The system of inequalities that models the possible dimensions of the garden is as follows:
Let L be the length of the garden and W be the width of the garden.
1. Length should be at least 110 ft: L ≥ 110
2. Distance around the garden should be no more than 380 ft: 2L + 2W ≤ 380
Therefore, the system of inequalities is:
L ≥ 110
2L + 2W ≤ 380
The graph is similar to option c.
A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft, and the distance around should be no more than 380 ft. Write a system of inequalities that models the possible dimensions of the garden. Graph the system to show all possible solutions.
(1 point)
Responses
a
The y-axis is labeled Length and is numbered from 0 to 300 with a step size of 100. The x-axis is labeled Width and is numbered from 0 to 200 with a step size of 100. A line starts at just below left-parenthesis 0 comma 200 right-parenthesis and goes through just to the left of left-parenthesis 200 comma 0 right-parenthesis. A second line starts at left-parenthesis 0 comma 110 right-parenthesis and goes through left-parenthesis 250 comma 110 right-parenthesis. The graph is shaded below the first line and above the second line.
Image with alt text: a The y-axis is labeled Length and is numbered from 0 to 300 with a step size of 100. The x-axis is labeled Width and is numbered from 0 to 200 with a step size of 100. A line starts at just below left-parenthesis 0 comma 200 right-parenthesis and goes through just to the left of left-parenthesis 200 comma 0 right-parenthesis. A second line starts at left-parenthesis 0 comma 110 right-parenthesis and goes through left-parenthesis 250 comma 110 right-parenthesis. The graph is shaded below the first line and above the second line.
bThe y-axis is labeled Length and is numbered from 0 to 300 with a step size of 100. The x-axis is labeled Width and is numbered from 0 to 200 with a step size of 100. A line starts at just below left-parenthesis 0 comma 200 right-parenthesis and goes through just to the left of left-parenthesis 200 comma 0 right-parenthesis. A second line starts at left-parenthesis 0 comma 110 right-parenthesis and goes through left-parenthesis 250 comma 110 right-parenthesis. The graph is shaded to the right of the first line and above the second line.
Image with alt text: b The y-axis is labeled Length and is numbered from 0 to 300 with a step size of 100. The x-axis is labeled Width and is numbered from 0 to 200 with a step size of 100. A line starts at just below left-parenthesis 0 comma 200 right-parenthesis and goes through just to the left of left-parenthesis 200 comma 0 right-parenthesis. A second line starts at left-parenthesis 0 comma 110 right-parenthesis and goes through left-parenthesis 250 comma 110 right-parenthesis. The graph is shaded to the right of the first line and above the second line.
cThe x-axis is labeled Width and is numbered from 0 to 200 with a step size of 100. The y-axis is labeled Length and is numbered from 0 to 300 with a step size of 100. A line starts at just below left-parenthesis 0 comma 200 right-parenthesis and goes through just to the left of left-parenthesis 200 comma 0 right-parenthesis. A second line starts at left-parenthesis 0 comma 110 right-parenthesis and goes through left-parenthesis 250 comma 110 right-parenthesis. The graph is shaded below the second line and to the left of the first line.
Image with alt text: c The x-axis is labeled Width and is numbered from 0 to 200 with a step size of 100. The y-axis is labeled Length and is numbered from 0 to 300 with a step size of 100. A line starts at just below left-parenthesis 0 comma 200 right-parenthesis and goes through just to the left of left-parenthesis 200 comma 0 right-parenthesis. A second line starts at left-parenthesis 0 comma 110 right-parenthesis and goes through left-parenthesis 250 comma 110 right-parenthesis. The graph is shaded below the second line and to the left of the first line.
dThe y-axis is labeled Length and is numbered from 0 to 300 with a step size of 100. The x-axis is labeled Width and is numbered from 0 to 200 with a step size of 100. A line starts at just below left-parenthesis 0 comma 200 right-parenthesis and goes through just to the left of left-parenthesis 200 comma 0 right-parenthesis. A second line starts at left-parenthesis 0 comma 110 right-parenthesis and goes through left-parenthesis 250 comma 110 right-parenthesis. The graph is below the second line and to the right of the first line.
Image with alt text: d The y-axis is labeled Length and is numbered from 0 to 300 with a step size of 100. The x-axis is labeled Width and is numbered from 0 to 200 with a step size of 100. A line starts at just below left-parenthesis 0 comma 200 right-parenthesis and goes through just to the left of left-parenthesis 200 comma 0 right-parenthesis. A second line starts at left-parenthesis 0 comma 110 right-parenthesis and goes through left-parenthesis 250 comma 110 right-parenthesis. The graph is below the second line and to the right of the first line.
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