Here, we are required to determine the solution to the equation: 13.7y = 6.2y + 30?
The solution to the equation is y = 7.5
The solution is thus,
- 13.7y = 6.2y + 30
- 13.7y - 6.2y = 30
- 7.5y = 30
Therefore, y = 30/7.5 = 4
Therefore, y = 4 is the solution to the equation.
Read more:
brainly.com/question/12184348
The equation of the line is ![y=-\frac{2}{5}x-5](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B5%7Dx-5)
Explanation:
Given that the line passes through the points (-5,-3)
The slope of the line is ![m=-\frac{2}{5}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B2%7D%7B5%7D)
We need to determine the equation of the line.
<u>Equation of the line:</u>
The equation of the line can be determined using the formula,
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Let us substitute the points (-5,-3) and the slope
in the above formula.
Thus, we have;
![y+3=-\frac{2}{5}(x+5)](https://tex.z-dn.net/?f=y%2B3%3D-%5Cfrac%7B2%7D%7B5%7D%28x%2B5%29)
Simplifying, we get;
![y+3=-\frac{2}{5}x-2](https://tex.z-dn.net/?f=y%2B3%3D-%5Cfrac%7B2%7D%7B5%7Dx-2)
Subtracting 3 from both sides of the equation, we get;
![y=-\frac{2}{5}x-5](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B5%7Dx-5)
Hence, the equation of the line in slope - intercept form is ![y=-\frac{2}{5}x-5](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B5%7Dx-5)
19)
6/x = x/12
x^2 = 72
x = √72
x = 6√2
y^2 = 12^2 + (√72)^2
y^2 = 144 + 72
y^2 = 216
y = 6√6
21)
14 - 8 = 6
y/8 = 6/y
y^2 = 48
y = √48
y = 4√3
x^2 = 6^2 +(√48)^2
x^2 = 36 + 48
x^2 = 84
x = √84
x = 2√21
Answer:
Other Endpoint (x₂,y₂) = (16,25)
Step-by-step explanation:
We are given endpoint = (4,-9) and midpoint(10,8) we need to find the other endpoint of line segment.
Let other endpoint be (x₂,y₂)
The formula used to find other endpoint is using formula of midpoint
![M(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=M%28x_m%2Cy_m%29%3D%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%29)
We have ![x_1=4 , y_1= -9 , x_m=10, y_m=8](https://tex.z-dn.net/?f=x_1%3D4%20%2C%20y_1%3D%20-9%20%2C%20x_m%3D10%2C%20y_m%3D8)
Using formula and finding (x₂,y₂)
![M(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\(10,8)=(\frac{4+x_2}{2},\frac{-9+y_2}{2})\\10=\frac{4+x_2}{2} , 8=\frac{-9+y_2}{2}\\Finding\ x_2\\10*2=4+x_2 \\20=4+x_2\\x_2=20-4, \\x_2=16\\Finding \ y_2\\8*2=-9+y_2\\16=-9+y_2\\y_2=16+9\\y_2=25](https://tex.z-dn.net/?f=M%28x_m%2Cy_m%29%3D%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%29%5C%5C%2810%2C8%29%3D%28%5Cfrac%7B4%2Bx_2%7D%7B2%7D%2C%5Cfrac%7B-9%2By_2%7D%7B2%7D%29%5C%5C10%3D%5Cfrac%7B4%2Bx_2%7D%7B2%7D%20%2C%208%3D%5Cfrac%7B-9%2By_2%7D%7B2%7D%5C%5CFinding%5C%20x_2%5C%5C10%2A2%3D4%2Bx_2%20%5C%5C20%3D4%2Bx_2%5C%5Cx_2%3D20-4%2C%20%5C%5Cx_2%3D16%5C%5CFinding%20%5C%20y_2%5C%5C8%2A2%3D-9%2By_2%5C%5C16%3D-9%2By_2%5C%5Cy_2%3D16%2B9%5C%5Cy_2%3D25)
So, x₂=16 and y₂=25.
So, Other Endpoint (x₂,y₂) = (16,25)