Answer:
65
Step-by-step explanation:
55 + 65 + 57 = 177
there are more factors, but I found this one the quickest.
hope this helps!
Answer:
B (5; 13)
Step-by-step explanation:
Midpoint (x) = (-1 + bx)/2 = 2
Bx - 1 = 4
Bx = 5
Midpoint (y) = (-3 + By)/2 = 5
By - 3 = 10
By = 13
B (5; 13)
![sinx=cosx-1 \\ \\ sinx-cosx=-1](https://tex.z-dn.net/?f=sinx%3Dcosx-1%20%5C%5C%20%20%5C%5C%20%0Asinx-cosx%3D-1)
Using the identity:
![sinx-cosx=- \sqrt{2}cos( \frac{ \pi }{4}+x)](https://tex.z-dn.net/?f=sinx-cosx%3D-%20%5Csqrt%7B2%7Dcos%28%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%2Bx%29%20%20)
, we get:
![- \sqrt{2}cos( \frac{ \pi }{4}+x)=-1 \\ \\ cos( \frac{ \pi }{4}+x)= \frac{1}{ \sqrt{2} } \\ \\ ](https://tex.z-dn.net/?f=-%20%5Csqrt%7B2%7Dcos%28%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%2Bx%29%3D-1%20%5C%5C%20%20%5C%5C%20%0Acos%28%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%2Bx%29%3D%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B2%7D%20%7D%20%5C%5C%20%20%5C%5C%20%0A%20)
There are two solutions to this equation:
1) ![\frac{ \pi }{4}+x= \frac{ \pi }{4} \\ \\ x=0](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%2Bx%3D%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%20%5C%5C%20%20%5C%5C%20%0Ax%3D0%20%20)
Since the period of cosine is 2π, so 0 + 2π = 2π will also be a solution to the given equation
2)
Therefore, there are 3 solutions to the given trigonometric equation.
F(x) = -3 + 7 = 4
g(x) = -7 + 3 = -4
f(-3) - g(3) = 4 - (-4) = 4 + 4 = 8