Idon’t understand this.. will someone ? will mark brainliest along with 20 points.

To say two quantities and "vary directly" with one another means that a change in one of the quantities results in a proportional change in the other quantity. For example, if , then is proportional to by a factor of 2, or is proportional to by a factor of 1/2. In other words, if you change by some fixed amount, then changes by double that amount.

Mathematically this means there is some constant scaling factor such that . In question 4, we're told varies directly with , which means there's some such that

We're given that when , so

Then when , we get

- - -

For to "vary inversely" with one another means that a change in one quantity results in an "opposite" change in the other. In other words, if increases, then decreases, and vice versa.

Mathematically, this is the same as saying there is some fixed number such that .

For example, if and we start with , then also. If we change to , then ; if , then , and so on.

In question 5, we're told varies inversely with , so that there is some constant for which

When , we have :

Then for , we get

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!