A linear pair is supplementary.
It always helps to draw out a diagram with the information you have - it makes the solving process more visual and sometimes easier. I have attached a diagram of this linear pair.
So, since a linear pair is supplementary, we know these two angles add to equal 180°. Let's write this in an equation.
(5<em>n</em> + 15) + (4<em>n</em> + 21) = 180
Solve for <em>n</em>.
(5<em>n</em> + 15) + (4<em>n</em> + 21) = 180
5<em>n</em> + 15 + 4<em>n</em> + 21 = 180
9<em>n</em> + 36 = 180
9<em>n</em> = 144
<em>n</em> = 16
We're not done yet - now we have to plug this in for <em>n</em> to find the angle measures.
5<em>n</em> + 15
5(16) + 15
80 + 15
95
4<em>n</em> + 21
4(16) + 21
64 + 21
85
Lastly, check your work by adding the angle measures.
95 + 85 = 180
<h3>Answer:</h3>m∠EFG = 95°
m∠GFH = 85°
Given:
The exponential function is:
To find:
The percentage rate of increase or decrease.
Solution:
The general exponential function is:
...(i)
Where, a is the initial value, |r| is the growth rate in decimals if r>0 and |r| is the decay rate in decimal if r<0.
The exponential function is:
It can be written as:
...(ii)
On comparing (i) and (ii), we get
Since r is negative, therefore the given function is a decreasing or decay function.
Now,
So, the rate of decrease is 0.06. Multiply this number by 100 to get the percentage.
Therefore, the rate of decrease is 6%.