College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Select the correct answer.

A construction company is analyzing which of its older projects need renovation. Building B was built two years before building C. Building D was built two years before building B. The product of building B's age and building D's age is at least 195. If [tex]x[/tex] represents the age of building C, which inequality represents this situation?

A. [tex]x^2 + 6x + 8 \geq 195[/tex]
B. [tex]z^2 + 8z + 16 \geq 195[/tex]
C. [tex]x^2 + 4 \geq 195[/tex]
D. [tex]x^2 + 4x + 4 \geq 195[/tex]

Answer :

To solve this problem, we need to represent the age relationships between the buildings with an inequality. Let's break it down step by step.

1. Variables and Relationships:
- Let [tex]\( x \)[/tex] be the age of building C.
- Building B was built 2 years before building C. Therefore, the age of building B is [tex]\( x + 2 \)[/tex].
- Building D was built 2 years before building B. Thus, the age of building D is [tex]\( (x + 2) + 2 = x + 4 \)[/tex].

2. Product of Ages:
- The product of the ages of building B and building D must be at least 195. This gives us the inequality:
[tex]\[
(x + 2)(x + 4) \geq 195
\][/tex]

3. Expand and Simplify:
- To simplify the inequality, we first expand the product on the left-hand side:
[tex]\[
(x + 2)(x + 4) = x^2 + 4x + 2x + 8
\][/tex]
Combine like terms:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]

4. Form the Inequality:
- The final inequality that represents the situation is:
[tex]\[
x^2 + 6x + 8 \geq 195
\][/tex]

Therefore, the correct inequality is
[tex]\[
\boxed{x^2 + 6x + 8 \geq 195}
\][/tex]

This corresponds to option A.