Answer:
![f ^{ - 1} (y) = \frac{y + 3}{2}](https://tex.z-dn.net/?f=f%20%5E%7B%20-%201%7D%20%28y%29%20%3D%20%20%5Cfrac%7By%20%2B%203%7D%7B2%7D%20)
Step-by-step explanation:
put y for f(x)
![y = \frac{1}{2} x - 3](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20-%203)
![y + 3 = \frac{1}{2} x](https://tex.z-dn.net/?f=y%20%2B%203%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20x)
![\frac{y + 3}{2} = x](https://tex.z-dn.net/?f=%20%5Cfrac%7By%20%2B%203%7D%7B2%7D%20%20%3D%20x)
![x = \frac{y + 3}{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7By%20%2B%203%7D%7B2%7D%20)
<u><em>The missing angle is 31 degrees.</em></u>
You can know this because the sum of the measures of a triangle is always 180.
All you have to do is add up the known measure of the triangle and subract that from 180
y=-5x-44
Step-by-step explanation:
5x+y=13 passes through (15,31)
rearrange the equation to y=mx+c
5x+y=13
y=-5x+13
substitute the points (15,31)
y=5x+c
31=5(15)+c
31=75+c
-44=c
y=-5x-44
Can be written as 5x+y=-44
It would be 91 trees a field because 637 divided by 7 equals 91 trees per field
Answer:
i. Colonel is about 201 feet away from the fire.
ii. Sarge is about 125 feet away from the fire.
Step-by-step explanation:
Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.
The total angle at the campfire from both the Colonel and Sarge =
+ ![34^{0}](https://tex.z-dn.net/?f=34%5E%7B0%7D)
= ![93^{0}](https://tex.z-dn.net/?f=93%5E%7B0%7D)
Thus,
<CAB =
-
= ![31^{0}](https://tex.z-dn.net/?f=31%5E%7B0%7D)
<CBA =
-
= ![56^{0}](https://tex.z-dn.net/?f=56%5E%7B0%7D)
Sine rule states;
=
= ![\frac{c}{Sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7BSin%20C%7D)
i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;
= ![\frac{c}{Sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7BSin%20C%7D)
= ![\frac{242}{Sin 93^{0} }](https://tex.z-dn.net/?f=%5Cfrac%7B242%7D%7BSin%2093%5E%7B0%7D%20%7D)
= ![\frac{242}{0.9986}](https://tex.z-dn.net/?f=%5Cfrac%7B242%7D%7B0.9986%7D)
cross multiply,
b = ![\frac{0.8290*242}{0.9986}](https://tex.z-dn.net/?f=%5Cfrac%7B0.8290%2A242%7D%7B0.9986%7D)
= 200.8993
Colonel is about 201 feet away from the fire.
ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;
= ![\frac{c}{Sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7BSin%20C%7D)
= ![\frac{242}{Sin 93^{0} }](https://tex.z-dn.net/?f=%5Cfrac%7B242%7D%7BSin%2093%5E%7B0%7D%20%7D)
= ![\frac{242}{0.9986}](https://tex.z-dn.net/?f=%5Cfrac%7B242%7D%7B0.9986%7D)
cross multiply,
a = ![\frac{0.5150*242}{0.9986}](https://tex.z-dn.net/?f=%5Cfrac%7B0.5150%2A242%7D%7B0.9986%7D)
= 124.8073
Sarge is about 125 feet away from the fire.