Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To determine Mario's profit [tex]\( p(x) \)[/tex] from mowing [tex]\( x \)[/tex] lawns, we need to use the given revenue function [tex]\( r(x) \)[/tex] and cost function [tex]\( c(x) \)[/tex]:
1. The revenue function is [tex]\( r(x) = 25x \)[/tex].
2. The cost function is [tex]\( c(x) = 6x + 15 \)[/tex].
Profit [tex]\( p(x) \)[/tex] is the difference between revenue [tex]\( r(x) \)[/tex] and cost [tex]\( c(x) \)[/tex]:
[tex]\[ p(x) = r(x) - c(x) \][/tex]
We will substitute the given functions for revenue and cost into this formula:
[tex]\[ p(x) = 25x - (6x + 15) \][/tex]
Next, distribute the negative sign across the terms inside the parentheses:
[tex]\[ p(x) = 25x - 6x - 15 \][/tex]
Combine the like terms [tex]\( 25x \)[/tex] and [tex]\( -6x \)[/tex]:
[tex]\[ p(x) = (25x - 6x) - 15 \][/tex]
[tex]\[ p(x) = 19x - 15 \][/tex]
Thus, Mario's profit from mowing [tex]\( x \)[/tex] lawns is:
[tex]\[ p(x) = 19x - 15 \][/tex]
The correct answer is:
[tex]\[ \boxed{C. \, p(x) = 19x - 15} \][/tex]
1. The revenue function is [tex]\( r(x) = 25x \)[/tex].
2. The cost function is [tex]\( c(x) = 6x + 15 \)[/tex].
Profit [tex]\( p(x) \)[/tex] is the difference between revenue [tex]\( r(x) \)[/tex] and cost [tex]\( c(x) \)[/tex]:
[tex]\[ p(x) = r(x) - c(x) \][/tex]
We will substitute the given functions for revenue and cost into this formula:
[tex]\[ p(x) = 25x - (6x + 15) \][/tex]
Next, distribute the negative sign across the terms inside the parentheses:
[tex]\[ p(x) = 25x - 6x - 15 \][/tex]
Combine the like terms [tex]\( 25x \)[/tex] and [tex]\( -6x \)[/tex]:
[tex]\[ p(x) = (25x - 6x) - 15 \][/tex]
[tex]\[ p(x) = 19x - 15 \][/tex]
Thus, Mario's profit from mowing [tex]\( x \)[/tex] lawns is:
[tex]\[ p(x) = 19x - 15 \][/tex]
The correct answer is:
[tex]\[ \boxed{C. \, p(x) = 19x - 15} \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.