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The function [tex]\( p(x) = -2(x-9)^2 + 100 \)[/tex] is used to determine the profit on T-shirts sold for [tex]\( x \)[/tex] dollars.

What would the profit from sales be if the price of the T-shirts were [tex]\( \$15 \)[/tex] apiece?

A. \[tex]$15
B. \$[/tex]28
C. \[tex]$172
D. \$[/tex]244

Sagot :

GinnyAnswer
To determine the profit from T-shirt sales when the price per T-shirt is [tex]$15, we need to evaluate the profit function \( p(x) = -2(x - 9)^2 + 100 \) at \( x = 15 \). Let's break down the process step-by-step: 1. Substitute \( x = 15 \) into the profit function \( p(x) \): \[ p(15) = -2(15 - 9)^2 + 100 \] 2. Calculate the expression inside the parentheses: \[ 15 - 9 = 6 \] 3. Square the result: \[ 6^2 = 36 \] 4. Multiply by \(-2\): \[ -2 \times 36 = -72 \] 5. Add 100 to the result: \[ -72 + 100 = 28 \] So, the profit from sales when the T-shirts are priced at $[/tex]15 apiece is [tex]\(\$28\)[/tex].

Thus, the correct answer is:
[tex]\(\$ 28\)[/tex]
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