Answer:
x + 49 + 28 = 180
Step-by-step explanation:
The angle adjacent to x on the left is vertically opposite 49° and is congruent.
The 3 angles then lie on a straight line and sum to 180° , that is
x + 49 + 28 = 180
Answer:
4
Step-by-step explanation:
hope this helps!
A linear equation is represented as:
.
The equation of the line is: ![y =3x - 14](https://tex.z-dn.net/?f=y%20%3D3x%20-%2014)
First, we calculate the slope (m) of ![6x + 18y = 11](https://tex.z-dn.net/?f=6x%20%2B%2018y%20%3D%2011)
Make y the subject
![18y = -6x + 11](https://tex.z-dn.net/?f=18y%20%3D%20-6x%20%2B%2011)
Divide by 18
![y = -\frac{1}{3}x + \frac{11}{18}](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B3%7Dx%20%2B%20%5Cfrac%7B11%7D%7B18%7D)
In ![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
slope
So, the slope of
is:
![m = -\frac 13](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%2013)
Since, the line is perpendicular to ![6x + 18y = 11](https://tex.z-dn.net/?f=6x%20%2B%2018y%20%3D%2011)
The slope of the line is:
![m_1 = -\frac{1}{m}](https://tex.z-dn.net/?f=m_1%20%3D%20-%5Cfrac%7B1%7D%7Bm%7D)
So, we have:
![m_1 = -\frac{1}{-1/3}](https://tex.z-dn.net/?f=m_1%20%3D%20-%5Cfrac%7B1%7D%7B-1%2F3%7D)
![m_1 = 3](https://tex.z-dn.net/?f=m_1%20%3D%203)
The line passes through (4,-2).
So, the equation is:
![y =m(x - x_1) + y_1](https://tex.z-dn.net/?f=y%20%3Dm%28x%20-%20x_1%29%20%2B%20y_1)
This gives:
![y =3(x - 4) -2](https://tex.z-dn.net/?f=y%20%3D3%28x%20-%204%29%20-2)
![y =3x - 12 -2](https://tex.z-dn.net/?f=y%20%3D3x%20-%2012%20-2)
![y =3x - 14](https://tex.z-dn.net/?f=y%20%3D3x%20-%2014)
Hence, the linear equation is:
![y =3x - 14](https://tex.z-dn.net/?f=y%20%3D3x%20-%2014)
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