An expression for a company's cost to make n bicycles is -0.017n? - 6.8n + 690. An expression for the revenue from selling these n bicycles is 70n. Profit is revenue minus cost. Which is an expression for the profit for making and selling n bicycles?

Rationale

-0.017n² + 63.2n + 690

To find the profit from making and selling n bicycles, we subtract the cost function from the revenue function. The cost function given is -0.017n² - 6.8n + 690, and the revenue function is 70n. Thus, the profit function simplifies to -0.017n² + 63.2n + 690.

A (-0.017n^2 - 76.8n + 690) YOUR ANSWER

This expression incorrectly combines the linear terms. While it retains the correct quadratic term of -0.017n², it mistakenly sums the revenue and cost terms, leading to a negative coefficient for n that does not accurately reflect the profit calculation.

B (0.017n^2 + 76.8n - 690) YOUR ANSWER

This option incorrectly changes the sign of the quadratic term and adds an incorrect positive linear term. The profit expression should maintain the negative quadratic term from the cost and a linear term that accurately reflects the revenue minus cost calculation, which does not happen here.

C (0.017n^2 + 63.2n + 690) YOUR ANSWER

Similar to option B, this choice also incorrectly alters the sign of the quadratic term. While it keeps the linear term correct, the positive coefficient for n² is not applicable in the context of profit calculation, as it should be negative due to the structure of the cost function.

D (-0.017n^2 + 63.2n + 690) CORRECT

This expression accurately reflects the profit calculation by maintaining the correct negative coefficient for the quadratic term from the cost function and adjusting the linear term appropriately to account for the revenue generated from selling the bicycles.

Conclusion

The profit from making and selling n bicycles is correctly expressed as -0.017n² + 63.2n + 690, derived from the difference between the revenue and cost functions. Each incorrect option fails to properly calculate the profit by mismanaging the signs or terms, highlighting the importance of careful algebraic manipulation in determining profit accurately.

An expression for a company's cost to make n bicycles is -0.017n? - 6.8n + 690. An expression for the revenue from selling these n bicycles is 70n. Profit is revenue minus cost. Which is an expression for the profit for making and selling n bicycles?

-0.017n² + 63.2n + 690

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