faithannr123
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Select the correct answer.

A home-based sign company uses this function to model its monthly profit, where [tex]$x$[/tex] is the price of each sign it sells.
[tex]
p(x)=-10x^2+498x-1,500
[/tex]

What is the company's profit if it sells each sign for [tex][tex]$\$[/tex]20$[/tex]?

A. [tex]$\$18,020$[/tex]
B. [tex][tex]$\$[/tex]14,420$[/tex]
C. [tex]$\$4,460$[/tex]
D. [tex][tex]$\$[/tex]1,402$[/tex]



Answer :

GinnyAnswer
To determine the company's profit if it sells each sign for \[tex]$20, we need to substitute \( x = 20 \) into the given profit function \( p(x) = -10x^2 + 498x - 1500 \). Given: \[ p(x) = -10x^2 + 498x - 1500 \] We need to find \( p(20) \). Step-by-step solution: 1. Substitute \( x = 20 \) into the profit function: \[ p(20) = -10(20)^2 + 498(20) - 1500 \] 2. Compute each term: - First term: \[ -10(20)^2 = -10 \cdot 400 = -4000 \] - Second term: \[ 498(20) = 9960 \] - Third term (constant): \[ -1500 \] 3. Combine the results: \[ p(20) = -4000 + 9960 - 1500 \] 4. Calculate the final result: \[ -4000 + 9960 = 5960 \] \[ 5960 - 1500 = 4460 \] Therefore, the company's profit when each sign is sold for \$[/tex]20 is \[tex]$4460. The correct answer is: C. \(\$[/tex]4,460\)

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