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yanalaym [24]
3 years ago
13

Ju Chan solved the previous question by finding the expression 4(-15). Which addition problem would give the same result? Choose

all that apply. A . 15 + 15 + 15 + 15
A . 15 + 15 + 15 +15 B . 4 + 4 + 4 + 4
C . (–1)(15 + 15 + 15 + 15)
D . (–15) + (–15) + (–15) + (–15)
Mathematics
1 answer:
Umnica [9.8K]3 years ago
3 0

Answer:

C. (-1)(15+15+15+15)

D. (-15)+(-15)+(-15)+(-15)

Step-by-step explanation:

The original expression: 4(-15)=-60

Let's try choice A: 15+15+15+15=60(not a negative number, so does not work)

Let's try choice B: 4+4+4+4=16(nowhere near -60)no

Let's try choice C: (-1)(15+15+15+15)=(-1)(60)=-60--yes

Let's try choice D: (-15)+(-15)+(-15)+(-15)=-60--yes

Only choices C and D work.

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\huge\text{Hey there!}


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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}

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3 years ago
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max2010maxim [7]

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3 years ago
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