Answer:
The measure of each angle is 143 degrees.
Step-by-step explanation:
We are given the following in the question:
A nonagon in which measure of seven angles are:
138, 154, 145, 132, 128, 147, 130.
Angle sum property of a nonagon:
- The sum of interior angles if a nonagon are 1260 degrees.
Let the two equal angle of nonagon be x degrees. Thus, we can write:
![138+154+ 145+132+ 128+ 147+ 130+2x = 1260\\\Rightarrow 974 + 2x = 1260\\\Rightarrow 2x = 1260 - 974\\\Rightarrow 2x = 286\\\Rightarrow x = 143](https://tex.z-dn.net/?f=138%2B154%2B%20145%2B132%2B%20128%2B%20147%2B%20130%2B2x%20%3D%201260%5C%5C%5CRightarrow%20974%20%2B%202x%20%3D%201260%5C%5C%5CRightarrow%202x%20%3D%201260%20-%20974%5C%5C%5CRightarrow%202x%20%3D%20286%5C%5C%5CRightarrow%20x%20%3D%20143)
Thus, the measure of two equal angles is 143 degrees.
Answer:
-3
Step-by-step explanation:
Numerator = y
Denominator = x
The change in x is +1
The change in y is -3
= -3
Answer: 1. y = 2(x + 4)² - 3
![\bold{2.\quad y=-\dfrac{1}{3}(x+8)^2-7}](https://tex.z-dn.net/?f=%5Cbold%7B2.%5Cquad%20y%3D-%5Cdfrac%7B1%7D%7B3%7D%28x%2B8%29%5E2-7%7D)
![\bold{3.\quad y=-\dfrac{1}{2}(x-7)^2+1}](https://tex.z-dn.net/?f=%5Cbold%7B3.%5Cquad%20y%3D-%5Cdfrac%7B1%7D%7B2%7D%28x-7%29%5E2%2B1%7D)
<u>Step-by-step explanation:</u>
Notes: The vertex form of a parabola is y = a(x - h)² + k
- (h, k) is the vertex
- p is the distance from the vertex to the focus
![\bullet\quad a=\dfrac{1}{4p}](https://tex.z-dn.net/?f=%5Cbullet%5Cquad%20a%3D%5Cdfrac%7B1%7D%7B4p%7D)
1)
![\text{Vertex}=(-4,-3)\qquad \text{Directrix}:y=-\dfrac{25}{8}\\\\\text{Given}:(h, k)=(-4, 3)\\\\p=\dfrac{-24}{8}-\dfrac{-25}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2](https://tex.z-dn.net/?f=%5Ctext%7BVertex%7D%3D%28-4%2C-3%29%5Cqquad%20%5Ctext%7BDirectrix%7D%3Ay%3D-%5Cdfrac%7B25%7D%7B8%7D%5C%5C%5C%5C%5Ctext%7BGiven%7D%3A%28h%2C%20k%29%3D%28-4%2C%203%29%5C%5C%5C%5Cp%3D%5Cdfrac%7B-24%7D%7B8%7D-%5Cdfrac%7B-25%7D%7B8%7D%3D%5Cdfrac%7B1%7D%7B8%7D%5C%5C%5C%5C%5C%5Ca%3D%5Cdfrac%7B1%7D%7B4p%7D%3D%5Cdfrac%7B1%7D%7B4%28%5Cfrac%7B1%7D%7B8%7D%29%7D%3D%5Cdfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D2)
Now input a = 2 and (h, k) = (-4, -3) into the equation y = a(x - h)² + k
y = 2(x + 4)² - 3
******************************************************************************************
2)
![\text{Vertex}=(-8,-7)\qquad \text{Directrix}:y=-\dfrac{-25}{4}\\\\\text{Given}:(h, k)=(-8, -7)\\\\p=\dfrac{-28}{4}-\dfrac{-25}{4}=\dfrac{-3}{4}}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-3}{4})}=\dfrac{1}{-3}=-\dfrac{1}{3}](https://tex.z-dn.net/?f=%5Ctext%7BVertex%7D%3D%28-8%2C-7%29%5Cqquad%20%5Ctext%7BDirectrix%7D%3Ay%3D-%5Cdfrac%7B-25%7D%7B4%7D%5C%5C%5C%5C%5Ctext%7BGiven%7D%3A%28h%2C%20k%29%3D%28-8%2C%20-7%29%5C%5C%5C%5Cp%3D%5Cdfrac%7B-28%7D%7B4%7D-%5Cdfrac%7B-25%7D%7B4%7D%3D%5Cdfrac%7B-3%7D%7B4%7D%7D%5C%5C%5C%5C%5C%5Ca%3D%5Cdfrac%7B1%7D%7B4p%7D%3D%5Cdfrac%7B1%7D%7B4%28%5Cfrac%7B-3%7D%7B4%7D%29%7D%3D%5Cdfrac%7B1%7D%7B-3%7D%3D-%5Cdfrac%7B1%7D%7B3%7D)
Now input a = -1/3 and (h, k) = (-8, -7) into the equation y = a(x - h)² + k
![\bold{y=-\dfrac{1}{3}(x+8)^2-7}](https://tex.z-dn.net/?f=%5Cbold%7By%3D-%5Cdfrac%7B1%7D%7B3%7D%28x%2B8%29%5E2-7%7D)
******************************************************************************************
3)
![\text{Focus}=\bigg(7,\dfrac{1}{2}\bigg)\qquad \text{Directrix}:y=\dfrac{3}{2}](https://tex.z-dn.net/?f=%5Ctext%7BFocus%7D%3D%5Cbigg%287%2C%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%29%5Cqquad%20%5Ctext%7BDirectrix%7D%3Ay%3D%5Cdfrac%7B3%7D%7B2%7D)
The midpoint of the focus and directrix is the y-coordinate of the vertex:
![\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1](https://tex.z-dn.net/?f=%5Cdfrac%7Bfocus%2Bdirectrix%7D%7B2%7D%3D%5Cdfrac%7B%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B3%7D%7B2%7D%7D%7B2%7D%3D%5Cdfrac%7B%5Cfrac%7B4%7D%7B2%7D%7D%7B2%7D%3D%5Cdfrac%7B2%7D%7B2%7D%3D1)
The x-coordinate of the vertex is given in the focus as 7
(h, k) = (7, 1)
Now let's find the a-value:
![p=\dfrac{2}{2}-\dfrac{3}{2}=\dfrac{-1}{2}}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}](https://tex.z-dn.net/?f=p%3D%5Cdfrac%7B2%7D%7B2%7D-%5Cdfrac%7B3%7D%7B2%7D%3D%5Cdfrac%7B-1%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5Ca%3D%5Cdfrac%7B1%7D%7B4p%7D%3D%5Cdfrac%7B1%7D%7B4%28%5Cfrac%7B-1%7D%7B2%7D%29%7D%3D%5Cdfrac%7B1%7D%7B-2%7D%3D-%5Cdfrac%7B1%7D%7B2%7D)
Now input a = -1/2 and (h, k) = (7, 1) into the equation y = a(x - h)² + k
![\bold{y=-\dfrac{1}{2}(x-7)^2+1}](https://tex.z-dn.net/?f=%5Cbold%7By%3D-%5Cdfrac%7B1%7D%7B2%7D%28x-7%29%5E2%2B1%7D)
Answer:
$180
Step-by-step explanation:
Since the discount is 40 percent and is also $72, We will cross multiply. 72 x 100 = 40 x what?
7200/40 = 180
The mirror was originally $180.
14 girls
Total students = 14+12 = 26
14/26 = 7/13
Answer = 7/13