Answer:
(1+√7,0),(1−√7,0)
Step-by-step explanation:
You can't factor the expression evenly, so use the quadratic formula.
a = 2
b= -4
c= -12
![\frac{-b+\sqrt{b^{2}-4ac } }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B%5Csqrt%7Bb%5E%7B2%7D-4ac%20%7D%20%7D%7B2a%7D)
![\frac{4+\sqrt{16{}-4(2)(-12)} }{2(2)}](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B%5Csqrt%7B16%7B%7D-4%282%29%28-12%29%7D%20%7D%7B2%282%29%7D)
![\frac{4+\sqrt{16-4(-24)} }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B%5Csqrt%7B16-4%28-24%29%7D%20%7D%7B4%7D)
![\frac{4+\sqrt{16+96} }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B%5Csqrt%7B16%2B96%7D%20%7D%7B4%7D)
![\frac{4+\sqrt{112} }{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B%5Csqrt%7B112%7D%20%7D%7B4%7D)
![\sqrt{112} = 4\sqrt{7}](https://tex.z-dn.net/?f=%5Csqrt%7B112%7D%20%3D%204%5Csqrt%7B7%7D)
End result: (1+√7,0),(1−√7,0)
Answer:
Step-by-step explanation:
Standard form of a circle is given by,
(x - a)² + (y - b)² = r²
Here, (a, b) is the center and 'r' is the radius of the circle.
For a circle having center (8, -4) and radius r = 1
Equation of the circle will be,
(x - 8)² + (y + 4)² = 1²
(x - 8)² + (y + 4)² = 1
Option (1) is the answer.
Question (2)
Circle with the center (-1, 0) and a point (2, -4) on it,
Radius of the circle = Distance between the center and the given point on circumference
= ![\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%7D)
= ![\sqrt{(-1-2)^2+(0+4)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-1-2%29%5E2%2B%280%2B4%29%5E2%7D)
= ![\sqrt{9+16}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2B16%7D)
= 5
Therefore, equation of the circle will be,
(x + 1)² + (y - 0)² = 5²
(x + 1)² + y² = 25
Answer:
Step-by-step explanation:
geometric progresion formula:
![a_n=a_1*r^{n-1}\\a_1=0.5\\r=10\\a_n=0.5*10^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_1%2Ar%5E%7Bn-1%7D%5C%5Ca_1%3D0.5%5C%5Cr%3D10%5C%5Ca_n%3D0.5%2A10%5E%7Bn-1%7D)
Answer:
18.84 ft
Step-by-step explanation:
The formula for the circumference of a circle is C = πd or C = 2πr
We will use C = 2πr since we have r given in the photo
- We just need to substitute our values into the formula:
- C = 2(3.14)(3) = 18.84 ft
Do you have to show ur work?