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Naddika [18.5K]
3 years ago
14

(25 points!!!!) draw the graph of the area bounded by these inequalities

Mathematics
1 answer:
Stels [109]3 years ago
3 0

Step-by-step explanation:

To draw the graph, follow these steps:

  1. Graph the lines using points from the equations. (the blue line shown should be dotted, unfortunately I cannot do that in the program I used)
  2. Determine which direction the inequalities are correct.  
  3. Find the boundary given.

The three inequalities given form a triangle.

The first equation, y ≤ 2x + 5, has a y-intercept at (0, 5) and a point at (-2, 1).

The second equation, y < -3x + 10, has points at (3, 1) and (2, 4).

Use two points to draw the lines.

After the lines are drawn, determine which side of the line the inequality works on. You can do this by testing points that are not on the line.

I will test each inequality using (0, 1):

y ≤ 2x + 5

0 ≤ 2 + 5

<em>This is correct</em>, so the inequality for y ≤ 2x + 5 will be shaded towards (0, 1).

y < -3x + 10

0 < -3 + 10

<em>This is correct,</em> so the inequality for y < -3x + 10 will be shaded towards (0, 1).

0 ≤ 1

<em>This is correct</em>, so the inequality for 0 ≤ y will be shaded upwards towards (0, 1).

The end result of this graph is all three inequalities being shaded (inwards).

The solution is a triangle with points at (1, 7), (3.33333, 0), and (-2.5, 0).

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Formula for Perimeter of Rectangle:

P = 2(L + W)

Plug in 160:

160 = 2(L + W)

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<span>So we can plug in '4W' for 'L' in the first equation.</span>
<span>160 = 2(L + W)

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Combine like terms:

160 = 2(5W)

160 = 10W

Divide 10 to both sides:

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Now we can plug this back into any of the two equations to find the length.

L = 4W

L = 4(16)

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So the width is 16, and the length is 64.</span>
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