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A carpenter is building a rectangular table. He wants the perimeter of the tabletop to be no more than 28 feet. He also wants the length of the tabletop to be greater than or equal to the square of 2 feet less than its width.
Create a system of inequalities to model the situation, where x represents the width of the tabletop and y represents the length of the tabletop. Then, use this system of inequalities to determine the viable solutions.

A. Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
B. No part of the solution region is viable because the length and width cannot be negative.
C. The entire solution region is viable.
D. Part of the solution region includes a negative length; therefore, not all solutions are viable for the given situation.

Respuesta :

MrRoyal

The solution from the system of inequalities is (a). Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.

The system of inequality

Let P represent the perimeter.

So, we have:

  • P ≤ 28 ---- i.e. perimeter not more than 28
  • y ≥ (x - 2)²

The perimeter is calculated using:

P = 2(x + y)

So, we have:

2(x + y) ≤ 28

y ≥ (x - 2)²

Next, we plot the system of inequalities (see attachment)

From the attached graph, we have some negative x values in the shaded region.

This means that not all solutions are viable

Hence, the true statement is (a)

Read more about inequalities at:

https://brainly.com/question/25275758

#SPJ1

Ver imagen MrRoyal

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