A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x^3+8x^2=450 can be used to find x. Find the side length of the original cube. Use a graphing calculator and a system of equations to find the answer. A. 4 inches B. 5 inches C. 9 inches D. 10 inches

Question

Mathematics

Giada Howell

7 June, 02:48

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x^3+8x^2=450 can be used to find x. Find the side length of the original cube. Use a graphing calculator and a system of equations to find the answer. A. 4 inches B. 5 inches C. 9 inches D. 10 inches

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Answers (1)

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David Kemp · Answer 1

This equation can be obtained simply by multiplying the three dimensions of the cube.

Length = x + 4

Width = 2x

Height = x

Volume = (x + 4) (2x) (x)

450 = 2x³ + 8x²

Using a graphing calculator and plotting this, we see that the solution of this equation is 5.

Therefore, the original side was 5 inches. The answer is B