Answer:
The equation for the perpendicular bisector of the line segment will be:
![y=-\frac{7}{2}x-13](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B7%7D%7B2%7Dx-13)
Step-by-step explanation:
Given the endpoints of the line segments
Determining the slope between (5,-4) and (-9, -8)
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(5,\:-4\right),\:\left(x_2,\:y_2\right)=\left(-9,\:-8\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%285%2C%5C%3A-4%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%28-9%2C%5C%3A-8%5Cright%29)
![m=\frac{-8-\left(-4\right)}{-9-5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-8-%5Cleft%28-4%5Cright%29%7D%7B-9-5%7D)
![m=\frac{2}{7}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2%7D%7B7%7D)
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = 2/7
Thus, the slope of the the new perpendicular line = – 1/m = (-1)/(2/7)= -7/2
Next, determining the mid-point between (5,-4) and (-9, -8)
![\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BMidpoint%5C%3Aof%5C%3A%7D%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3A%5Cquad%20%5Cleft%28%5Cfrac%7Bx_2%2Bx_1%7D%7B2%7D%2C%5C%3A%5C%3A%5Cfrac%7By_2%2By_1%7D%7B2%7D%5Cright%29)
![\left(x_1,\:y_1\right)=\left(5,\:-4\right),\:\left(x_2,\:y_2\right)=\left(-9,\:-8\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%285%2C%5C%3A-4%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%28-9%2C%5C%3A-8%5Cright%29)
![=\left(\frac{-9+5}{2},\:\frac{-8-4}{2}\right)](https://tex.z-dn.net/?f=%3D%5Cleft%28%5Cfrac%7B-9%2B5%7D%7B2%7D%2C%5C%3A%5Cfrac%7B-8-4%7D%7B2%7D%5Cright%29)
Refine
![=\left(-2,\:-6\right)](https://tex.z-dn.net/?f=%3D%5Cleft%28-2%2C%5C%3A-6%5Cright%29)
We know that the point-slope form of equation of line is
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
where
- m is the slope of the line
substituting the slope of the perpendicular line -7/2 and the point (-2, -6)
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
![y-\left(-6\right)=-\frac{7}{2}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-%5Cleft%28-6%5Cright%29%3D-%5Cfrac%7B7%7D%7B2%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
![y+6=-\frac{7}{2}\left(x+2\right)](https://tex.z-dn.net/?f=y%2B6%3D-%5Cfrac%7B7%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29)
Subtract 6 from both sides
![y+6-6=-\frac{7}{2}\left(x+2\right)-6](https://tex.z-dn.net/?f=y%2B6-6%3D-%5Cfrac%7B7%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29-6)
![y=-\frac{7}{2}x-13](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B7%7D%7B2%7Dx-13)
Therefore, the equation for the perpendicular bisector of the line segment will be:
![y=-\frac{7}{2}x-13](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B7%7D%7B2%7Dx-13)
Answer: x = 1, y = 1
Step-by-step explanation:
Step 1: Solve for x
Multiply bottom equation by 2.
5x + 2y = 7
2(3x – y = 2)
___________
5x + 2y = 7
+ 6x - 2y = 4
___________
11x = 11 divide each side by 11 x = 1
Step 2: Solve for y
Substitute x=1 into any equation. We will do equation 1.
5x + 2y = 7 5*1 + 2y = 7
5 + 2y = 7
subtract 5 from each side.
2y = 2 divide each side by 2
y = 1
Answer:
283500
Step-by-step explanation:
Your answer is
![383000-99500](https://tex.z-dn.net/?f=383000-99500)
Which is 283500
Hope this helps Please hit the crown :D
Answer:
I believe the answer for this question would be C:14
I hope this is correct and helps
Answer:
16.2$
Step-by-step explanation:
Price of the notebooks: 15$
Tax Rate: 8%
Tax: 15$ * 8% = 1.2$
Price after Tax: 15$ + 1.2$ = 16.2$