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3 years ago

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The ratios in a equivalent ratio table are 3:12, 4:16, and 5:20. If the ratio is 10, what is the second number? Justify your rea

soning.

1 answer:

anzhelika [568]3 years ago

5 0

Answer:

40

Step-by-step explanation:

If you look at the ratios you can see the pattern of the first number being multiplied by 4 everytime. Therefore you must multiply 10 by 4.

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Question : In the given figure , ∆ APB and ∆ AQC are equilateral triangles. Prove that PC = BQ.

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Answer:

See Below.

Step-by-step explanation:

We are given that ΔAPB and ΔAQC are equilateral triangles.

And we want to prove that PC = BQ.

Since ΔAPB and ΔAQC are equilateral triangles, this means that:

$PA\cong AB\cong BP\text{ and } QA\cong AC\cong CQ$

Likewise:

$\angle P\cong \angle PAB\cong \angle ABP\cong Q\cong \angle QAC\cong\angle ACQ$

Since they all measure 60°.

Note that ∠PAC is the addition of the angles ∠PAB and ∠BAC. So:

$m\angle PAC=m\angle PAB+m\angle BAC$

Likewise:

$m\angle QAB=m\angle QAC+m\angle BAC$

Since ∠QAC ≅ ∠PAB:

$m\angle PAC=m\angle QAC+m\angle BAC$

And by substitution:

$m\angle PAC=m\angle QAB$

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$\angle PAC\cong \angle QAB$

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