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3 years ago

Which expressions have the same solution as –4(6)? Check all that apply.

Mathematics

2 answers:

geniusboy [140]3 years ago

8 0

Answer:

4(-6), 6(-4), 12(-2)

Step-by-step explanation:

-4(6) = -4 x 6 = -24

4(-6) = 4 x -6 = -24

6(-4) = 6 x -4 = -24

12(-2) = 12 x -2 = -24

AlladinOne [14]3 years ago

8 0

Answer:

–4(– 6) no

4(– 6) correct

6(– 4) correct

–8(2) no

12(– 2 correct

Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

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:

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

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3 years ago