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1 year ago

What theorem is used to prove △ABC≅△DEC given that C is the midpoint of EB?

Mathematics

1 answer:

sergiy2304 [10]1 year ago

8 0

The theorem is used to prove △ABC≅△DEC is Side-Angle-Side(SAS) theorem

The two triangles are

△ABC and △DEC

Here we have to prove that the △ABC and △DEC are congruent

It is given that

The length of AC = The length of CD

The angle ACB = The angle ECD

The point C is the midpoint of EB

Therefore,

The length of BC = The length of EC

Therefore, the two sides and one angle of triangle ABC is equal to the two sides and one angle of triangle DEC, so the both triangles are congruent by SAS rule

Hence, the theorem is used to prove △ABC≅△DEC is Side-Angle-Side(SAS) theorem.

Learn more about congruence of triangle here

brainly.com/question/20521780

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Which of the following is true about radiation from the sun?

bearhunter [10]

This isn't a math question and should be in the science section. However, I will still answer the question. The answer is choice B.

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Here's a further breakdown

A. False. The radiation or energy from the sun can travel through air or else you wouldn't feel the sun's rays. Also, plant life wouldn't be alive without that energy going through the air.

B. True. The rays travel through a vacuum of space. If they couldn't travel through space, then the same problem comes up as in choice A: the issue of not feeling the sun's rays.

C. False. They rays have different frequencies. Because there are many wavelengths (see choice D below), this means there are different frequencies. Recall that f = 1/w where f is the frequency and w is the wavelength.

D. False. The rays are made of different wavelengths. The visible light portion is what we can see, though there is a lot more to the electromagnetic spectrum (eg: ultraviolet light).

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So once again, the answer is choice B

6 0

3 years ago

What is the difference of the polynomials?

Vilka [71]

Answer:

$8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6$

Step-by-step explanation:

We want to simplify;

$(8r^6s^3-9r^5s^4+3r^4s^5)-(2r^4s^5-5r^3s^6-4r^5s^4)$

We expand the bracket to obtain;

$8r^6s^3-9r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6+4r^5s^4$

We now group the like terms to obtain;

$8r^6s^3-9r^5s^4+4r^5s^4+3r^4s^5-2r^4s^5+5r^3s^6$

We now simplify to get;

$8r^6s^3-5r^5s^4+r^4s^5+5r^3s^6$

The correct answer is C

3 0

3 years ago

Read 2 more answers

Help please! 20 points!

vladimir1956 [14]

$x+100+3x=180\\4x=80\\x=20$

5 0

3 years ago

Read 2 more answers

Determine the value of x which r || s. then find m<1 and m<2.

slava [35]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

2067 Supp Q.No. 2a Find the sum of all the natural numbers between 1 and 100 which are divisible by 5. Ans: 1050

Alborosie

Answer:

1050

Step-by-step explanation:

Natural Numbers are positive whole numbers. They aren't negative, decimals, fractions. We can just divide 5 into 100 to find how many natural numbers go up to 100 and just add them but that is just to much.

There is a easier method.

E.g: Natural Numbers that are divisible by a Nth Number. is the same as adding the Nth Numbers to a multiple of that Nth Term. For example, let say we need to find numbers divisible by 2. We know that 4 is divisible by 2 because 4/2=2. We can add the Nth numbers which is 2 to 4. 4+2=6. And 6 is divisible by 2 because 6/2=3. We can call this a arithmetic series. A series which has a pattern of adding a common difference

Back to the problem, we can use the sum of arithmetic series formula,

$y = x( \frac{z {}^{1} + {z}^{n} }{2} )$

Where x is the number of terms in our sequence. Z1 is the fist term of our series. ZN is our last term. And y is the sum of all of the terms

The first term is 5, the numbers of terms being added is 20 because 100/5=20. The last term is 100.

$y = 20( \frac{5 + 100}{2} )$

$y = 20( \frac{105}{2} )$

$y = 1050$

5 0

3 years ago