Question

A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x^3+6x^2-27x=140 can be used to find x.

height(x+9)in width(x-3)in length x in
What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer.

The length is 7 inches, the width is 4 inches, and the height is 16 inches.
The length is 5 inches, the width is 2 inches, and the height is 14 inches.
The length is 4 inches, the width is 1 inch, and the height is 13 inches.
The length is 3 inches, the width is 0 inches, and the height is 12 inches.

Answer 1

The answer is:
B. The length is 5 inches, the width is 2 inches, and the height is 14 inches.
Hope this helps! :)

Answer 2

For this case we have the following equation for the volume:

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Rewriting the equation we have:

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We factor the equation to find the roots of the polynomial.

We have then:

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Then, we discard the negative roots, because the dimensions of the figure must be positive.

We have then that the length is:

`image`

The height is:

`image`

The width is:

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Thus, the dimensions are:

`image`

Answer:

The length is 5 inches, the width is 2 inches, and the height is 14 inches.