1. prove that for any natural value of n the value of the expression:
a) (n+1)^2–(n–1)^2 is divisible by 4
b) (2n+3)^2–(2n–1)^2 is divisible by 8

(a)

Use the fact that . In this case a=n+1, b=n-1.

I am using "4|expression" to denote that 4 should divide the expression:

(b)

Same trick

i need a picure

step-by-step explanation:

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)