Answer:
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)