Answer: (1,5)
Step-by-step explanation:
1. To solve this, use the midpoint formula:
![(\frac{x1+x2}{2}, \frac{y1+y2}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx1%2Bx2%7D%7B2%7D%2C%20%5Cfrac%7By1%2By2%7D%7B2%7D%29)
2. Insert your values into the equation to get your answer
![(\frac{-3+5}{2}, \frac{5+5}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B-3%2B5%7D%7B2%7D%2C%20%5Cfrac%7B5%2B5%7D%7B2%7D%29)
3. Simplify the formula
(1, 5)
4. The midpoint is (1, 5)
The sides of this triangle are 5x,6x abd 7x,
The perimeter of a triangle is the sum of all sides
We can suggest this inequation:
5x+6x+7x<54
18x<54
x<54/18
x<3
Therefore the lenght of the longest side would be:
7x<(7*3)
7x<21
Answer: the lenght of the longest side would be <21
So since both of these lines are solid lines and not dashed, that means that the inequalities will have either ≤ or ≥.
Starting with the vertical line, since every point on that line is (0,y), this means that this line is x_0. And since the shaded region on this line is to the left of this line, this means that this inequality is x ≤ 0.
Now with this next line, I'll be forming it using the slope-intercept form (y = mx+b, m = slope and b = y-intercept). From looking at the graph, we can tell that the y-intercept is (-5,0). To find the slope, the equation is
. For this, the two points I'll be using are (-4,-8) and (8,1).
Our equation will look and be solved like this: ![\frac{1-(-8)}{8-(-4)}=\frac{9}{12} =\frac{3}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1-%28-8%29%7D%7B8-%28-4%29%7D%3D%5Cfrac%7B9%7D%7B12%7D%20%3D%5Cfrac%7B3%7D%7B4%7D%20%20)
And since the region shaded is below the line, ≤ symbol will be used with our inequality.
Using the information above, our inequality is y ≤ 3/4x - 5.
In short, the system of inequalities is x ≤ 0 and y ≤ 3/4x - 5.