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

A.
[tex]x^2 - 2y > 7000[/tex]
[tex]2x + 5y < 1000[/tex]

B.
[tex]x^2 - 2y \geq 7000[/tex]
[tex]2x + 5y < 1000[/tex]

C.
[tex]x^2 - 2y > 7000[/tex]
[tex]2x + 5y \leq 1000[/tex]

D.
[tex]x^2 - 2y \leq 7000[/tex]
[tex]2x + 5y \leq 1000[/tex]

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the first inequality equation be represented as A

Let the second inequality equation be represented as B

Now , value of a company’s stock is represented by the expression x² - 2y

And , company’s goal is to maintain a stock value of at least $ 7,000

So , the inequality is x² - 2y ≥ 7000

And , the company’s purchases are modeled by 2x + 5y

Also , the company's purchases should be below $ 1,000

So , the inequality is 2x + 5y < 1000

Hence , the inequalities are solved

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