For an inscribed quadrilateral, opposite angles add up to 180 degrees. In this case, if we are looking for the measure of angle D, we can use the fact that angles I & D add up to 180 degrees. Since angle I = 117:
117 + D = 180
D = 63 degrees
Answer:
5
Step-by-step explanation:
cos 60° = y / 10
y = 10 * 1/2 = 5
Cancel out the terms from one side first then do it for the other one. 4 example make x and individual by multiply the other side by 9 the evaluate. do the same for y
The given function is
![f(x)=4\cos \text{(}\pi x)+1](https://tex.z-dn.net/?f=f%28x%29%3D4%5Ccos%20%5Ctext%7B%28%7D%5Cpi%20x%29%2B1)
The general form of the cosine function is
![y=a\cos (bx+c)+d](https://tex.z-dn.net/?f=y%3Da%5Ccos%20%28bx%2Bc%29%2Bd)
a is the amplitude
2pi/b is the period
c is the phase shift
d is the vertical shift
By comparing the two functions
a = 4
b = pi
c = 0
d = 1
Then its period is
![\begin{gathered} \text{Period}=\frac{2\pi}{\pi} \\ \text{Period}=2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BPeriod%7D%3D%5Cfrac%7B2%5Cpi%7D%7B%5Cpi%7D%20%5C%5C%20%5Ctext%7BPeriod%7D%3D2%20%5Cend%7Bgathered%7D)
The equation of the midline is
![y_{ml}=\frac{y_{\max }+y_{\min }}{2}](https://tex.z-dn.net/?f=y_%7Bml%7D%3D%5Cfrac%7By_%7B%5Cmax%20%7D%2By_%7B%5Cmin%20%7D%7D%7B2%7D)
Since the maximum is at the greatest value of cos, which is 1, then
![\begin{gathered} y_{\max }=4(1)+1 \\ y_{\max }=5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_%7B%5Cmax%20%7D%3D4%281%29%2B1%20%5C%5C%20y_%7B%5Cmax%20%7D%3D5%20%5Cend%7Bgathered%7D)
Since the minimum is at the smallest value of cos, which is -1, then
![\begin{gathered} y_{\min }=4(-1)+1 \\ y_{\min }=-4+1 \\ y_{\min }=-3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_%7B%5Cmin%20%7D%3D4%28-1%29%2B1%20%5C%5C%20y_%7B%5Cmin%20%7D%3D-4%2B1%20%5C%5C%20y_%7B%5Cmin%20%7D%3D-3%20%5Cend%7Bgathered%7D)
Then substitute them in the equation of the midline
![\begin{gathered} y_{ml}=\frac{5+(-3)}{2} \\ y_{ml}=\frac{2}{2} \\ y_{ml}=1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_%7Bml%7D%3D%5Cfrac%7B5%2B%28-3%29%7D%7B2%7D%20%5C%5C%20y_%7Bml%7D%3D%5Cfrac%7B2%7D%7B2%7D%20%5C%5C%20y_%7Bml%7D%3D1%20%5Cend%7Bgathered%7D)
The answers are:
Period = 2
Equation of the midline is y = 1
Maximum = 5
Minimum = -3
Answer:
y=2x+b
Step-by-step explanation: