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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]2x + 5y[/tex]. The company's goal is to maintain a stock value of at least [tex]7000[/tex] while keeping the purchases below [tex]1000[/tex].

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]

To solve the problem, we need to model the company's goals using a system of inequalities. Here's how we can do this step-by-step:

1. Understanding the Stock Value Expression:
- The company's stock value is expressed as [tex]$x^2 - 2y$[/tex].
- The company wants this value to be at least [tex]$7,000.
- This condition can be written as the inequality: $x^2 - 2y \geq 7000$.

2. Understanding the Purchases Expression:
- The company's purchases are represented by $2x + 5y$.
- The goal is to keep these purchases below $[/tex]1,000.
- This condition can be expressed as: [tex]$2x + 5y < 1000$[/tex].

So, combining these two conditions, we create a system of inequalities that represents the scenario:

- First inequality: [tex]$x^2 - 2y \geq 7000$[/tex] (which ensures the stock value is at least [tex]$7,000).
- Second inequality: $2x + 5y < 1000$ (which ensures the purchases remain below $[/tex]1,000).

This system of inequalities accurately models the company's goals as described in the problem.