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notsponge [240]
3 years ago
14

Triangle A B C is reflected over side A C and then is dilated to form smaller triangle D E C. Angles B C A and D C E are right a

ngles. Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triangle DEC. Which statements about the two triangles must be true? Select three options. △ABC ~ △DEC ∠B ≅ ∠E 3BC = 2EC 3DE = 2AB 3m∠A = 2m∠D 2m∠A = 3m∠D
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
4 0

Answer:

A. △ABC ~ △DEC

B. ∠B ≅ ∠E

D. 3DE = 2AB

Step-by-step explanation:

Transformation involves the reshaping or resizing of a given figure. The types are: reflection, dilation, rotation and translation.

In the given question, the two operations performed on triangle ABC are reflection and dilation to form triangle DEC. The length of each side of triangle DEC is two-third of that of ABC. Therefore, the correct statements about the two triangles are:

i. △ABC ~ △DEC

ii. ∠B ≅ ∠E

iii. 3DE = 2AB

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Comparing Leaking Pool Problem
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Answer:

<em>Pool 1 leaks faster than pool 2.</em>

Step-by-step explanation:

<u>Rates of change</u>

The rate of change (ROC) is a measure that compares two quantities, usually to know how fast one variable changes in time.

We are given two rates of change for two pools that are leaking. The first one loses 2/3 gallon in 15 minutes, and the other loses 3/4 gallon in 20 minutes.

To compare them, we are required to express time in hours. Recall one hour has 60 minutes, or equivalently, one minute has 1/60 hours. Converting both times, we have:

15 minutes = 15/60 = 1/4 hours

20 minutes = 20/60 = 1/3 hours

Now compute both rates of change:

Pool 1:

\displaystyle ROC_1=\frac{2/3}{1/4}=\frac{8}{3}\approx 2.67\ gal/h

Pool 2:

\displaystyle ROC_2=\frac{3/4}{1/3}=\frac{9}{4}= 2.25\ gal/h

Comparing both ratios, it's clear pool 1 leaks faster than pool 2.

8 0
3 years ago
What is the square root of 16x^36
Blababa [14]

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8 0
3 years ago
Read 2 more answers
Len walks 3/10 mile in the morning. He walks 2/5 mile in the afternoon to a friends house. Len says that he walks a total of 5/1
andre [41]
No he walks 7/10 of a mile
you have to make 2/5 have a common denominator with 3/10
so 2×2=4 (numerator)
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7 0
3 years ago
The cylinder shown has a volume of 150 cubic inches and its height is equal to its
harina [27]

Answer:

Volume of sphere = 200 in³

Step-by-step explanation:

Given:

Volume of cylinder = 150 in³

Height = Radius

Radius of cylinder = Radius of sphere

Find:

Volume of sphere = ?

Computation:

Volume\ of\ cylinder = \pi r^2h\\\\Given\ r=h\\\\So, \\\\Volume\ of\ cylinder = \pi r^2r\\\\150 = \pi r^3\\\\

Volume\ of\ sphere =\frac{4}{3} \pi r^3\\\\We\ know \ that , \pi r^3 = 150\\\\ Volume\ of\ sphere =\frac{4}{3} \times 150\\\\Volume\ of\ sphere =200

Volume of sphere = 200 in³

7 0
3 years ago
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dezoksy [38]

Answer:

Infinite solutions.

Step-by-step explanation:

If an equation is an identity, then there will be infinite solutions that the identity will have.

Let, us assume that an identity equation is given by

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Now, putting any real values of a and b the identity will be satisfied.

Therefore, there are infinite solutions for an identity equation. (Answer)

3 0
3 years ago
Read 2 more answers
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