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natima [27]
2 years ago
12

Supply the missing reasons to complete the proof.

Mathematics
1 answer:
MAXImum [283]2 years ago
7 0

Answer:

3. ASA

4. Corresponding sides of congruent triangles are congruent

Step-by-step explanation:

I marked this in the attached image. ∠B ≅∠E, ∠ACE ≅ ∠DCE, and the side between them BC ≅ EC, so the the triangles ΔACB and ΔDCE are congruent by ASA.

If the triangles are congruent, then all corresponding angles and sides are also congruent.

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The two hot-air balloons in the drawing are 48.2 and 61.0 m above the ground. A person in the left balloon observes that the rig
yuradex [85]

The horizontal distance between the two balloons is 54.1478... meters.

<u><em>Explanation</em></u>

According to the below diagram, A and B are the positions of two balloons which are 48.2 meter and 61.0 meter above the ground respectively.

Horizontal distance between two balloons is AC, which is x meter.

A person in the left balloon observes that the right balloon is 13.3° above the horizontal. That means, ∠BAC = 13.3°

According to the diagram,  BC= 61.0-48.2=12.8 meter

Now in right angle triangle ABC.....

tan(13.3)=\frac{BC}{AC}\\ \\ tan(13.3)= \frac{12.8}{x} \\ \\ x= \frac{12.8}{tan(13.3)}=54.1478...

So, the horizontal distance between the two balloons is 54.1478... meters.

3 0
4 years ago
John has $6.10 in quarters and nickels in his pocket. If John has 34 coins in his pocket, how many of the coins are quarters?
Luden [163]
34 = q + n
6.1 = .25q + .05n

-1.7 = -.05q - .05n
6.1 = .25q + .05n

4.4 = .2q
q = 22

22 of the coins are quarters.
7 0
3 years ago
Can someone help me with this please?!
STALIN [3.7K]

Answer:

  see below for a graph

Step-by-step explanation:

The first inequality does not include the "equal to" case, so its boundary is graphed with a dashed line. If we consider only the y term, we have y < ..., so the shading is below the line.

__

The second inequality includes the "equal to" case, so its boundary line is solid. Again, considering only the y-term, we have y ≥ ..., so the shading is above the line.

__

We find that points (-6, 0) and (0, 6) will satisfy both inequalities, as will any point in the doubly-shaded area.

8 0
4 years ago
$35 belt; 40% discount
Anvisha [2.4K]

Answer:

$15, brainliest please

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
How to solve this<br><br>6m+6+7(1-3m)=-32​
lesantik [10]

Answer:

m=15

Step-by-step explanation:

BODMAS

6m+6+7-3m=-32

collect like terms

6m-3m+6+7=-32

3m+13=-32

3m=-32-13

3m=45

m=45/3

m=15

5 0
4 years ago
Read 2 more answers
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