Answered

Ask questions, share knowledge, and connect with a vibrant community on IDNLearn.com. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.

The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters. Which system of inequalities represents the possible length in meters, [tex]\( l \)[/tex], and the possible width in meters, [tex]\( w \)[/tex], of the pool?

[tex]\[
\begin{aligned}
l + 2w & \geq 62 \\
w & \geq 10
\end{aligned}
\][/tex]

(Note: The original text had some repeated and incorrect inequalities. The corrected system of inequalities represents the conditions provided in the question.)

Sagot :

GinnyAnsweridn
Let's break down and solve the inequalities step-by-step to find the constraints on [tex]\( w \)[/tex] (the width of the rectangular pool). We are given the following system of inequalities:

1. [tex]\( w \leq 10 - 1 \)[/tex]
2. [tex]\( 21 + 2w \geq 62 \)[/tex]

First, let's solve each inequality individually.

Step 1: Solve [tex]\( w \leq 10 - 1 \)[/tex]

[tex]\[ w \leq 9 \][/tex]

So, the first constraint is [tex]\( w \leq 9 \)[/tex].

Step 2: Solve [tex]\( 21 + 2w \geq 62 \)[/tex]

First, isolate the term involving [tex]\( w \)[/tex]:

[tex]\[ 2w \geq 62 - 21 \][/tex]
[tex]\[ 2w \geq 41 \][/tex]

Next, solve for [tex]\( w \)[/tex] by dividing both sides by 2:

[tex]\[ w \geq \frac{41}{2} \][/tex]
[tex]\[ w \geq 20.5 \][/tex]

So, the second constraint is [tex]\( w \geq 20.5 \)[/tex].

Combining the Results:

We need [tex]\( w \leq 9 \)[/tex] and [tex]\( w \geq 20.5 \)[/tex] to hold simultaneously. However, examining these two inequalities shows that there are no values of [tex]\( w \)[/tex] that can simultaneously satisfy [tex]\( w \leq 9 \)[/tex] and [tex]\( w \geq 20.5 \)[/tex]. Hence, there is no range of [tex]\( w \)[/tex] values that satisfy both conditions together.

This inconsistency means that within the context of these constraints, there are no possible values for [tex]\( w \)[/tex] that can describe the width of the rectangular pool.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.