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$BUSINESS Saini Sprinkler Company installs irrigation systems. To track monthly costs C and revenues R, they use the following functions, where x is the number of systems they install. {:[R(x)=8x^(2)+12 x+4],[C(x)=7x^(2)+20 x-12]:} The monthly profit can be found by subtracting cost from revenue. P(x)=R(x)-C(x) Find a function to project monthly profit and use it to find the break-even point where the profit is zero.$

$3$ . BUSINESS Saini Sprinkler Company installs irrigation systems. To track monthly costs $C$ and revenues $R$ , they use the following functions, where $x$ is the number of systems they install. $\newline$ $\begin{array}{l} R(x)=8 x^{2}+12 x+4 \\ C(x)=7 x^{2}+20 x-12 \end{array}$ $\newline$ The monthly profit can be found by subtracting cost from revenue. $\newline$ $P(x)=R(x)-C(x)$ $\newline$ Find a function to project monthly profit and use it to find the break-even point where the profit is zero.

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Math Problems

Grade 7

Solve two-step equations: word problems

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3

. BUSINESS Saini Sprinkler Company installs irrigation systems. To track monthly costs

C

and revenues

R

, they use the following functions, where

x

is the number of systems they install.

\newline

\begin{array}{l} R(x)=8 x^{2}+12 x+4 \\ C(x)=7 x^{2}+20 x-12 \end{array}

\newline

The monthly profit can be found by subtracting cost from revenue.

\newline

P(x)=R(x)-C(x)

\newline

Find a function to project monthly profit and use it to find the break-even point where the profit is zero.

Write Revenue and Cost Functions: Write down the revenue function $R(x)$ and the cost function $C(x)$ . $R(x) = 8x^2 + 12x + 4$ $C(x) = 7x^2 + 20x - 12$
Subtract to Find Profit Function: Subtract the cost function $C(x)$ from the revenue function $R(x)$ to get the profit function $P(x)$ . $P(x) = R(x) - C(x)$ $P(x) = (8x^2 + 12x + 4) - (7x^2 + 20x - 12)$
Simplify Profit Function: Simplify the profit function $P(x)$ by combining like terms. $P(x) = 8x^2 + 12x + 4 - 7x^2 - 20x + 12$ $P(x) = x^2 - 8x + 16$