Answer:
8.5
Step-by-step explanation:
So the line segment that is tangent to the circle is 8, and AO is 11.7.
When you connect them, they are perpendicular, so you have a right triangle with one unknown leg that we will call X, a leg that is 8, and a hypotenuse that is 11.7.
If you use the Pythagorean Theorem, you will find that the leg is √72.89, which is approximately 8.5.
That leg is the radius.
This might be wrong so check it.
Answer:
The slope of the line is 6
Step-by-step explanation:
The slope of the line is given by
m=(y2-y1)/(x2-x1)
m =(8-2)/(2-1)
= 6/1
The slope of the line is 6
Y-Y=m(X-X)
Y-2=-5(X-6)
Y-2=-5x+30
Y=-5x+32
0.026, 0.071, 0.079, 0.089
Given
![\begin{gathered} 4x+2y=18 \\ y=-2x+9 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%204x%2B2y%3D18%20%5C%5C%20y%3D-2x%2B9%20%5Cend%7Bgathered%7D)
Part A
Checking for
![\begin{gathered} (4,1) \\ x=4 \\ y=1 \\ 4x+2y=18\ldots\text{equation 1} \\ \text{and } \\ y=-2x+9\ldots\text{equation 2} \\ substitute\text{ for x=4 and y=1 in equation 1} \\ 4(4)+2(1)=18 \\ 16+2=18 \\ 18=18 \\ substitute\text{ for x=4 and y=1 in equation }2 \\ 1=-2(4)+9 \\ 1=-8+9_{}_{} \\ 1=1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%284%2C1%29%20%5C%5C%20x%3D4%20%5C%5C%20y%3D1%20%5C%5C%204x%2B2y%3D18%5Cldots%5Ctext%7Bequation%201%7D%20%5C%5C%20%5Ctext%7Band%20%7D%20%5C%5C%20y%3D-2x%2B9%5Cldots%5Ctext%7Bequation%202%7D%20%5C%5C%20substitute%5Ctext%7B%20for%20x%3D4%20and%20y%3D1%20in%20equation%201%7D%20%5C%5C%204%284%29%2B2%281%29%3D18%20%5C%5C%2016%2B2%3D18%20%5C%5C%2018%3D18%20%5C%5C%20substitute%5Ctext%7B%20for%20x%3D4%20and%20y%3D1%20in%20equation%20%7D2%20%5C%5C%201%3D-2%284%29%2B9%20%5C%5C%201%3D-8%2B9_%7B%7D_%7B%7D%20%5C%5C%201%3D1%20%5Cend%7Bgathered%7D)
Yes (4,1) is a solution
Part B
![\begin{gathered} x=-5\text{ and y=19} \\ 4x+2y=18 \\ 4(-5)+2(19)=18 \\ -20+38=18 \\ 18=18 \\ \text{and} \\ y=-2x+9 \\ 19=-2(-5)+9 \\ 19=10+9 \\ 19=19 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D-5%5Ctext%7B%20and%20y%3D19%7D%20%5C%5C%204x%2B2y%3D18%20%5C%5C%204%28-5%29%2B2%2819%29%3D18%20%5C%5C%20-20%2B38%3D18%20%5C%5C%2018%3D18%20%5C%5C%20%5Ctext%7Band%7D%20%5C%5C%20y%3D-2x%2B9%20%5C%5C%2019%3D-2%28-5%29%2B9%20%5C%5C%2019%3D10%2B9%20%5C%5C%2019%3D19%20%5Cend%7Bgathered%7D)
Yes (-5,19) it is a solution
Part C
![\begin{gathered} x=5\text{ and y=}-3 \\ 4x+2y=18 \\ 4(5)+2(-3)=18 \\ 20-6=18 \\ 14\ne18 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D5%5Ctext%7B%20and%20y%3D%7D-3%20%5C%5C%204x%2B2y%3D18%20%5C%5C%204%285%29%2B2%28-3%29%3D18%20%5C%5C%2020-6%3D18%20%5C%5C%2014%5Cne18%20%5Cend%7Bgathered%7D)
No (5,-3) is not a solution
Part D
![\begin{gathered} x=6\text{ and y=0} \\ 4x+2y=18 \\ 4(6)+2(0)=18 \\ 24+0=18 \\ 24\ne18 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D6%5Ctext%7B%20and%20y%3D0%7D%20%5C%5C%204x%2B2y%3D18%20%5C%5C%204%286%29%2B2%280%29%3D18%20%5C%5C%2024%2B0%3D18%20%5C%5C%2024%5Cne18%20%5Cend%7Bgathered%7D)
No (6,0) it is not solution
The final answer