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Burka [1]
3 years ago
8

Explain why the triangles are similar. Then find the value of x.

Mathematics
1 answer:
djyliett [7]3 years ago
8 0
Answer: Choice A) AA postulate; 18

---------------------------------------------------------------------------------------

Work Shown:

The triangles are similar to each other due to the AA (angle angle) postulate. The top angles are overlapping or shared angles. So that's the first pair. The second pair of angles is either bottom pair of angles, from the fact that corresponding angles are congruent. This is only true if the lines are parallel.

Due to the similar triangles, we can set up the proportion and solve for x
8/(8+4) = 12/x
8/12 = 12/x
8*x = 12*12 ... cross multiply
8x = 144
x = 144/8
x = 18

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Number\ is\ divisible\ by\ 3\ if\ the\ sum\ of\ the\ digits\ is\ divisible\ by\ 3.\\\\8,264\\\\8+2+6+4=20-
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7 0
3 years ago
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Solve 3x + 23 + x = 7. x = −4 x = 4 x = −0.25 x = 0.25
Maksim231197 [3]
<h2>______________________________</h2><h2>Solve for x | Solution and Explanation </h2>

______________________________________________

Hello! So...

We are given the following:

Solve for x.

3x+23+x=7

====================

1. Group the like terms.

  • 3x+x+23=7

====================

2. Add similar elements (3x+x=4x).

  • 4x+23=7

====================

3. Subtract 23 from both sides.

  • 4x + 23 - 23 = 7 - 23

====================

4. Simplify.

  • 4x=-16

====================

5. Divide both sides by 4.

  • \frac{4x}{4} =\frac{-16}{4}

====================

6. Simplify.

  • x=-4 (aka. Option A)

====================

Hope this helps!

3 0
1 year ago
How much money should be deposited today in an account that earns 6% compounded monthly so that it will accumulate to $1000000 (
aleksandr82 [10.1K]

Answer:

The principal investment required to get  a total amount of $ 1,000,000.00  from compound interest at a rate of 6% per year  compounded 12 times per year  over 45 years  is $ 67,659.17.

Step-by-step explanation:

Given

  • Accrued Amount A = $1000000
  • Interest rate r = 6% = 0.06
  • Time period t = 45 years
  • Compounded monthly n = 12

To determine:

  • Principle amount P = ?

Using the formula

A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}

P\:=\frac{A}{\left(1\:+\:\frac{r}{n}\right)^{nt}}

substituting A = 1000000, r =  0.06, t = 45, and n = 12

P\:=\frac{1000000}{\left(1\:+\:\frac{0.06}{12}\right)^{12\cdot 45}}\:

    =\frac{1000000}{1.005^{540}}

P = 67659.17 $

Therefore, the principal investment required to get  a total amount of $ 1,000,000.00  from compound interest at a rate of 6% per year  compounded 12 times per year  over 45 years  is $ 67,659.17.

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Answer:

Step-by-step explanation:

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