Question

Which of the following is an equivalent expression for the volume prism that’s has a height of (1/2x-3) inches, a length of (x+5), and a width of (x-4)?

A. (1/2x^3 -3x^2 -4x +5) inches
B. (1/2x^3 -5/2x^2 -13x +60) inches
C. (5/2x^3 -1/2x^2 -4x+ 20)
D. (5/2x^3 -3/2x^2 +13x+ 20)

Answer 1

the correct answer is D. (5/2x^3 -3/2x^2 +13x+ 20). Hope this helps ;) don't forget to rate this answer !

Explanation:

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism. In this case, the height of the prism is (1/2x-3), the length is (x+5), and the width is (x-4).

Substituting these values into the volume formula, we get:

V = (1/2x-3)(x+5)(x-4)

Expanding this expression using the distributive property, we get:

V = (1/2x^2 - 3x)(x+5)(x-4)

Using the distributive property again, we get:

V = (1/2x^2 - 3x)(x^2 + x - 20)

Using the distributive property once more, we get:

V = 1/2x^3 - 3x^2 - 4x + 20

This expression is equivalent to the expression in answer choice D. Therefore, the correct answer is D. (5/2x^3 -3/2x^2 +13x+ 20)