Answer:
x=95
Step-by-step explanation:
First, we can simplify the equation. 10c-760=190. We can +760 on both sides. 10c=950. We can do 950/10=95.
Answer: Franco played for 30 minutes longer than Lain.
Step-by-step explanation:
3 times 60= 180
180-150=30 minutes
Answer:
x^3+6x^2-17x+2
Step-by-step explanation:
(x-2)*(x^2+8x-1)
=x(x^2+8x-1)-2(x^2+8x-1)
=x^3+8x^2-x-2x^2-16x+2
collect like terms
= x^3+6x^2-17x+2
Answer:
J 1
--------
x^2 -x
Step-by-step explanation:
x+1
----------
x^3-x
Factor out an x in the denominator
x+1
----------
x(x^2-1)
We can factor the terms in the parentheses because it is a difference of squares
x+1
----------
x(x-1) (x+1)
Canceling the x+1 terms
1
----------
x(x-1)
Distribute in the denominator
1
--------
x^2 -x
Answer:
<em>Center: (3,3)</em>
<em>Radius: </em>
<em />
Step-by-step explanation:
<u>Midpoint and Distance Between two Points</u>
Given two points A(x1,y1) and B(x2,y2), the midpoint M(xm,ym) between A and B has the following coordinates:
![\displaystyle x_m=\frac{x_1+x_2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_m%3D%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D)
![\displaystyle y_m=\frac{y_1+y_2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y_m%3D%5Cfrac%7By_1%2By_2%7D%7B2%7D)
The distance between both points is given by:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Point (5,7) is the center of circle A, and point (1,-1) is the center of the circle B. Given both points belong to circle C, the center of C must be the midpoint from A to B:
![\displaystyle x_m=\frac{5+1}{2}=\frac{6}{2}=3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x_m%3D%5Cfrac%7B5%2B1%7D%7B2%7D%3D%5Cfrac%7B6%7D%7B2%7D%3D3)
![\displaystyle y_m=\frac{7-1}{2}=\frac{6}{2}=3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y_m%3D%5Cfrac%7B7-1%7D%7B2%7D%3D%5Cfrac%7B6%7D%7B2%7D%3D3)
Center of circle C: (3,3)
The radius of C is half the distance between A and B:
![d=\sqrt{(1-5)^2+(-1-7)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%281-5%29%5E2%2B%28-1-7%29%5E2%7D)
![d=\sqrt{16+64}=\sqrt{80}=\sqrt{16*5}=4\sqrt{5}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B16%2B64%7D%3D%5Csqrt%7B80%7D%3D%5Csqrt%7B16%2A5%7D%3D4%5Csqrt%7B5%7D)
The radius of C is d/2:
![r =4\sqrt{5}/2 = 2\sqrt{5}](https://tex.z-dn.net/?f=r%20%3D4%5Csqrt%7B5%7D%2F2%20%3D%202%5Csqrt%7B5%7D)
Center: (3,3)
Radius: ![2\sqrt{5}](https://tex.z-dn.net/?f=2%5Csqrt%7B5%7D)