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The value of a company's stock is represented by the expression [tex]$x^2 - 2y$[/tex], and the company's purchases are modeled by [tex][tex]$2x + 5y$[/tex][/tex]. The company's goal is to maintain a stock value of at least [tex]$7,000, while keeping the purchases below $[/tex]1,000. Which system of inequalities represents this scenario?

A.
[tex]\[
\begin{array}{l}
x^2 - 2y \ \textgreater \ 7000 \\
2x + 5y \ \textless \ 1000
\end{array}
\][/tex]

B.
[tex]\[
\begin{array}{r}
x^2 - 2y \geq 7000 \\
2x + 5y \ \textless \ 1000
\end{array}
\][/tex]

C.
[tex]\[
\begin{array}{l}
x^2 - 2y \ \textgreater \ 7000 \\
2x + 5y \leq 1000
\end{array}
\][/tex]

D.
[tex]\[
\begin{array}{c}
x^2 - 2y \leq 7000 \\
2x + 5y \leq 1000
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To solve this problem, we need to represent the company's goals using a system of inequalities.

1. For the company's stock value goal:
- It is stated that the company wants to maintain a stock value of at least [tex]$7,000. - The expression for stock value is \( x^2 - 2y \). - "At least $[/tex]7,000" means the stock value should be greater than or equal to [tex]$7,000. - This can be written as an inequality: \( x^2 - 2y \geq 7000 \). 2. For the company's purchase constraint: - The company wants to keep purchases below $[/tex]1,000.
- The expression for purchases is [tex]\( 2x + 5y \)[/tex].
- "Below [tex]$1,000" means the purchases should be less than $[/tex]1,000.
- This can be written as an inequality: [tex]\( 2x + 5y < 1000 \)[/tex].

Putting both inequalities together, we get the system of inequalities that represents the scenario:

[tex]\[ \begin{array}{r} x^2 - 2y \geq 7000 \\ 2x + 5y < 1000 \end{array} \][/tex]

Therefore, the correct answer is:

[tex]\[ \begin{array}{r} x^2 - 2y \geq 7000 \\ 2x + 5y < 1000 \end{array} \][/tex]
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