Warren is a caterer. He needs to put 39 carrot sticks and 52 celery sticks on plates. Each plate
should have the same number of carrot sticks
and the same number of celery sticks. He also
wants to use all of the carrots and all of the
celery. Which is the greatest number of plates
he can use?

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:

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

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step-by-step explanation:

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