To find the system of inequalities and graph representing the possible dimensions of the pen, we need to consider the given conditions.
The length of the pen should be at least 60 ft, which can be represented by the inequality: y ≥ 60.
The distance around the pen should be no more than 260 ft. Since the fence consists of four sides, the perimeter can be found using the formula: Perimeter = 2(length + width).
We can rewrite this formula as: length + width ≤ Perimeter/2.
In this case, Perimeter = 260 ft, so the inequality becomes: length + width ≤ 260/2.
Simplifying further, we have: length + width ≤ 130.
Combining both inequalities, the system of inequalities representing the possible dimensions of the pen is:
y ≥ 60 (to satisfy the minimum length condition)
length + width ≤ 130 (to satisfy the perimeter condition)
Now, let's graph these inequalities on a coordinate plane.
Label the x-axis as "Width" and the y-axis as "Length".
Graph a solid horizontal boundary line at y = 60 and shade above it to represent the inequality y ≥ 60.
Graph the line length + width = 130. This line passes through the points (0, 130) and (130, 0), and shade below it to represent the inequality length + width ≤ 130.
The overlapping shaded region between the two lines represents the possible dimensions of the pen.
So, the correct response is:
One quadrant of a coordinate plane is shown.
The y-axis is numbered from 0 to 140 and has a step size of 20. It is labeled Length.
The x-axis is numbered from 0 to 140 and has a step size of 20. It is labeled Width.
Two lines intersect on the coordinate plane. The first line goes from (0, 130) to (130, 0). The second line goes through the points (0, 60) and (0, 150). The coordinate plane is shaded above the first line and below the second line.