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The formula for volume of this rectangular prism is:

V = 2x 3 + 17x 2 + 46x + 40



Find an expression for the missing side length. Show all of your work for full credit.

The formula for volume of this rectangular prism is V 2x 3 17x 2 46x 40 Find an expression for the missing side length Show all of your work for full credit class=

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carlosego
 By definition, the volume of a rectangular prism is given by:
 [tex]V = (w) * (h) * (l) [/tex]
 Where,
 l: length
 h: height
 w: width
 Substituting values we have:
 [tex]2x ^ 3 + 17x ^ 2 + 46x + 40 = (w) * (x + 2) * (x + 4) [/tex]
 From here, we clear the value of w.
 [tex]w = (2x ^ 3 + 17x ^ 2 + 46x + 40) / ((x + 2) * (x + 4)) [/tex]
 Factoring the numerator we have:
 [tex]w = ((x + 2) * (x + 4) * (2x + 5)) / ((x + 2) * (x + 4)) [/tex]
 Canceling similar terms we have:
 [tex]w = 2x + 5 [/tex]
 Answer:
 The missing side is of length:
 w = 2x + 5
MrRoyal

The volume of a rectangular prism is the product of its dimension.

The missing side length is 2x + 5.

The volume is given as:

[tex]\mathbf{V = 2x^3 + 17x^2 + 46x + 40}[/tex]

Let the missing side be y.

So, we have:

[tex]\mathbf{V = (x + 2) \times ( x + 4) \times y}[/tex]

So, we have:

[tex]\mathbf{(x + 2) \times ( x + 4) \times y = 2x^3 + 17x^2 + 46x + 40}[/tex]

Factorize

[tex]\mathbf{(x + 2) \times ( x + 4) \times y = (x + 2) \times (x + 4) \times (2x +5)}[/tex]

Cancel out common factors

[tex]\mathbf{y = (2x +5)}[/tex]

Remove brackets

[tex]\mathbf{y = 2x +5}[/tex]

Hence, the missing side length is 2x + 5.

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https://brainly.com/question/22885718

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