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2 years ago

Find the greatest number that will divide 63, 45 and 69 so as to leave the same remainder.

Mathematics

1 answer:

jeka57 [31]2 years ago

7 0

Answer:

Step-by-step explanation:

Let n be unknown divisor and a be the same remainder, then

$63=q_1\cdot n+a\\ \\45=q_2\cdot n+a\\ \\69=q_3\cdot n+a$

Subtract a from all equalities:

$63-a=q_1\cdot n\\ \\45-a=q_2\cdot n\\ \\69-a=q_3\cdot n$

Subtract them:

$63-45=(q_1-q_2)n\Rightarrow 18=(q_1-q_2)n\\ \\69-63=(q_3-q_1)n\Rightarrow 6=(q_3-q_1)n\\ \\69-45=(q_3-q_2)n\Rightarrow 24=(q_3-q_2)n$

The greatest number is 6. When you divide numbers 63, 45, 69 by 6, you'll get remainders 3, 3, 3, respectively.

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PLEASE HELP

Tems11 [23]

QUESTION A

The given multiplication problem is

$\frac{39}{64} \times \frac{8}{13}$

Factor each term to obtain;

$\frac{13\times 3}{8\times8} \times \frac{8}{13}$

Cancel out the common factors to obtain;

$\frac{1\times 3}{8\times1} \times \frac{1}{1}$

Simplify to get;

$\frac{3}{8}$

QUESTION B

The given multiplication problem is

$\frac{2}{3}\times \frac{1}{5}\times \frac{4}{7}$

This the same as

$\frac{2\times 1\times 4}{3\times 5\times 7}$

This simplifies to;

$\frac{8}{105}$

QUESTION C

The given problem is

$\frac{3}{5}\times \frac{10}{12} \times \frac{1}{2}$

This is the same as

$\frac{3}{5}\times \frac{5}{6} \times \frac{1}{2}$

$=\frac{1}{1}\times \frac{1}{2} \times \frac{1}{2}$

This simplifies to

$=\frac{1}{4}$

QUESTION D.

The given expression is

$\frac{4}{9}\times 54$

Factor the 54 to obtain;

$\frac{4}{9}\times 9\times 6$

Cancel the common factors to get;

$\frac{4}{1}\times 1\times 6$

This simplifies to;

$=24$

QUESTION E

The given problem is

$20\times 3\frac{1}{5}$

Convert the mixed numbers to improper fraction to obtain;

$=20\times \frac{16}{5}$

$=4\times5 \times \frac{16}{5}$

Cancel the common factors to get;

$=4\times1 \times \frac{16}{1}$

$=64$

QUESTION F

The multiplication problem is

$11 \times 2 \frac{7}{11}$

Convert the mixed numbers to improper fractions to obtain;

$11 \times \frac{29}{11}$

Cancel out the common factors to get;

$=1 \times \frac{29}{1}$

Simplify;

$=29$

QUESTION G

The given problem is

$5\frac{1}{3}\times 5\frac{1}{8}$

Convert to improper fractions;

$=\frac{16}{3}\times \frac{41}{8}$

Cancel out the common factors to get;

$=\frac{2}{3}\times \frac{41}{1}$

$=\frac{82}{3}$

Convert back to mixed numbers

$=27\frac{1}{3}$

QUESTION H

The given expression is

$10\frac{2}{3} \times 1\frac{3}{8}$

Convert to improper fraction to get;

$\frac{32}{3} \times \frac{11}{8}$

Cancel common factors to get;

$=\frac{4}{3} \times \frac{11}{1}$

Simplify

$=\frac{44}{3}$

Convert back to mixed numbers;

$=14\frac{2}{3}$

7 0

2 years ago

A triangle has one leg that measures 14 feet and the hypotenuse is 50 feet. What is the length of the other leg?

Aliun [14]

Ok so we are using the Pythagorean theorem so were gonna do A^2 + B^2 = C^2

It don't say which leg we have so you can use either a or b.
Which would get us 14^2 + B^2 = 50^2
14*14 =196 , 50 *50 =2500
Then we have to subtract the two.
So 2500 - 196 = 2,304
Then you take the take the square root of that answer and you have your other leg.
The square root of 2,304 is 48
So the missing leg = 48

8 0

3 years ago

Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the value of the expression was 8.5. Select all the state

Darina [25.2K]

Answer:

C) Jayden divided 14 by 2 and then added 1.5.

Step-by-step explanation:

Jayden did

(14/2)+1.5 which is 8.5

so C is correct.

Hope this helps plz hit the crown :D

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Michael has finished 25% of an art project that has taken

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It will take him 16 hours. Hope it helps

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Answer:

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Step-by-step explanation:

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