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3 years ago

2. The sum of two numbers is 67 and their difference is 3. Find the two numbers.

Mathematics

1 answer:

nydimaria [60]3 years ago

3 0

Answer:

35 and 32

Step-by-step explanation:

35 and 32

because when we add 35 and 32 then their sum is 67

when we subtract 35 and 32 then their difference is 3

I hope u understand it

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Prove the divisibility of the following numbers:

Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

$75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}$

(B)

$72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}$

In this case, it is easier to also factor the divisor to primes:

$72^{63}=2^{189}\cdot 3^{126}$

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

$2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}$

6 0

3 years ago

For the following questions find the other half of the fraction.

valentina_108 [34]

Answer:

1) 3/5= 6/10

2) 3/6= 6/12

3) 4/10= 2/5

4) 3/4= 6/8

5) 5/10 = 1/2

6) 4/6= 8/12

7) 5/5= 10/10

8) 1/2= 6/12

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2 years ago

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S_A_V [24]

Answer:

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Step-by-step explanation:

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Write an expression which solves for the radius of an object having the circumference of 30 feet

Likurg_2 [28]

$circumference=30ft.\\\\circumference=2\pi r\ (r-radius)\\\\2\pi r=30\ \ \ \ /:2\pi\\\\r=\frac{30}{2\pi}\\\\r=\frac{15}{\pi}\ (ft)\\\\\frac{15}{\pi}\approx\frac{15}{3.14}\approx4.78\ (ft)$

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3 years ago

Read 2 more answers

Find the distance between the points (-2, 4) and (5, 4). 3 7 8

Lina20 [59]

Try this solution:
distance= $\sqrt{(5-(-2)^2+(4-4)^2} = \sqrt{49} =7.$

answer: 7

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3 years ago