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larisa [96]
3 years ago
7

Find the length of the missing side. Give your answer in the simplest radical form.

Mathematics
1 answer:
taurus [48]3 years ago
6 0

Answer:

x = 2\sqrt{5}

Step-by-step explanation:

Use Pythagorean theorem,

Hypotenuse² = base² + altitude²

x² = (√8)² + 4²

  =  8 + 16

  = 20

x = √20 = \sqrt{2*2*5} = 2\sqrt{5}

x = 2\sqrt{5}

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Darren bought some paint. He used 2 1/4 gallons painting his living room. After that, he had 3 5/6 gallons left. How much paint
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Answer: 6\frac{1}{12}\ gallons

Step-by-step explanation:

We can make the conversion from mixed numbers to improper fractions:

  • Multiply the whole number part by the denominator of the fraction.
  • Add the numerator of the fraction and the product obtained (This sum will be the new numerator).
  • The denominator is the same.

Then:

2\frac{1}{4}=\frac{(2*4)+1}{4}=\frac{9}{4}\\\\3\frac{5}{6}=\frac{(6*3)+5}{6}=\frac{23}{6}

We need to add the fractions in order to calculate the amount of paint Darren bought. Since the denominators are differente, we must find the Least Common Denominator (LCD):

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Then:

\frac{9}{4}+\frac{23}{6}=\frac{27+46}{12}=\frac{73}{12}\ gallons

To convert this improper fraction to a mixed number:

  • When you divide 73 by 12 you get a quotient of 6. This will be the whole number.
  • The remainder obtained is 1. This will be the numerator of the fraction.
  • The denominator does not change.

Then:

\frac{73}{12}\ gallons=6\frac{1}{12}\ gallons

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