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n200080 [17]
3 years ago
9

They ratio of pencils to erasers is 4:1 if their are 20 pencils how many erasers are there

Mathematics
1 answer:
velikii [3]3 years ago
8 0
Let x be the number of erasers
4 = 20
1 = x

4x = 20

x = 5
 therefore there are 5 number of erasers 
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Answer: About 6.71 units

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Question number 8. Prove that 3 + √5 is an irrational number.​
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Let's assume the opposite of the statement i.e., 3 + √5 is a rational number.

\\  \sf \: 3 +  \sqrt{5}  =  \frac{a}{b}   \\  \\   \qquad \: \tiny \sf{(where \:  \: a \:  \: and \:  \: b \:  \: are \:  \: integers \:  \: and \:  \: b \:  \neq \: 0)} \\

\\  \sf \:  \sqrt{5}  =  \frac{a}{b}  - 3 =  \frac{a - 3b}{b}  \\

Since, a, b and 3 are integers. So,

\\ \sf \:  \frac{p - 3b}{b}  \\  \\  \qquad \tiny \sf{ \: (is \:  \: a \:  \: rational \:  \: number \:) } \\

Here, it contradicts that √5 is an irrational number.

because of the wrong assumption that 3 + √5 is a rational number.

\\

Hence, 3 + √5 is an irrational number.

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3 years ago
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