The average (arithmetic mean) of y numbers is x. if 30 is added to the set of numbers, then the average will be x − 5. what is the value of y in terms of x ?

y =

Step-by-step explanation:

Let the total numbers are n.

If the average of y numbers is x then we can form an equation

⇒

⇒ n = --------(1)

Now 30 is added to the set of numbers then average becomes (x - 5)

⇒

⇒ (n + 1) =

⇒ n = - 1 ----- (2)

Now we equate the values of n from equation 1 and 2

= - 1

y(x - 5) = x(y + 30) - x(x - 5)  [ By cross multiplication ]

xy - 5y = xy + 30x - x² + 5x

xy - xy - 5y = 35x - x²

-5y = 35x - x²

x² - 35x = 5y

y =

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)