To solve this problem, we need to know that the adjacent interior angles (2 and 5, or 3 and 4) between two parallel lines are supplementary.
This means that ∠2+∠5 = 180 °
which means
x+50 + 4x+30 = 180
collect similar terms and solve
5x + 80 = 180
5x = 180-80 = 100
x=20 °
∠2 = x+50 = 20+50 = 70 °
But ∠ 1 = ∠ 2 (vertical angles)
therefore
∠ 1 = 70 °
Find the equations of the lines...
First find the slope...(y2-y1)/(x2-x1)=m
m=(6-1)/(8-5)=5/3 and it passes through (5,1) so
y=mx+b becomes:
y=5x/3+b and using (5,1)
1=5(5)/3+b
1=25/3+b
3/3-25/3=b
b=-22/3 so
y1=(5x-22)/3
.... now y2...
m=(8-3)/(-1--4)=5/3 (note it has the same slope as y1...
y=5x/3+b and using the point (-1,8)
8=5(-1)/3+b
8=-5/3+b
24/3+5/3=b
b=29/3, now note that the y-intercept is different...
y2=(5x+29)/3
Since these lines have the same slope but different y-intercepts, they are parallel to each other. (and will never intersect.)
Greatest Common Factor: 12-1/3 = -4/12, 7/4 = 21/12-4/12 + 21/12 = 17/12
Answer in simplest form: 17/12
Answer:
x - 3
Step-by-step explanation:
We know that the area of a square is length times width.
We also know that a quadratic can be factored:
(x - 3)²
So if each side is (x - 3), then when we do length times width, we get x² - 6x + 9. So our answer is choice D.
The square root of 255+266 is 241. I can't help you with shortcuts as I'm bad at explaining, but I'm sure there are websites that can help you.
