If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?

We are given the coordinates:
(n, 180)
(5, n)

If y varies directly as x, the equation is likely linear. The answer should be n = 30.

Why? Because the proportions of this, n / 180 must equal 5 / n.
n / 180 = 5 / n
Multiply both sides by n
n^2 / 180 = 5
Multiply by 180
n^2 = 900
Square root both sides
n = 30

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the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is