Answer:
B) 105.20
Step-by-step explanation:
491.60 + 157.68 - 68.44 = 581.20
Answer is 82
substitute z for 9
9^2 = 81+ 1= 82
Answer:
![x + 2y= 2](https://tex.z-dn.net/?f=x%20%2B%202y%3D%202)
Step-by-step explanation:
Given
Points:
![F = (4,9)](https://tex.z-dn.net/?f=F%20%3D%20%284%2C9%29)
![G = (1,3)](https://tex.z-dn.net/?f=G%20%3D%20%281%2C3%29)
Required
Determine the equation of line that is perpendicular to the given points and that pass through ![(2,0)](https://tex.z-dn.net/?f=%282%2C0%29)
First, we need to determine the slope, m of FG
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Where
--- ![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
--- ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
![m = \frac{3 - 9}{1 - 4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3%20-%209%7D%7B1%20-%204%7D)
![m = \frac{- 6}{- 3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-%206%7D%7B-%203%7D)
![m =2](https://tex.z-dn.net/?f=m%20%3D2)
The question says the line is perpendicular to FG.
Next, we determine the slope (m2) of the perpendicular line using:
![m_2 = -\frac{1}{m}](https://tex.z-dn.net/?f=m_2%20%3D%20-%5Cfrac%7B1%7D%7Bm%7D)
![m_2 = -\frac{1}{2}](https://tex.z-dn.net/?f=m_2%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
The equation of the line is then calculated as:
![y - y_1 = m_2(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20m_2%28x%20-%20x_1%29)
Where
![m_2 = -\frac{1}{2}](https://tex.z-dn.net/?f=m_2%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
![(x_1,y_1) = (2,0)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%282%2C0%29)
![y - 0 = -\frac{1}{2}(x - 2)](https://tex.z-dn.net/?f=y%20-%200%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%28x%20-%202%29)
![y = -\frac{1}{2}(x - 2)](https://tex.z-dn.net/?f=y%20%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%28x%20-%202%29)
![y = -\frac{1}{2}x + 1](https://tex.z-dn.net/?f=y%20%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%20%2B%201)
Multiply through by 2
![2y = -x + 2](https://tex.z-dn.net/?f=2y%20%3D%20-x%20%2B%202)
Add x to both sides
![x + 2y= -x +x+ 2](https://tex.z-dn.net/?f=x%20%2B%202y%3D%20-x%20%2Bx%2B%202)
![x + 2y= 2](https://tex.z-dn.net/?f=x%20%2B%202y%3D%202)
Hence, the line of the equation is ![x + 2y= 2](https://tex.z-dn.net/?f=x%20%2B%202y%3D%202)
Answer:
Step-by-step explanation:
x² - 2x + y² - 4y - 4 = 0
x² - 2x + y² - 4y = 4
complete the squares
(x² - 2x + x₀) + (y² - 4y + y₀) = 4
the unknown number will be the square of half of the x¹ coefficient
(x² - 2x + 1) + (y² - 4y + 4) = 4 + 1 + 4
(x - 1)² + (y - 2)² = 9
This tells us that the circle is centered on (1, 2)
Which is also a point on the diameter
2x - y + a = 0
a = y - 2x
a = 2 - 2(1)
a = 0