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Nikitich [7]
3 years ago
11

8 times the difference between a number and 6 ls equal to 4 times the number.

Mathematics
2 answers:
In-s [12.5K]3 years ago
6 0

Answer:

A. 12

Step-by-step explanation:

Let the number be A

8 x (A - 6) = 4 x A

Expand the left side

8 x A - 8 x 6 = 4A

8A - 48 = 4A

Add 48 to both sides

8A - 48 + 48 = 4A + 48

8A = 4A + 48

Subtract 4A from both sides

8A - 4A = 4A - 4A + 48

4A = 48

Divide both sides by 4

A = 48/4

A = 12

Sveta_85 [38]3 years ago
4 0

Answer:

the answer is 12 because 8 × 6 = 48 ÷ 4 = 12

Step-by-step explanation:

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A certain positive integer has exactly 20 positive divisors. What is the smallest number of primes that could divide the integer
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As per my explanation to (b) above, the largest number of primes that could factor such a number is 4.

Note that  2,3,5 and 7   are the smallest primes, then use the reasoning from

(b) above. we are looking for four exponents, that, when 1 is added to each and all are multiplied together, would equal 20.

But no such integers  k, l, m, and n  exist such that (k + 1)(l + 1)(m + 1) (n + 1)  = 20 where k, l,m, and n ≥ 1 so this number, whatever it is, can't have 4 prime factors

Let's drop 7 out of the mix and suppose it has just 3 prime factors 2, 3, and 5 again we are looking for three exponents,  that, when 1 is added to each and all are multiplied together, would equal 20.  Put another way, we are looking for k, l and m ≥ 1   such that (k + 1)(l + 1)(m + 1) = 20

Note that the  only possibility here  is when we have 2 *2 *5  = 20 and the smallest possible product would be 2^(4 )* 3^(1) * 5^(1) =  2^4 * 3 * 5 = 240

Now......the only remaining possibility is  that this number is composed of the two smallest primes, 2 and 3,  and we are looking for  some k  and l ≥ 1 such that (k + 1)(l + 1) = 20 clearly, the only possibilities  are when k = 4 and l = 5, or vice-versa

So this number would factor as either 2^3 * 3^4   = 648  or 2^4 * 3^3 = 432 and both are > 240.

Learn more about positive integers at

brainly.com/question/1367050

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Step-by-step explanation:

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