c plus 16 close

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