Answer:
see explanation
Step-by-step explanation:
Calculate C by adding corresponding components of A + B
C = ![\left[\begin{array}{ccc}4\\-7.5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C-7.5%5C%5C%5Cend%7Barray%7D%5Cright%5D)
+ ![\left[\begin{array}{ccc}-2.5\\5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2.5%5C%5C5%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}4-2.5\\-7.5+5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4-2.5%5C%5C-7.5%2B5%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}1.5\\-2.5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1.5%5C%5C-2.5%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Well, we are told that in the beginning, it has traveled 30km vertically, so do not forget to add that on at the end.
Next it says that it traveled 40km 30 degrees from vertical, so we set up a sin equation to solve for the missing side, n:
sin(angle)= opposite/hypotenuse:
sin(30) = n/40
40sin30=n
n=20km
Then it says at an angle of 45 degrees, it goes 100km. This means that we are given the hypotenuse of a right triangle, and we need to find the side that goes up and down. We shall call this length x.
We know that the angle opposite x is 45 degrees.
So, we will use sin to solve for x:
sin(angle)= opposite/hypotenuse
sin45= x/100
100sin45=x
x=70.711km
But remember, I said not to forget about that 30km from the very beginning? So we add up all of our vertical heights:
30km + 20km+ 70.711km = 120.711km
80+20 is ten times 8+2, if you factor out 10 from 80+20 we get 10(8+2)
The expression 
means "all the numbers stricktly greater than -4"
Since the number line is oriented with positive direction going to the right, a number is greater than another if its sits to its right.
So, we want all the numbers to the right of -4, excluded -4 itself.
So, the answer is D.
