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rusak2 [61]
2 years ago
5

Please help me with the questions

Mathematics
1 answer:
Grace [21]2 years ago
4 0

Answer:

x = 5

x = 2

Step-by-step explanation:

2(2x + 4) = 8x - 12

2x + 4 = 4x - 6

x + 2 = 2x - 3

x = 5

Question 17

8/4 = (x + 2)/(2x - 2)

2(2x - 2) = x + 2

4x - 4 = x + 2

3x = 6

x = 2

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2 years ago
Rob is a geologist. He is surveying a conical crater that was created by a meteor impact. From one end to another, the crater fo
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Answer:

  • equation: d(h) = 0.25|h -1600| -400
  • depth is 250 ft at 1000 ft and 2200 ft from the west edge

Step-by-step explanation:

The crater shape can be modeled by an absolute value function with a slope of 0.25. The vertex of the function will not be at (0, 0) but will be at (1600, -400). The usual methods of translating functions apply. Horizontal displacement of the vertex is subtracted from the independent variable; vertical displacement is added to the function value.

  d(h) = 0.25×|h -1600| -400

We know the horizontal displacement is 1600 ft, because the depth changes at a rate of 1/4 foot for each horizontal foot. A depth change of 400 feet will require 1600 horizontal feet to accomplish.

__

At a depth of 250 ft, the distance from the west edge can be found from ...

  -250 = 0.25|h -1600| -400

  150 = 0.25|h -1600| . . . . . . . . add 400

  600 = |h -1600| . . . . . . . . . . . multiply by 4

This resolves to two equations:

  • -600 = h -1600   ⇒   h = 1000
  • 600 = h -1600   ⇒   h = 2200

The depth is 250 ft at distances of 1000 ft and 2200 ft from the west edge.

_____

<em>Comment on the equation</em>

We have chosen to make depths be negative numbers. If you want the equation to give positive numbers for depth, multiply it by -1:

  d = 400 -0.25×|h -1600|

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