Answer:
sec(60) = 2
Step-by-step explanation:
sec(theta) = 1/cos(theta)
theta = 60o
cos(60) = 1/2 = 0.5
sec(theta) = 1/0.5 = 2
![1) y=-5^{-x}, y = x+5 , \\ \\ -5^{-x}=x+5 \\ \\ ln(-5^{-x})=ln(x+5) \\ \\ ln(- \frac{1}{5^{x}} )=ln(x+5), you cannot find ln of negative number, so it is going to be "0" solutions. ](https://tex.z-dn.net/?f=1%29%20y%3D-5%5E%7B-x%7D%2C%20y%20%3D%20x%2B5%20%2C%0A%5C%5C%20%5C%5C%20-5%5E%7B-x%7D%3Dx%2B5%0A%5C%5C%20%5C%5C%20%20ln%28-5%5E%7B-x%7D%29%3Dln%28x%2B5%29%0A%5C%5C%20%5C%5C%20ln%28-%20%5Cfrac%7B1%7D%7B5%5E%7Bx%7D%7D%20%29%3Dln%28x%2B5%29%2C%0A%0Ayou%20cannot%20find%20ln%20of%20negative%20number%2C%20so%20it%20is%20going%20to%20be%0A%0A%20%220%22%20solutions.%0A)
The graphs of these equations will not intersect.
![2) y = 4(1.2)^{x}, y = x+7 \\ \\ x+7= 4(1.2)^{x} graphs have 2 intersects, so two solutions.](https://tex.z-dn.net/?f=2%29%20y%20%3D%204%281.2%29%5E%7Bx%7D%2C%20y%20%3D%20x%2B7%0A%5C%5C%20%5C%5C%20x%2B7%3D%204%281.2%29%5E%7Bx%7D%0A%0Agraphs%20have%202%20intersects%2C%20so%20two%20solutions.)
3)
Answer:
![x=6\\ \\y=-6](https://tex.z-dn.net/?f=x%3D6%5C%5C%20%5C%5Cy%3D-6)
Step-by-step explanation:
Given the system of two equations:
![\left\{\begin{array}{l}-4x-2y=-12\\ \\4x+8y=-24\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D-4x-2y%3D-12%5C%5C%20%5C%5C4x%2B8y%3D-24%5Cend%7Barray%7D%5Cright.)
Add these two equations (left side add to left side and right side add to right side):
![-4x-2y+4x+8y=-12+(-24)\\ \\-2y+8y=-12-24\\ \\6y=-36\\ \\y=-6](https://tex.z-dn.net/?f=-4x-2y%2B4x%2B8y%3D-12%2B%28-24%29%5C%5C%20%5C%5C-2y%2B8y%3D-12-24%5C%5C%20%5C%5C6y%3D-36%5C%5C%20%5C%5Cy%3D-6)
Substitute
into the first equation:
![-4x-2\cdot (-6)=-12\\ \\-4x+12=-12\\ \\-4x=-12-12\\ \\-4x=-24\\ \\x=6](https://tex.z-dn.net/?f=-4x-2%5Ccdot%20%28-6%29%3D-12%5C%5C%20%5C%5C-4x%2B12%3D-12%5C%5C%20%5C%5C-4x%3D-12-12%5C%5C%20%5C%5C-4x%3D-24%5C%5C%20%5C%5Cx%3D6)