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LuckyWell [14K]
3 years ago
7

56 less than the quotient of a number and 4 is -52

Mathematics
1 answer:
const2013 [10]3 years ago
3 0
X - the number

The algebraic expression:
\frac{x}{4}-56=-52

The solution:
\frac{x}{4}-56=-52 \ \ \ |+56 \\
\frac{x}{4}=4 \ \ \ |\times 4 \\
x=16

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What additional information would be needed to prove that the triangles are congruent using the ASA congruence theorem? ON ≅ MN
dybincka [34]

Answer:

ΔLNO ≅ ΔLMN iff ∠LNO = ∠LNM

Step-by-step explanation:

Lets get started using the statement that...

<em> In ΔLON and ΔLMN</em>

 <u><em> Side ON ≅ Side MN </em></u>

<u><em>   Side LN ≅ Side  NM </em></u>

<u><em>     ∠LON ≅ ∠LMN</em></u>

To Prove: ∠LON ≅ ∠LMN by ASA congruence theorem.

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Hence, using this we will prove that the triangles are congruent by ASA congruence rule.

<u><em>In ΔLON and ΔLMN</em></u>

 Side ON ≅ Side MN

 ∠LNO ≅ ∠LNM ( ∵ common )

 ∠LON ≅ ∠LMN (∵ Given )

<u>⇒ ΔLON ≅ ΔLMN ( By ASA congruence theorem).</u>

4 0
4 years ago
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Answer:

A sample size of at least 87 will be needed.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.98}{2} = 0.01

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.01 = 0.99, so z = 2.325

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

M = 5, \sigma = 20

So

M = z*\frac{\sigma}{\sqrt{n}}

5 = 2.325*\frac{20}{\sqrt{n}}

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A sample size of at least 87 will be needed.

4 0
3 years ago
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