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Over [174]
2 years ago
12

In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.

Mathematics
1 answer:
krek1111 [17]2 years ago
8 0

Answer:

AC = 14 sqrt(2) = 19.80    

Step-by-step explanation:

Below is the diagram showing you how this has been set up. The figure is a trapezoid which means BC and AD are parallel. AC is a transversal of the parallel lines.

Givens

  • <ABC = <ACD                          
  • ABCD  is a trapezoid
  • BC = 14
  • AD = 28
  • AC is a transversal of BC and AD

Solution

  • <ABC = <ACD                Given
  • <DAC = <ACB                Alternate interior angles.
  • ΔACB ≅ΔDAC               AA
  • <BAC = <ADC                Angles of similar triangles are equal
  • AC /28 = 14/AC              Form a proportion from corresponding sides
  • AC*AC = 14 * 28             Cross multiply the proportion. Combine
  • AC^2 = 392                    Express as prime factors.
  • AC^2 = 7*7*2*2*2           Take the square root of both sides
  • sqrt(AC)^2 = sqrt(7*7*2*2*2)
  • AC = 7*2 * sqrt(2)
  • AC = 14 sqrt(2) = 19.80    

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3 years ago
What is the slope of the line that passes through the point (-9,8) and (-3-1)?
natulia [17]

Answer:

Step-by-step explanation:

(x₁, y₁) = (-9 ,8)   and (x₂ , y₂) = (-3 , -1)

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2 years ago
Which ordered pair is the solution to the system of equations? {x+3y=-12, y= 1/3x-6?
Julli [10]

For this, I'll be using the substitution method. Since y = 1/3x - 6, replace the y variable in the first equation with 1/3x - 6 and solve for x:

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Now that we have the value of x, plug it into either equation to solve for y:

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denpristay [2]
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Tasya [4]

Answer:

Natasha gets 84

Step-by-step explanation:

Here, we want to know how much Natasha gets

Krutika gets 2 times as much as Natasha

If Natasha gets x, Krutika gets 2x

If Natasha gets x, Richard will get x/3 ( 3 times of this is what Natasha gets)

Now let us have a ratio;

K : N : R

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To get the amount Natasha gets, we add up all ratio; (6x + 3x + x ) = 10x

Natasha gets 3x of the total ratio

That will be;

3x /10x * 280

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= 84

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3 years ago
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