Answer:
(a+b)(a-b) = a^2 - b^2
Step-by-step explanation:
Answer:
equal chance
Step-by-step explanation:
1.
Left side of a graph is a line that passes through points
![A=(-1,-1)](https://tex.z-dn.net/?f=A%3D%28-1%2C-1%29)
and
![B=(1,4)](https://tex.z-dn.net/?f=B%3D%281%2C4%29)
so we can write its equation as:
![(y-y_A)=\dfrac{y_B-y_A}{x_B-x_A}(x-x_A)\\\\\\ \big(y-(-1)\big)=\dfrac{4-(-1)}{1-(-1)}\big(x-(-1)\big)\\\\\\ y+1=\dfrac{4+1}{1+1}(x+1)\\\\\\y+1=\dfrac{5}{2}(x+1)\\\\\\y+1=\dfrac{5}{2}x+\dfrac{5}{2}\\\\\\y=\dfrac{5}{2}x+\dfrac{5}{2}-1\\\\\\\boxed{y=\frac{5}{2}x+\frac{3}{2}}](https://tex.z-dn.net/?f=%28y-y_A%29%3D%5Cdfrac%7By_B-y_A%7D%7Bx_B-x_A%7D%28x-x_A%29%5C%5C%5C%5C%5C%5C%0A%5Cbig%28y-%28-1%29%5Cbig%29%3D%5Cdfrac%7B4-%28-1%29%7D%7B1-%28-1%29%7D%5Cbig%28x-%28-1%29%5Cbig%29%5C%5C%5C%5C%5C%5C%0Ay%2B1%3D%5Cdfrac%7B4%2B1%7D%7B1%2B1%7D%28x%2B1%29%5C%5C%5C%5C%5C%5Cy%2B1%3D%5Cdfrac%7B5%7D%7B2%7D%28x%2B1%29%5C%5C%5C%5C%5C%5Cy%2B1%3D%5Cdfrac%7B5%7D%7B2%7Dx%2B%5Cdfrac%7B5%7D%7B2%7D%5C%5C%5C%5C%5C%5Cy%3D%5Cdfrac%7B5%7D%7B2%7Dx%2B%5Cdfrac%7B5%7D%7B2%7D-1%5C%5C%5C%5C%5C%5C%5Cboxed%7By%3D%5Cfrac%7B5%7D%7B2%7Dx%2B%5Cfrac%7B3%7D%7B2%7D%7D)
2.
Right side of a graph is a parabola with vertex
![V=(3,-3)](https://tex.z-dn.net/?f=V%3D%283%2C-3%29)
that passes through point
![P=(1,1)](https://tex.z-dn.net/?f=P%3D%281%2C1%29)
. Its equation:
![y=a(x-x_V)^2+y_V\\\\y=a(x-3)^2+(-3)\\\\y=a(x-3)^2-3](https://tex.z-dn.net/?f=y%3Da%28x-x_V%29%5E2%2By_V%5C%5C%5C%5Cy%3Da%28x-3%29%5E2%2B%28-3%29%5C%5C%5C%5Cy%3Da%28x-3%29%5E2-3)
Substitute
![x=1](https://tex.z-dn.net/?f=x%3D1)
and
![y=1](https://tex.z-dn.net/?f=y%3D1)
to calculate parameter
![a](https://tex.z-dn.net/?f=a)
![1=a(1-3)^2-3\\\\1=a(-2)^2-3\\\\1=4a-3\\\\4a=4\quad|:4\\\\a=1](https://tex.z-dn.net/?f=1%3Da%281-3%29%5E2-3%5C%5C%5C%5C1%3Da%28-2%29%5E2-3%5C%5C%5C%5C1%3D4a-3%5C%5C%5C%5C4a%3D4%5Cquad%7C%3A4%5C%5C%5C%5Ca%3D1)
and we have the equation of parabola:
![y=a(x-3)^2-3\\\\y=1\cdot(x-3)^2-3\\\\y=(x-3)^2-3\\\\y=x^2-2\cdot x\cdot3+3^2-3\\\\y=x^2-6x+9-3\\\\\boxed{y=x^2-6x+6}](https://tex.z-dn.net/?f=y%3Da%28x-3%29%5E2-3%5C%5C%5C%5Cy%3D1%5Ccdot%28x-3%29%5E2-3%5C%5C%5C%5Cy%3D%28x-3%29%5E2-3%5C%5C%5C%5Cy%3Dx%5E2-2%5Ccdot%20x%5Ccdot3%2B3%5E2-3%5C%5C%5C%5Cy%3Dx%5E2-6x%2B9-3%5C%5C%5C%5C%5Cboxed%7By%3Dx%5E2-6x%2B6%7D)
From 1. and 2. full equation for graph is:
Answer:
Logan's average is 2,250 meters per hour
Step-by-step explanation:
60 ÷ 1/3 = 20
1/3 of an hour is 20 min
Logan swam 750 meters in 20 minutes
20min × 3 = 60min = 1 hour
750 meters × 3 = 2250
Logan's average is 2,250 meters per hour
Answer:
g = 9. I hope that I help my buddy out :)