Question

profit is the difference between revenue and cost. the revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial $2x^3 + 30x - 130$. the cost, in dollars, of producing the skateboards can be modeled by $2x^3 - 3x - 520$. the variable x represents the number of skateboards sold. what expression represents the profit? $27x - 650$ $27x + 390$ $33x - 650$ $33x + 390$

Explanation:

Step1: Recall Profit Formula

Profit = Revenue - Cost. So we need to subtract the cost polynomial from the revenue polynomial.
Revenue: \(2x^3 + 30x - 130\)
Cost: \(2x^3 - 3x - 520\)
Profit = \((2x^3 + 30x - 130) - (2x^3 - 3x - 520)\)

Step2: Distribute the Subtraction

Distribute the negative sign to each term in the cost polynomial:
\(2x^3 + 30x - 130 - 2x^3 + 3x + 520\)

Step3: Combine Like Terms

• For \(x^3\) terms: \(2x^3 - 2x^3 = 0\)
• For \(x\) terms: \(30x + 3x = 33x\)
• For constant terms: \(-130 + 520 = 390\)

So the profit expression is \(33x + 390\).

Answer:

\(33x + 390\) (corresponding to the last option, e.g., if the last option is D. \(33x + 390\), then D. \(33x + 390\))