Theresa is 14 years younger than her brother jonathan. together, their total age in years is 35. a) how many years old is theresa? b) how many years old is jonathan?

A) The age of Theresa is 10 years 6 months old

B) Jonathan age is 24 years and 6 months old

Solution:

Given, Theresa is 14 years younger than her brother Jonathan.  

Let the age of Theresa be "n" years

Then the age of Jonathan will be "n + 14" years

Together, their total age in years is 35

A) Finding age of Theresa:

Jonathan age + Theresa age = 35  

n + 14 + n = 35  

2n + 14 = 35  

2n = 35 - 14  

2n = 21  

n = 10.5

So, age of Theresa is 10 years 6 months  

B) Finding age of Jonathan

Now, we know that n = 10.5  

Then Jonathan age = n + 14 = 10.5 + 14 = 24.5 years

So, Jonathan is 24 years and 6 months old

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)