Iam thinking of a number between 20 and 50. it is even and has 9 factors. what is it?

36

Explanation:

36 is a composite number, and it is 6 squared. 36 = 1 x 36, 2 x 18, 3 x 12, 4 x 9, or 6 x 6. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Prime factorization: 36 = 2 x 2 x 3 x 3, which can also be written 36 = 2² x 3². Since √36 = 6, a whole number, 36 is a perfect square.

The answer is 36

Step-by-step explanation:

Since the number has nine factors, it must be a root.

6*6 is 36, and 6 counts as one number when factored because it is a root.

1,2,3,4,6,9,12,18,36 This is the factors of 36.

36 is also even, so it matches the statement.

 10 hours

Step-by-step explanation:

The 10hp pump takes x hours to empty the pool which means it gets of the job done in one hour.

The 6hp pump takes x+5 hours to empty the pool which means it gets of the job done in one hour.  

Together, they can get of the job done in one hour.

It is given that together they get the job done in 6 hours which means they get of the job done in one hour.

10 hp pump + 6 hp pump = Together

Multiply by 6x(x+5) to eliminate the denominator:

Simplify and solve for x:

6(x + 5) + 6x = x(x + 5)

6x +  30 + 6x = x² + 5x

       12x + 30 = x² + 5x

                  0 = x² - 7x - 30

                  0 = (x - 10)(x + 3)

                  0 = x - 10         0 = x + 3

                  10 = x             -3 = x

Since the number of hours cannot be negative, disregard x = -3.

So, the only valid answer is x = 10.