The best way to do this is to draw a picture of ΔFKL and include line segment KM that is perpendicular to FL. This creates ΔFKM which is a 45°-45°-90° triangle and ΔLKM which is a 30°-60°-90° triangle.
Find the lengths of FM and ML. Then, FM + ML = FL
<u>FM</u>
ΔFKM (45°-45°-90°): FK is the hypotenuse so FM = 
<u>ML</u>
ΔLKM (30°-60°-90°): from ΔFKM, we know that KM = 
, so KL = 
<u>FM + ML = FL</u>
= 
Writing the word problem as an equation you get:
x - 18 ≥ -12
Now to solve for x:
Add 18 to both sides of the inequality:
x ≥ -12 + 18
Simplify:
x ≥ 6
(2 − 3i) + (x + yi) = 6
We add the left hand side
(2+x) + (-3+y)i = 6
6 can be written in a+ib
6 can be written as 6 + 0i
(2+x) + (-3+y)i = 6 +0i
Now we frame 2 equations
2 + x= 6
-3 + y =0
Solve the first equation
2 + x = 6
Subtract 2 from both sides
x = 4
solve the second equation
-3 + y =0
Add 3 on both sides
y= 3
So x+yi is 4+3i
Answer:
see below
Step-by-step explanation:
To find the combined length of Pine and Elm and the lengths together
Pine +Elm
We are estimating by rounding to the nearest whole number
Pine is 2.7 so it rounds to 3 because we look at the .7 and since .7 is greater than .5 it rounds the 2 to 3
Elm is 8.9 so it rounds to 9 because we look at the .9 and since .9 is greater than .5 it rounds the 8 to 9
2.7 + 8.9 rounds to 3+9 = 12
12 is reasonable because the actual answer is 2.7+8.9 = 11.6 which rounds to 12
