College

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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 [tex]C[/tex], which inequality represents this situation?

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

Answer :

Let's analyze the given problem step-by-step. We are asked to determine an inequality that represents the ages of the buildings under the given conditions.

1. Age Definitions:
- Let [tex]\( x \)[/tex] represent the age of Building C.
- Building B was built 2 years before Building C, so the age of Building B is [tex]\( x - 2 \)[/tex].
- Building D was built 2 years before Building B, so the age of Building D is [tex]\( (x - 2) - 2 \)[/tex], which simplifies to [tex]\( x - 4 \)[/tex].

2. Age Products:
- We are given the condition that the product of the ages of Building B and Building D is at least 195. This can be expressed as:
[tex]\[
\text{Age of Building B} \times \text{Age of Building D} \geq 195
\][/tex]
- Substituting the ages we defined:
[tex]\[
(x - 2) \times (x - 4) \geq 195
\][/tex]

3. Expanding the Product:
- We need to expand the left-hand side of the inequality:
[tex]\[
(x - 2)(x - 4)
\][/tex]
- Using the distributive property (FOIL method):
[tex]\[
x(x - 4) - 2(x - 4)
\][/tex]
[tex]\[
= x^2 - 4x - 2x + 8
\][/tex]
[tex]\[
= x^2 - 6x + 8
\][/tex]

4. Inequality Formation:
- We then substitute back into the inequality:
[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]
- To standardize the form, we move 195 to the left-hand side to simplify further:
[tex]\[
x^2 - 6x + 8 - 195 \geq 0
\][/tex]
[tex]\[
x^2 - 6x - 187 \geq 0
\][/tex]

Since we need to match the original form provided in the options, the inequality directly before simplifying with the 195 on the right-hand side is:

[tex]\[
x^2 - 6x + 8 \geq 195
\][/tex]

This corresponds to:

- C. [tex]\( x^2 - 6x + 8 \geq 195 \)[/tex]

Thus, the appropriate inequality that represents this situation is:

C. [tex]\( x^2 - 6x + 8 \geq 195 \)[/tex]

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada