Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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 :

GinnyAnswer
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.
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.