<div>Joe wants to fence a rectangular pen for his goats. The length of the pen should be at least 60 ft, and the distance around should be no more than 260 ft. Which system of inequalities and graph represent the possible dimensions of the pen?</div>
Let's assume the length of the pen is x feet and the width of the pen is y feet.
Based on the given information, we can set up the following system of inequalities:
1) Length of the pen should be at least 60 ft: x ≥ 60
2) Distance around the pen should be no more than 260 ft: 2(x + y) ≤ 260
To graph this system of inequalities, we can start by graphing the first inequality, x ≥ 60:
The line x = 60 represents all the possible lengths greater than or equal to 60 ft. We can draw a vertical line at x = 60.
Next, let's graph the second inequality, 2(x + y) ≤ 260:
Divide both sides of the inequality by 2, we get:
x + y ≤ 130
The line x + y = 130 represents all possible values that make the sum of x and y less than or equal to 130. We can draw a diagonal line from (0, 130) to (130, 0).
Now, let's shade the feasible region. The feasible region is the region that satisfies both inequalities. In this case, the feasible region is below the line x + y = 130 and to the right of the line x = 60.
The graph of the system of inequalities and the feasible region would look like this:
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60 130
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So, the graph above represents the possible dimensions of the rectangular pen.