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Fiesta28 [93]
3 years ago
5

Given: △ABC, E∈ AB m∠ABC=m∠ACE AB=34, AC=20 Find: AE

Mathematics
1 answer:
LenaWriter [7]3 years ago
4 0

Answer:

AE = 11.76 units

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

Given : E ∈ AB, m∠ABC = m∠ACE, AB = 34 and AC = 20

To find AE :

In ΔABC and ΔACE,

m∠ABC = m∠ACE ( Given )

∠A = ∠A    ( Common angle for both the triangles )

By AA postulate of similarity of triangles, ΔABC ~ ΔACE

So, proportion of the corresponding will be equal.

\implies \frac{AC}{AB}=\frac{CE}{BC}=\frac{AE}{AC}\\\\\implies\frac{AC}{AB}=\frac{AE}{AC}\\\\\implies\frac{20}{34}=\frac{AE}{20}\\\\\implies AE=\frac{20\times 20}{34}\approx 11.76

Hence, AE = 11.76 units

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What is the radius of the cone?
gayaneshka [121]

Answer:

r = 6 in

Step-by-step explanation:

V = \pi r^{2} \frac{h}{3} = 216\pi

r²h/3 = 216

r² (18/3) = 6 r² = 216

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3 0
2 years ago
The morning temp. In Atlanta, Georgia is 21 1/4 degrees. During the day it warms up 6 2/7 degrees. What is the new temp
pogonyaev

Answer:

27 15/28 degrees

Step-by-step explanation:

Since we are adding 21 1/4 to 6 2/7, we need to find the LCD, or, least common denominator, so that we can add 1/4 and 2/7 together.

1*4=4             1*7=7

2*4=8           2*7=14

3*4=12          3*7=21

4*4=16          <u>4*7=28</u>

5*4=20

6*4=24

<u>7*4=28</u>

Since we had to multiply 7 four times to get it equal to 28, we need to take 2/7 * 4/4. This will give you 8/28. Then, since we multiplied 4 seven times to get it equal to 28, we need to take 1/4 *7/7. This will give you 7/28. Finally, you need to add 8/28 and 7/28 since they now share the same denominator.

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For our last step, we need to add the whole numbers together so the answer is complete.

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6 0
2 years ago
Simplify in fraction form<br> 60a+64≥80a−92
lukranit [14]

Answer:

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Step-by-steep explanation:

60a+64≥80a−92

Step 1: Subtract 80a from both sides.

60a+64≥80a−92

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Step 2: Subtract 64 from both sides.

−20a+64≥−92

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−20a≥−156

Step 3: Divide both sides by -20.

−20a≥−156

a≤39/5

5 0
2 years ago
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