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Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial [tex]\(2x^3 + 30x - 130\)[/tex]. The cost, in dollars, of producing the skateboards can be modeled by [tex]\(2x^3 - 3x - 520\)[/tex]. The variable [tex]\(x\)[/tex] represents the number of skateboards sold.

What expression represents the profit?

A. [tex]\(27x - 650\)[/tex]
B. [tex]\(27x + 390\)[/tex]
C. [tex]\(33x - 650\)[/tex]
D. [tex]\(33x + 390\)[/tex]



Answer :

GinnyAnswer
To determine the profit, we start by recalling that the profit is the difference between the revenue and the cost.

Given:
- The revenue polynomial [tex]\( R(x) = 2x^3 + 30x - 130 \)[/tex]
- The cost polynomial [tex]\( C(x) = 2x^3 - 3x - 520 \)[/tex]

We need to find the profit polynomial [tex]\( P(x) \)[/tex] by subtracting the cost polynomial from the revenue polynomial:

[tex]\[ P(x) = R(x) - C(x) \][/tex]

Let's break it down step by step:

1. Subtract the like terms of the polynomials:

[tex]\[ P(x) = (2x^3 + 30x - 130) - (2x^3 - 3x - 520) \][/tex]

2. Distribute the negative sign to the terms in the cost polynomial:

[tex]\[ P(x) = 2x^3 + 30x - 130 - 2x^3 + 3x + 520 \][/tex]

3. Combine the like terms:

- The [tex]\(2x^3\)[/tex] terms cancel each other out:
[tex]\[ 2x^3 - 2x^3 = 0 \][/tex]

- The [tex]\(30x\)[/tex] and [tex]\(3x\)[/tex] terms combine:
[tex]\[ 30x + 3x = 33x \][/tex]

- The constants [tex]\(-130\)[/tex] and [tex]\(520\)[/tex] terms combine:
[tex]\[ -130 + 520 = 390 \][/tex]

4. Putting it all together, we get:

[tex]\[ P(x) = 33x + 390 \][/tex]

Thus, the expression that represents the profit is:

[tex]\[ \boxed{33x + 390} \][/tex]

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