The formula for a straight line is y=mx+b, where m is the slope and b is the y-intercept.
To find out the slope, we use a formula known as rise/run.
Rise means how high a point goes between any two points and run is how far the space is between any two points.
We can see that there are two points give to us. Now we ask our self how high do we have to go to reach the second points’ height. If we count it we go five UP. Meaning that the rise is positive 5.
Now we see how far the two points are. If we count it, we go 1 space the LEFT meaning -1 since going left on a graph means x is getting smaller.
Now that we have he two values, we put them into rise/run
5/-1=-5
So our value of m is -5
Meaning y=-5x+b
We still have our value of b to find and we can do this by choosing any one point on the graph and substituting it into the equation. We know that one of our points is (3,0)
We put these into the equation
y=-5x+b
0=-15+b
b=15
Therefore, y=-5x+15
Focus on the top line angles for now.
Those two angles combine to the straight angle ABC, which is 180 degrees.
(angleABY) + (angleYBC) = angle ABC
(x+25)+(2x+50) = 180
(x+2x) + (25+50) = 180
3x+75 = 180
3x = 180-75
3x = 105
x = 105/3
x = 35
We'll use this x value to find that:
- angle YBC = 2x+50 = 2*35+50 = 70+50 = 120 degrees
- angle BEF = 5x-55 = 5*35-55 = 175-55 = 120 degrees
Angles YBC and BEF are corresponding angles (they are both in the northeast corner of their respective four-corner angle configuration). They are both 120 degrees. Since we have congruent corresponding angles, we have effectively proven that AC is parallel to DF. Refer to the converse of the corresponding angles theorem.
The regular version of the "corresponding angles theorem" says that if two lines are parallel, then the corresponding angles are congruent. The converse reverses the logic of the conditional statement. Meaning that if the corresponding angles are congruent, then the lines are parallel.
Answer:
105+54=x
Step-by-step explanation:
<h3>
Answer: 11.2 inches</h3>
Work Shown:
(real height)/(scale height) = (real length)/(scale length)
(10 feet)/(8 inches) = (14 feet)/(x inches)
10/8 = 14/x
10x = 8*14
10x = 112
x = 112/10
x = 11.2 inches
Subtract 12 from both sides
4(2x + 2) > 100 - 12
Simplify 100 - 12 to 88
4(2x + 2) > 88
Divide both sides by 4
2x + 2 > 88/4
Simplify 88/4 to 22
2x + 2 > 22
Subtract 2 from both sides
2x > 22 - 2
Simplify 22 - 2 to 20
2x > 20
Divide both sides by 2
x > 20/2
Simplify 20/2 to 10
<u>x > 10</u>
