Prove that given any 17 integers, there exist nine of them whose sum is divisible by 9.

(it might to use the fact that given any five integer you can find three whose sum is divisible by 3)

This is a simple consequence of the Zero-sum problem: https://en.wikipedia.org/wiki/Zero-sum_problem

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

square root

step-by-step explanation: