Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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

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

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

Sagot :

GinnyAnswer
To determine the profit we would earn from selling T-shirts at a price of [tex]$15 each, we need to substitute \( x = 15 \) into the profit function \( p(x) = -2(x-9)^2 + 100 \). Here are the steps: 1. Start with the given profit function: \[ p(x) = -2(x-9)^2 + 100 \] 2. Substitute \( x = 15 \) into the function: \[ p(15) = -2(15-9)^2 + 100 \] 3. Calculate the expression inside the parentheses first: \[ 15 - 9 = 6 \] 4. Now square the result: \[ 6^2 = 36 \] 5. Multiply this squared result by \(-2\): \[ -2 \times 36 = -72 \] 6. Finally, add 100 to -72 to find the profit: \[ -72 + 100 = 28 \] So, the profit when the T-shirts are sold for $[/tex]15 each would be \$28. Thus, the correct answer is:

[tex]\(\boxed{28}\)[/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.