Simplify the expression below.
1 answer:
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Step 1) Draw a dashed line through the points (0,6) and (4,7). These two points are on the line y = (1/4)x+6. To find those points, you plug in x = 0 to get y = 6. Similarly, plug in x = 4 to get y = 7. The dashed line indicates that none of the points on this line are part of the solution set.
Step 2) Draw a dashed line through (0,-1) and (1,1). These two points are on the line y = 2x-1. They are found in a similar fashion as done in step 1.
Step 3) Shade the region that is above both dashed lines. We shade above because of the "greater than" sign. This is shown in the attached image I am providing below. The red shaded region represents all of the possible points that are the solution set. Once again, any point on the dashed line is not in the solution set.
Step 2) Draw a dashed line through (0,-1) and (1,1). These two points are on the line y = 2x-1. They are found in a similar fashion as done in step 1.
Step 3) Shade the region that is above both dashed lines. We shade above because of the "greater than" sign. This is shown in the attached image I am providing below. The red shaded region represents all of the possible points that are the solution set. Once again, any point on the dashed line is not in the solution set.
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Answer:
7. d. l = 6.48 cm, w = 6.48 cm
8. d. square
Step-by-step explanation:
For a given area, the perimeter can always be shortened by reducing the length of the long side and increasing the length of the short side. When you get to the point where you can't do that, then you have the minimum perimeter. You will reach that point when the sides are the same length: the rectangle is a square.
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7. In light of the above, the best dimensions are √42 ≈ 6.48 cm for length and width.
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8. In light of the above, the shape is a square.
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The attached graph shows the length of one side (x) and the associated perimeter. The other side is 42/x, which will also be 6.48.
