the sum of the ages of an uncle and nephew 2 years ago was 40.In 2 years time from now the age of the uncle will be 3 times that of his nephew by then. Find their ages now

Uncle is 34. Nephew is 10.

Step-by-step explanation:

Let u equal the age of the uncle, and n equal the age of the nephew.

First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:

Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:

We now have a system of equations and can solve accordingly.

First, from the first equation, we can determine that:

We can substitute this into the second equation.

Thus, the nephew's age is 10.

And the uncle's age is 44-10 or 34.

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)