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ivolga24 [154]
3 years ago
13

Hello please help me answer :) ( WILL GIVE BRAINLST)

Mathematics
1 answer:
Vanyuwa [196]3 years ago
4 0

Answer:

Answer is given

:) mark me brainliest

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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
100xyz-75xy factor completely ​
yarga [219]

the factored form is

-25xy(-4z+3)

6 0
3 years ago
I would like to have an answer for this thanks!
Scilla [17]

The final amount of the compound interest after 6 years would be $ 294, 122, 500

<h3>How to determine the final amount</h3>

The formula for the final amount is given as;

A = P( 1 + \frac{r}{n}) ^n^t

Where

A = final amount

P = principal interest

r = interest rate

n = number of times

t = time of periods

We have,

A = 2500 ( 1 + \frac{6}{1}) ^1^*^6

A = 2500 ( 7)^6

A = 2500 × 117, 649

A =$ 294, 122, 500

Thus, the final amount of the compound interest after 6 years would be $ 294, 122, 500

Learn more about compound interest here:

brainly.com/question/24924853

#SPJ1

6 0
2 years ago
A publishing company creates a book for young children. To find the number of pictures on the page, the book says to multiply th
Eddi Din [679]

Answer:

B

Step-by-step explanation:

B is the only choice that has both all of the steps, and all of the steps in the right order.

5 0
3 years ago
Pls help me. ill mark u brainliest
yarga [219]
I don’t know if you added a picture and if you did i cannot see— sorry :(
7 0
3 years ago
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