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alex41 [277]
2 years ago
13

The three lines given below form a triangle. Find the coordinates of the vertices of the triangle.

Mathematics
1 answer:
LenKa [72]2 years ago
8 0

Answer:

  • (3, 5), (1, 2) and (5, 1)

Step-by-step explanation:

Make three systems with pairs of lines and solve them to work out the vertices.

1) <u>Line 1 and line 2</u>

  • -3x + 2y = 1
  • 2x + y = 11

<u>Double the second equation and subtract equations:</u>

  • -3x + 2y - 2(2x + y) = 1 - 2(11)
  • -3x - 4x = 1 - 22
  • -7x = - 21
  • x = 3

<u>Find y:</u>

  • 2*3 + y = 11
  • 6 + y = 11
  • y = 11 - 6
  • y = 5

The point is (3, 5)

2) <u>Line 1 and line 3</u>

  • -3x + 2y = 1
  • x + 4y = 9

<u>Triple the second equation and add up equations:</u>

  • -3x + 2y + 3(x + 4y) = 1 + 3(9)
  • 2y + 12y = 1 + 27
  • 14y = 28
  • y = 2

<u>Find x:</u>

  • x + 4*2 = 9
  • x + 8 = 9
  • x = 1

The point is (1, 2)

3) <u>Line 2 and line 3</u>

  • 2x + y = 11
  • x + 4y = 9

<u>Double the second equation and subtract the equations:</u>

  • 2x + y - 2(x + 4y) = 11 - 2(9)
  • y - 8y = 11 - 18
  • - 7y = - 7
  • y = 1

<u>Find x:</u>

  • x + 4*1 = 9
  • x + 4 = 9
  • x = 5

The point is (5, 1)

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Answer:

Mixed number - 2 8/15

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Step-by-step explanation:

3+9+26=38

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38/15 convert to a mixed number =

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Refer to the diagram shown below.

The volume of the container is 10 m³, therefore
x*2x*h = 10
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h = 5/x²        (1)

The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
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The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
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The minimum cost is determined by C' = 0.
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x³ = 180/40 = 4.5
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The second derivative of C is
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The total cost is
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Answer: $163.54

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Answer:

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Step-by-step explanation:

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x^{2} +8x+16 = 38 + 16

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x + 4 = \sqrt{54} or x + 4 = -\sqrt{54}

x+4=3\sqrt{6} or x+4=-3\sqrt{6}

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Therefore, a = -4, b = 3 and c = 6 (OR)

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Answer:

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