Simplify 5k+7+3k. <br> Please Help me

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

PLEASE HELP!! WILL GIVE BRAINLIEST!!!

marishachu [46]

Answer:

120

Step-by-step explanation:

GIVE ME THE BRAINLEST POINTS NOW

5 0

2 years ago

Read 2 more answers

Please check these please

antoniya [11.8K]

-5x=60

The first thing we want to do is to divide -5 on both sides. We do this because -5x, is the same as -5 times x and we want to do the inverse of that.

After we divide on both sides, we get x=60/-5

We know that 60 divided by -5 is -12.

Therefore our answer is: x=-12

----------------------------------------------------------------------------------------------------------

5= n + 2

We always want to get the variable to be alone, so if we subtract by 5 we would be doing the opposite of getting the variable alone. Although, if we subtract by 2 on both sides, we would get the variable alone and the answer would be 3=n

Therefore our answer is: False

----------------------------------------------------------------------------------------------------------

2(x-7)

By looking at this question, we see x being subtracted by 7. Then we see that 2 is being multiplied to that.

Therefore our answer is: C

----------------------------------------------------------------------------------------------------------

The product of a number and 4 increased by 8

In these types of questions, it's smart to break it up. We will start with the product of a number and 4. We know that a number is a variable and if we look at the multiple choice answers we can see that the variable they chose to use is n. We also know that a product is when numbers get multiplied. So that means 4 and n get multiplied which turns into 4n.

For the other part of the problem, we know that increased by 8 means added my 8. Now that we got our answers, we put then together.

Therefore our answer is: A 4n+8

----------------------------------------------------------------------------------------------------------

Pls give a like if this helped you!!!

4 0

1 year ago

Read 2 more answers

Which statements are true about the ordered pair (2, 3) and the system of equations?

kifflom [539]

The answer is f when 2,3 is put in for the x and y then 18 should come out 3×2=6
4×3=12 12+6=18

7 0

3 years ago

((help? just a bit of help!))

Monica [59]

Find the common denominator of 6 and 4.
6: 6, 12...
4: 8, 12...

We can use 12 for this example.

5/6 to ?/12.
12 / 6 = 2, therefore do 5 x 2.
5 x 2 = 10. 10/12.

1/4 to ?/12.
12 / 4 = 3, therefore do 3 x 1.
3 x 1 = 3. 3/12.

13/12. 1 1/12.

I believe you ran out of space or didn't put answer D. I researched this question and concluded that the other choice is 1 and 1/12.

The answer is 1 and 1/12.

5 0

3 years ago

Simplify 5k+7+3k. Please Help me