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? (1 point) Responses 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 left-parenthesis 0 comma 130 right-parenthesis to left-parenthesis 130 comma 0 right-parenthesis. The second line goes through the points left-parenthesis 0 comma 60 right-parenthesis and left-parenthesis 0 comma 150 right-parenthesis. The coordinate plane is shaded to the left of the first line and above the second line. Image with alt text: y is greater than or equal to 60. 2x plus 2y is less than or equal to 260. The first quadrant of a coordinate plane with the x axis labeled Width and the y axis labeled Length. A solid horizontal boundary line is graphed through the point (0, 60) and shaded above the boundary line. A second solid boundary line passes through the points (0, 130) and (130, 0) and is shaded below the boundary line. The overlapping shaded region includes the points (0, 80), (20, 80), (40, 80). 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 left-parenthesis 0 comma 130 right-parenthesis to left-parenthesis 130 comma 0 right-parenthesis. The second line goes through the points left-parenthesis 0 comma 60 right-parenthesis and left-parenthesis 0 comma 150 right-parenthesis. The coordinate plane is shaded to the left of the first line and above the second line. The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y less than or equal to 60; this is graphed as a horizontal line at y = 60. The second inequality is 2 x plus 2 y less than or equal to 260; this is graphed as a line that goes roughly from left parenthesis 0 comma 130 right parenthesis to left parenthesis 130 comma 0 right parenthesis. The area below (but not between) the two lines is shaded. Image with alt text: y is less than or equal to 60. 2x plus 2y is less than or equal to 260. The first quadrant of a coordinate plane with the x axis labeled Width and the y axis labeled Length. A solid horizontal boundary line is graphed through the point (0, 60) and is shaded below the boundary line. A second solid boundary line passes through the points (0, 130) and (130, 0) and is shaded below the boundary line. The overlapping shaded region includes the points (0, 40), (20, 20), (60, 50). The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y less than or equal to 60; this is graphed as a horizontal line at y = 60. The second inequality is 2 x plus 2 y less than or equal to 260; this is graphed as a line that goes roughly from left parenthesis 0 comma 130 right parenthesis to left parenthesis 130 comma 0 right parenthesis. The area below (but not between) the two lines is shaded. 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 left-parenthesis 0 comma 130 right-parenthesis to left-parenthesis 130 comma 0 right-parenthesis. The second line goes through the points left-parenthesis 0 comma 60 right-parenthesis and left-parenthesis 0 comma 150 right-parenthesis. The coordinate plane is shaded to the right of the first line and above the second line. Image with alt text: y is greater than or equal to 60. 2x plus 2y is greater than 260. The first quadrant of a coordinate plane with the x axis labeled Width and the y axis labeled Length. A solid horizontal boundary line is graphed through the point (0, 60) and is shaded above the boundary line. A second solid boundary line passes through the points (0, 130) and (130, 0) and is shaded above the boundary line. The overlapping shaded region includes the points (0, 130), (60, 100), (80, 120). 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 left-parenthesis 0 comma 130 right-parenthesis to left-parenthesis 130 comma 0 right-parenthesis. The second line goes through the points left-parenthesis 0 comma 60 right-parenthesis and left-parenthesis 0 comma 150 right-parenthesis. The coordinate plane is shaded to the right of the first line and above the second line. The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y less than or equal to 60; this is graphed as a horizontal line at y = 60. The second inequality is 2 x plus 2 y greater than or equal to 260; this is graphed as a line that goes roughly from left parenthesis 0 comma 130 right parenthesis to left parenthesis 130 comma 0 right parenthesis. To the right of where the two lines intersect, the area between them is shaded. Image with alt text: y is less than 60. 2x plus 2y is greater than or equal to 260. The first quadrant of a coordinate plane with the x axis labeled Width and the y axis labeled Length. A solid horizontal boundary line is graphed through the point (0, 60) and is shaded below the boundary line. A second solid boundary line passes through the points (0, 130) and (130, 0) and is shaded above the boundary line. The overlapping shaded region includes the points (100, 40), (120, 40), (130, 50). The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y less than or equal to 60; this is graphed as a horizontal line at y = 60. The second inequality is 2 x plus 2 y greater than or equal to 260; this is graphed as a line that goes roughly from left parenthesis 0 comma 130 right parenthesis to left parenthesis 130 comma 0 right parenthesis. To the right of where the two lines intersect, the area between them is shaded.

