The distance from his home to his work place is 118.125 miles
<h3>How to find the distance from his home to his work place?</h3>
He drove from home to work at an average speed of 45 mph. Therefore,
speed = 45 mph
let
time = x
speed = distance / time
distance = 45x
His return trip home took 45 minutes longer because he could only drive at 35 mph. Therefore,
45 minutes = 0.75 hours
distance = 35(x + 0.75)
distance = 35x + 26.25
Therefore,
45x = 35x + 26.25
45x - 35x = 26.25
10x = 26.25
x = 26.25 / 10
x = 2.625
Therefore,
distance = 45(2.625) = 118.125 miles
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since it has a diameter of 28, then its radius must be half that or 14.
![\textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=14 \end{cases}\implies A=\pi (14)^2\implies A=196\pi ~\hfill \stackrel{\stackrel{semi-circle}{half~that}}{98\pi }](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D14%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%20%2814%29%5E2%5Cimplies%20A%3D196%5Cpi%20~%5Chfill%20%5Cstackrel%7B%5Cstackrel%7Bsemi-circle%7D%7Bhalf~that%7D%7D%7B98%5Cpi%20%7D)
Answer:
x=38 degrees
Step-by-step explanation:
supplemental angle to 114 degrees is 66 degrees
180=x+2x+66
3x=114
x=38 degrees
