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Select the correct answer.

Shawn is packing these two boxes with food collected during his school's canned food drive.

Which expression represents the total volume of the two boxes?

A. [tex]21x^3 - 48x^2 - 199x[/tex]
B. [tex]27x^3 + 48x^2 - 99x[/tex]
C. [tex]13z^2 + 20x - 57[/tex]
D. [tex]84x^3 - 282x^2 - 138x - 336[/tex]

Answer :

To find the expression that represents the total volume of the two boxes, we need to add the algebraic expressions for each box's volume.

The two expressions we are considering are:
1. [tex]\( 21x^3 - 48x^2 - 199x \)[/tex]
2. [tex]\( 27x^3 + 48x^2 - 99x \)[/tex]

Let's add these expressions together term by term:

1. Cubic Terms:
[tex]\[
21x^3 + 27x^3 = 48x^3
\][/tex]

2. Quadratic Terms:
[tex]\[
-48x^2 + 48x^2 = 0x^2
\][/tex]

3. Linear Terms:
[tex]\[
-199x - 99x = -298x
\][/tex]

Now, combine these results to form the total volume expression:
[tex]\[
48x^3 + 0x^2 - 298x
\][/tex]

Simplifying this gives:
[tex]\[
48x^3 - 298x
\][/tex]

Although this calculation does not directly match any of the provided answers, it seems there might have been a misunderstanding or typographical error in the context or listed options, as the expected procedure and terms used were evident. However, based on the problem conditions and the result shared indirectly, this approach was used.

Please verify the expressions provided or the criteria used to need addressing to match a listed choice. Let's ensure the expressions and their combinations align properly with either numerical analysis or expression available explicitly.

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