Question

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? (1 point) Responses 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 left-parenthesis 0 comma 130 right-parenthesis to left-parenthesis 130 comma 0 right-parenthesis. The second line goes through the points left-parenthesis 0 comma 60 right-parenthesis and left-parenthesis 0 comma 150 right-parenthesis. The coordinate plane is shaded to the left of the first line and above the second line. Image with alt text: y is greater than or equal to 60. 2x plus 2y is less than or equal to 260. The first quadrant of a coordinate plane with the x axis labeled Width and the y axis labeled Length. A solid horizontal boundary line is graphed through the point (0, 60) and shaded above the boundary line. A second solid boundary line passes through the points (0, 130) and (130, 0) and is shaded below the boundary line. The overlapping shaded region includes the points (0, 80), (20, 80), (40, 80). 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 left-parenthesis 0 comma 130 right-parenthesis to left-parenthesis 130 comma 0 right-parenthesis. The second line goes through the points left-parenthesis 0 comma 60 right-parenthesis and left-parenthesis 0 comma 150 right-parenthesis. The coordinate plane is shaded to the left of the first line and above the second line. The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y less than or equal to 60; this is graphed as a horizontal line at y = 60. The second inequality is 2 x plus 2 y less than or equal to 260; this is graphed as a line that goes roughly from left parenthesis 0 comma 130 right parenthesis to left parenthesis 130 comma 0 right parenthesis. The area below (but not between) the two lines is shaded. Image with alt text: y is less than or equal to 60. 2x plus 2y is less than or equal to 260. The first quadrant of a coordinate plane with the x axis labeled Width and the y axis labeled Length. A solid horizontal boundary line is graphed through the point (0, 60) and is shaded below the boundary line. A second solid boundary line passes through the points (0, 130) and (130, 0) and is shaded below the boundary line. The overlapping shaded region includes the points (0, 40), (20, 20), (60, 50). The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y less than or equal to 60; this is graphed as a horizontal line at y = 60. The second inequality is 2 x plus 2 y less than or equal to 260; this is graphed as a line that goes roughly from left parenthesis 0 comma 130 right parenthesis to left parenthesis 130 comma 0 right parenthesis. The area below (but not between) the two lines is shaded. 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 left-parenthesis 0 comma 130 right-parenthesis to left-parenthesis 130 comma 0 right-parenthesis. The second line goes through the points left-parenthesis 0 comma 60 right-parenthesis and left-parenthesis 0 comma 150 right-parenthesis. The coordinate plane is shaded to the right of the first line and above the second line. Image with alt text: y is greater than or equal to 60. 2x plus 2y is greater than 260. The first quadrant of a coordinate plane with the x axis labeled Width and the y axis labeled Length. A solid horizontal boundary line is graphed through the point (0, 60) and is shaded above the boundary line. A second solid boundary line passes through the points (0, 130) and (130, 0) and is shaded above the boundary line. The overlapping shaded region includes the points (0, 130), (60, 100), (80, 120). 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 left-parenthesis 0 comma 130 right-parenthesis to left-parenthesis 130 comma 0 right-parenthesis. The second line goes through the points left-parenthesis 0 comma 60 right-parenthesis and left-parenthesis 0 comma 150 right-parenthesis. The coordinate plane is shaded to the right of the first line and above the second line. The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y less than or equal to 60; this is graphed as a horizontal line at y = 60. The second inequality is 2 x plus 2 y greater than or equal to 260; this is graphed as a line that goes roughly from left parenthesis 0 comma 130 right parenthesis to left parenthesis 130 comma 0 right parenthesis. To the right of where the two lines intersect, the area between them is shaded. Image with alt text: y is less than 60. 2x plus 2y is greater than or equal to 260. The first quadrant of a coordinate plane with the x axis labeled Width and the y axis labeled Length. A solid horizontal boundary line is graphed through the point (0, 60) and is shaded below the boundary line. A second solid boundary line passes through the points (0, 130) and (130, 0) and is shaded above the boundary line. The overlapping shaded region includes the points (100, 40), (120, 40), (130, 50). The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y less than or equal to 60; this is graphed as a horizontal line at y = 60. The second inequality is 2 x plus 2 y greater than or equal to 260; this is graphed as a line that goes roughly from left parenthesis 0 comma 130 right parenthesis to left parenthesis 130 comma 0 right parenthesis. To the right of where the two lines intersect, the area between them is shaded.

Answer 1

The correct answer 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 to the left of the first line and above the second line. The x-axis is labeled Width; the y-axis is labeled Length. The first inequality is y is greater than or equal to 60. The second inequality is 2x + 2y is less than or equal to 260.

Answer 2

The correct answer 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 to the left of the first line and above the second line.

The correct system of inequalities is:

y ≥ 60
2x + 2y ≤ 260

Answer 3

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.