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romanna [79]
2 years ago
9

QR is the radius of R and PQ is the tangent to R. Find the value of x.

Mathematics
1 answer:
steposvetlana [31]2 years ago
5 0

Answer:

x = 39

Step-by-step explanation:

We know that PRQ is a right triangle, so we use the pythagorean theorem to solve the problem. The theorem states that a^2 + b^2 = c^2. Let's assume that the length of RP is c, the length of PQ is a and x is b. We plug the lengths into the equation and solve it:

80^2 + x^2 = 89^2

6400 +x^2 = 7921

x^2 = 1521

x = \sqrt{1521}

x = 39

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8% of a number is 20
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To find what the number is, we need to set up proportional fractions.
Currently, we have 8% of a number is 20.
To set up our fractions, put 100% under 8% as a fraction first.

It should look like this: 8/100 (hint: per-cent means per-hundred).

Now, we have 20 out of a number, x. This is because we are claiming that 20 is 8% of a number (if we just reword the question without changing the concept).
It should look like this: 20/x.

Our proportional fractions are:
20/x = 8/100.

To solve for this, we need to cross-multiply the denominator of 8/100 (bottom number, 100) with the numerator of 20/x (top number, 20).

This product equation should look like this:
20 x 100 (when simplified, we get 2000).

Now, we need to cross multiply the numerator of 8/100 (top number, 8) with the denominator of 20/x (bottom number, x).

This product equation should look like this:
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8x = 2000.

To solve for x, divide both sides by 8 (remember, what you do to one side of an equation, you must do it to the other).

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x = 250

Your final answer is:

8% of 250 is 20.

I hope this helps!
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