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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.

Respuesta :

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

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

[tex] x ^ 3 + 6x ^ 2-27x = 140
[/tex]

Rewriting the equation we have:

[tex] x ^ 3 + 6x ^ 2-27x-140 = 0
[/tex]

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

We have then:

[tex] (x-5) (x + 4) (x + 7) = 0
[/tex]

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

We have then that the length is:

[tex] x = 5
[/tex]

The height is:

[tex] x + 9 = 5 + 9 = 14
[/tex]

The width is:

[tex] x-3 = 5-3 = 2
[/tex]

Thus, the dimensions are:

[tex] 5 * 14 * 2
[/tex]

Answer:

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

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