Answer:
82
Step-by-step explanation:
Answer:
0.375
Step-by-step explanation:
Answer:
Step-by-step explanation:
A kite is a quadrilateral that has only one line of symmetry, and bisecting diagonals.
From the graph,
AB = 6 units
BC = 8 units
CD = 8 units
AD = 6 units
i. Has exactly one pair of congruent sides. Examples are; AB = AD and BC = CD.
ii. The diagonals are perpendicular. AC is at right angle to DB.
iii. The diagonals bisect each other. AC bisects DB, or vice versa.
Therefore, quadrilateral ABCD is a kite.
Answer: 130 degrees
Step-by-step explanation:
105+80+45+x=360
230+x=360
-230 both sides
X=130 degrees
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