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3 years ago

Proving the Parallelogram Side Theorem

Mathematics

1 answer:

zzz [600]3 years ago

4 0

Answer:

Statements Reasons

1. ABCD is a parallelogram 1. Given

2. Seg. AB is parallel to seg. CD 2. Def of parallelogram

3. Seg. AD is parallel to seg. BC 3. Def of parallelogram

4. Draw seg. BD 4. Between 2 pts there is 1 line

5. <ABD is congr <CDB 5. Alt. Int. < Theorem

6. <BDA is cong <DBC 6. Alt. Int. < Theorem

7. Seg. BD is congr seg. BD 7. Congr. of seg's is reflexive

8. Triangle BAD is congr tr. DCB 8. SAS Postulate

9. AB is congr CD 9. CPCTC

10. BC is congr DA 10. CPCTC

11. AB = CD; BC = DA 11. Def of congr. seg's

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pantera1 [17]

Factoring we get

(x + 2)(x + 1) / (x + 1)(x + 1)

The excluded value is x = -1

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3 years ago

Read 2 more answers

Consider a value to be significantly low if its z score less than or equal to minus−2 or consider a value to be significantly hi

katrin2010 [14]

Answer:

Test scores of 10.2 or lower are significantly low.

Test scores of 31.4 or higher are significantly high.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 20.8, \sigma = 5.3$

Identify the test scores that are significantly low or significantly high.

Significantly low

Z = -2 and lower.

So the significantly low scores are thoses values that are lower or equal than X when Z = -2. So

$Z = \frac{X - \mu}{\sigma}$

$-2 = \frac{X - 20.8}{5.3}$

$X - 20.8 = -2*5.3$

$X = 10.2$

Test scores of 10.2 or lower are significantly low.

Significantly high

Z = 2 and higher.

So the significantly high scores are thoses values that are higherr or equal than X when Z = 2. So

$Z = \frac{X - \mu}{\sigma}$

$2 = \frac{X - 20.8}{5.3}$

$X - 20.8 = 2*5.3$

$X = 31.4$

Test scores of 31.4 or higher are significantly high.

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3 years ago

Which steps will generate an expression equivalent to 17(+5)

Bingel [31]

For this case we must indicate an expression equivalent to:

$17 (x + 5)$

By definition we have that the distributive property establishes that:

$a (b + c) = ab + ac$

Then, applying the property to the given expression we have:

$17 (x + 5) = 17 * x + 17 * 5 = 17x + 85$

Thus, an equivalent expression is:

$17x + 85$

ANswer:

$17x + 85$

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3 years ago

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LuckyWell [14K]

Answer:

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1 pound of flour = $0.500

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2 years ago

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soldi70 [24.7K]

Answer:

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Step-by-step explanation:

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3 years ago