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3 years ago

Which theorem or postulate can be used to prove ΔRPQ ≅ ΔRST? Given R is the midpoint of QT and QT bisects PS at R.

Mathematics

2 answers:

liq [111]3 years ago

4 0

Answer:

SSS

If this answer is correct, please mark brainliest.

nikklg [1K]3 years ago

3 0

Answer:

Step-by-step explanation:

The graph of this problem is attached. There you can observe that we demonstrate the congruence using SAS postulate, which is Side-Angle-Side.

This is the postulate we should use because the mid point divides in equal parts by definition, that means, sides RP and RS are congruent, and sides QR and TR are congruent. In addition, angles QRP and TRS are congruent, because they are vertical angle.

So, we have Side-Angle-Side as congruent parts. Therefore, the postulate we have to use is SAS, option C.

You might be interested in

A recent survey describes the total sleep time per night among college students as approximately Normally distributed with mean

marin [14]

Answer:

a) $\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981$

b) We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

c) $z = \frac{6.9-6.72}{0.0981}= 1.835$

And we can use the z normal table or excel and we got:

$P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the total sleep time of a population, and for this case we know the distribution for X is given by:

$X \sim N(6.72,1.26)$

Where $\mu=6.72$ and $\sigma=1.26$

(a) What is the standard deviation for the average time in hours? (Round your answer to four decimal places.)

For this case the sample mean have the following distirbution

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the deviation is given by:

$\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981$

in minutes?= (Round your answer to three decimal places.)

(b) Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean. (Round your answer to four decimal places.)

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

(c) What is the probability that your average will be below 6.9 hours? (Round your answer to four decimal places.)

For this case we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And we can find the z score for 6.9 and we got:

$z = \frac{6.9-6.72}{0.0981}= 1.835$

And we can use the z normal table or excel and we got:

$P(Z$

4 0

3 years ago

Determine whether each statement is always, sometimes, or never true. Explain your reasoning. (By the way, this has to do with a

Norma-Jean [14]

A). |x| = |-x|
This is always true.
The definition of 'absolute' value is 'size of the number without its sign'.
That's what this expression says.

b). |x| = -|x|
This is never true, because an absolute value is never negative.
This one would true if x=0 . So maybe some people might say
it's sometimes true, but that doesn't feel right to me. I say never.

c). |-x| = -|x|
This looks to me like exactly the same situation as (b),
and I would say all the same things about it.

6 0

3 years ago

Read 2 more answers

If m∠EBF = 6x + 4 and m∠CBF = 7x – 2, find m∠EBF.

olganol [36]

Answer:

Step-by-step

I hope it's helped

6 0

2 years ago

Read 2 more answers

Solve the following system of equations by substitution<br> 2x – 3y = -1<br> y = x - 1

Aliun [14]

Answer:

(4, 3)

Step-by-step explanation:

Plug in x - 1 where y is. The equation will turn in 2x - 3(x - 1) = -1. Distribute, and you'll have 2x -3x + 3 = -1. Combine like terms (2x and -3x) and you'll have -x + 3 = -1. Subtract 3 from both sides, and you'll have -x = -4. Divide by -x (or -1) on both sides, and you'll have x = 4. Since y = x - 1, y = 3, since 4 - 1 = 3. Sorry if this sounds repetitive btw. Good luck :D

7 0

3 years ago

What is 47.4 rounded to the nearest tenth place

expeople1 [14]

The answer is 47.4 because u don't rounded because it's a zero

8 0

3 years ago