What is the measure of

Mathematics

1 answer:

stepan [7]2 years ago

7 0

Answer:

Angle A is 37 degrees, Angle B is 82 degrees, Angle C is 61 degrees

Step-by-step explanation:

Exterior angles are the supplement of interior angles, so subtract 143 from 180 to find Angle A.

180 - 143 = 37

All angles add up to 180.

37 + 61 = 98

180 - 98 = 82

Angle B is 82 degrees.

Hope this helped. :)

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A recent survey of 128 high school students indicated the following information about release times from school

Tju [1.3M]

Answer:

If we convert the percentages into numbers of students, including the margin of error:

Group 1: 40-49 (earlier) (31%-39%)

Group 2: 21-30 (same) (16%-24%)

Group 3: 45-55 (later) (35%-43%)

Group 4: 3-12 (no opinion) (2%-10%)

Interval estimate for group 1 is 40-49 students, and for group 3 is 45-55 students. The earlier group 1 could persuade the no opinion group 4 to join them. This would change the interval to 43-61, compared to 45-55 for group 3. In percentages this comes to 34%-47% approx.

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2 years ago

What is the following quotient?

seropon [69]

Answer: Choice B) $\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\$

==========================================

Work Shown:

$\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\$

This shows why choice B is the answer.

---------------

Explanation:

In the second step, I multiplied top and bottom by $(\sqrt{11}+\sqrt{3})$
This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is $\sqrt{a}-\sqrt{b}$ and you want to rationalize the denominator, then you should multiply top and bottom by $\sqrt{a}+\sqrt{b}$ . The same applies in reverse as well.