Mr. Jones needs to build a rectangular fence in his backyard to keep their dog safe. The length of the fence (y) 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?
Let's assume that the length of the fence is represented by "y" and the width of the fence is represented by "x".
According to the given information:
1) The length of the fence (y) should be at least 60 ft, which can be represented as: y >= 60
2) The distance around the fence should be no more than 260 ft, which can be represented as: 2x + 2y <= 260 (since the distance around the rectangle is equal to the sum of the lengths of all four sides of the rectangle)
So, the system of inequalities representing the possible dimensions of the pen is:
y >= 60
2x + 2y <= 260
To graph this system of inequalities, we need to plot the two equations on the coordinate plane.
The inequality y >= 60 represents a horizontal line passing through (0, 60) with a slope of 0 and shaded towards the positive y-axis.
The inequality 2x + 2y <= 260 can be rearranged as x + y <= 130, which represents a line passing through (130, 0) with a slope of -1 and shaded below the line.
The graph of the system of inequalities would look like this:
*[illustration rectangular_fence_graph.png]