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murzikaleks [220]
3 years ago
5

Helppp! (m−3+4n)⋅(−8)

Mathematics
1 answer:
-BARSIC- [3]3 years ago
4 0

Answer:

-8m + 3 - 32n

Step-by-step explanation:

Distributive Property

-8m + 3 - 32n

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Let n be the smallest positive integer that is a multiple of 75 and has exactly 75 positive integral divisors, including itself
Juli2301 [7.4K]

Answer:

n=2^4 3^4 5^2 =32400 and then we have:

\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432

Step-by-step explanation:

From the info given by the problem we need an integer defined as the smallest positive integer that is a multiple of 75 and have 75 positive integral divisors, and we are assuming that 1 is one possible divisor.

Th first step is find the prime factorization for the number 75 and we see that

75=3 5^2

And we know that 3 =2+1 and 5=3+2 and if we replace we got:

75 = (2+1)(4+1)^2 = (2+1)(4+1)(4+1)

And in order to find 75 integral divisors we need to satisify this condition:

n= a^{r_1 -1}_1 a^{r_2 -1}_2 *...... such that a_1 *a_2*....=75

For this case we have two prime factors important 3 and 5. And if we want to minimize n we can use a prime factor like 2. The least common denominator between 2 and 4 is LCM(2,4) =4. So then the need to have the prime factors 2 and 3 elevated at 4 in order to satisfy the condition required, and since 5 is the highest value we need to put the same exponent.

And then the value for n would be given by:

n=2^4 3^4 5^2 =32400 and then we have:

\frac{n}{75}=\frac{2^4 3^4 5^2}{3 5^2}=432

8 0
3 years ago
A chef combines 5 quarts of pineapple​ juice, 4 pints of​ milk, and 4 cups of apple juice to make smoothies. How many cups can b
GarryVolchara [31]

Answer:

32 US cups.

Step-by-step explanation:

5 quarts is equal to 20 cups.  4 pints is equal to eight cups.  4 cups of apple juice just stays the same.  20 + 8 + 4 = 32.  32 cups can be filled with smoothies.

Thanks, 5 stars, and brainliest! Please?

6 0
3 years ago
I worked for 12 hours each day for 6 days then the next day I worked 9 hours how many did I work in all
nikitadnepr [17]

Answer:

81

Step-by-step explanation:

12(6) + 9

72 + 9

81......

4 0
3 years ago
Read 2 more answers
Help me with math work please
shutvik [7]

2. b=-15   4. b=9   5. m=6 b=1   6. m=-4 b=140

6 0
3 years ago
This is due Monday but I want to get it done today, because the teacher is still going to check it, and I have practicly nothing
Crank
You don’t have anything attached:(
7 0
3 years ago
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