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The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width. Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Write the equation that represents the volume of the storage container in terms of its width.

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musiclover10045
the length is 2 feet more than the width so L = w+2
 so volume = (w+2) * w * 6
 use distributive property:

(w*w + 2*w) * 6 =
(w^2+2w) *6 =

use distributive property again:

w^2 *6 + 2w*6 = 

6w^2 +12w

The equation represents the volume of the storage container in terms of its width is 6w^2+12w.

The length is 2 feet more than the width

So,[tex]L = w+2[/tex]

What is the volume of the container?

[tex]volume = (w+2) * w * 6[/tex]

use distributive property:

[tex]= (w^2+2w) * 6[/tex]

[tex]=(w^2+2w) *6[/tex]

use the distributive property again:

[tex]=w^2 *6 + 2w*6[/tex]

[tex]=6w^2 +12w[/tex]

Therefore the equation represents the volume of the storage container in terms of its width is 6w^2+12w.

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