Answer:
See below:
Step-by-step explanation:
We can first setup an equation by doing the following:
![4(2-x) = 3(x+1)\\8-4x=3x+3\\8-7x=3\\-7x=3-8\\-7x=-5\\x=-5/-7 (5/7)](https://tex.z-dn.net/?f=4%282-x%29%20%3D%203%28x%2B1%29%5C%5C8-4x%3D3x%2B3%5C%5C8-7x%3D3%5C%5C-7x%3D3-8%5C%5C-7x%3D-5%5C%5Cx%3D-5%2F-7%20%20%285%2F7%29)
Whole proccess above!
If you would like an explanation, please let me know so.
Its basically algebra and it's mainly on how you interpret it!
Have a nice day!
Answer:
The coordinates of K is (-5,1)
Step-by-step explanation:
Given
![J = (-9,-5)](https://tex.z-dn.net/?f=J%20%3D%20%28-9%2C-5%29)
![L = (5,16)](https://tex.z-dn.net/?f=L%20%3D%20%285%2C16%29)
![JK:KL = 2:5](https://tex.z-dn.net/?f=JK%3AKL%20%3D%202%3A5)
Required
Determine K
Using Line ratio formula;
We have:
![K(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})](https://tex.z-dn.net/?f=K%28x%2Cy%29%20%3D%20%28%5Cfrac%7Bmx_2%20%2B%20nx_1%7D%7Bm%2Bn%7D%2C%5Cfrac%7Bmy_2%20%2B%20ny_1%7D%7Bm%2Bn%7D%29)
Where
![(x_1,y_1) = (-9,-5)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-9%2C-5%29)
![(x_2,y_2) = (5,16)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%285%2C16%29)
![m:n = 2:5](https://tex.z-dn.net/?f=m%3An%20%3D%202%3A5)
So; we have:
![K(x,y) = (\frac{2 * 5 + 5 * -9}{2+5},\frac{2 * 16 + 5 * -5}{2+5})](https://tex.z-dn.net/?f=K%28x%2Cy%29%20%3D%20%28%5Cfrac%7B2%20%2A%205%20%2B%205%20%2A%20-9%7D%7B2%2B5%7D%2C%5Cfrac%7B2%20%2A%2016%20%2B%205%20%2A%20-5%7D%7B2%2B5%7D%29)
![K(x,y) = (\frac{10 -45}{7},\frac{32 -25}{7})](https://tex.z-dn.net/?f=K%28x%2Cy%29%20%3D%20%28%5Cfrac%7B10%20-45%7D%7B7%7D%2C%5Cfrac%7B32%20-25%7D%7B7%7D%29)
![K(x,y) = (\frac{-35}{7},\frac{7}{7})](https://tex.z-dn.net/?f=K%28x%2Cy%29%20%3D%20%28%5Cfrac%7B-35%7D%7B7%7D%2C%5Cfrac%7B7%7D%7B7%7D%29)
![K(x,y) = (-5,1)](https://tex.z-dn.net/?f=K%28x%2Cy%29%20%3D%20%28-5%2C1%29)
Answer:
by alternate interior angles
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
<u><em>Alternate interior angles</em></u> are formed when a transversal (in this problem line T) passes through two lines (line L1 and line L2) . The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. When the lines are parallel, the alternate interior angles are congruent.
so
----> by alternate interior angles
----> by alternate interior angles
we have that
![m\angle 3=39^o](https://tex.z-dn.net/?f=m%5Cangle%203%3D39%5Eo)
therefore
![m\angle 6=39^o](https://tex.z-dn.net/?f=m%5Cangle%206%3D39%5Eo)
See the attachment on how to graph this problem.
(0-0)÷(-3-5)=0
it is zero