Answer:
12
Step-by-step explanation:
Since M is a midpoint of LN, we can see 3x equal to x+8. Remove 1 x to get 2x=8. Solve for x to get x=4. <em>Note that this is not the end to your problem. They asked for the length of MN, not the value of x.</em><em> </em>Plugging x into MN give you 4+8, which is 12.
(If you need to show work, here it is)
3x=x+8
2x=8
x=4
MN=x+8
MN=4+8
MN=12
Given :
Heather spend 2/7 of her money buying presents.
She then had €48.65 left.
To Find :
The initial amount of money she had.
Solution :
Let, initial amount she had is €x.
So,
![x - \dfrac{2x}{7} = 48.65\\\\\dfrac{5x}{7} = 48.65 \\\\x = \dfrac{48.65\times 7}{5}](https://tex.z-dn.net/?f=x%20-%20%5Cdfrac%7B2x%7D%7B7%7D%20%3D%2048.65%5C%5C%5C%5C%5Cdfrac%7B5x%7D%7B7%7D%20%3D%2048.65%20%5C%5C%5C%5Cx%20%3D%20%5Cdfrac%7B48.65%5Ctimes%207%7D%7B5%7D)
x = €68.11
Therefore, initially he had €68.11 .
Slope formula: m = ![\frac{(y2 - y1)}{(x2 - x1)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28y2%20-%20y1%29%7D%7B%28x2%20-%20x1%29%7D)
<em>Slope of segment BC:</em>
First, we substitute B (5, 2) for (x₁, y₁) and C (11, -6) for (x₂, y₂)
m BC =
= ![\frac{-8}{6} = -\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-8%7D%7B6%7D%20%3D%20-%5Cfrac%7B4%7D%7B3%7D)
Slope of BC = A. ![-\frac{4}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7B3%7D)
<em>Slope of segment AB:</em>
We substitute A (-3, -4) for (x₁, y₁) and B (5, 2) for (x₂, y₂)
m AB = ![\frac{(2 - (-4))}{(5 - (-3))} = \frac{(2 + 4)}{(5 + 3)} = \frac{6}{8} = \frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%282%20-%20%28-4%29%29%7D%7B%285%20-%20%28-3%29%29%7D%20%3D%20%5Cfrac%7B%282%20%2B%204%29%7D%7B%285%20%2B%203%29%7D%20%3D%20%5Cfrac%7B6%7D%7B8%7D%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D)
Slope of AB = C. ![\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D)
a straight line = 180 degrees so:
4x+16 + 92 = 180
4x +108 = 180
4x=72
x = 72/4 = 18
x= 18