14.
Angles 4 and 6 are supplementary, because they are on the same line. Supplementary angles add up to 180 degrees, and a line must be 180 degrees.
15.
Angles 1 and 8 are congruent, because they are alternate exterior angles
16.
m = y2 - y1 / x2 - x1
m = 7 - 2 / 4 - 5
m = 5 / -1
m = -5
17.
m = 3 - 3 / 7 - (-5)
m = 0 / 12
m = 0
18.
m = 1 - (-2) / 5 - (-4)
m = 3 / 9
m = 1/3
19.
A = (0, 3) - B = (3,0)
m = 0 - 3 / 3 - 0
m = -3 / 3
<em>m = -1</em>
C = (0, -2) - D = (4, 2)
m = 2 - (-2) / 4 - 0
m = 4 / 4
<em>m = 1</em>
Perpendicular, because the slopes are opposite reciprocals.
20.
E = (1, 2) - F = (0, 0)
m = 0 - 2 / 0 - 1
m = -2 / -1
<em>m = 2</em>
G = (1, -3) - H = (3, 0)
m = 0 - (-3) / 3 - 1
<em>m = 3 / 2</em>
Neither, because the slopes are different.
21.
I = (0, 1) - J = (2, -4)
m = -4 - 1 / 2 - 0
<em>m = -5/2</em>
K = (-1, -2) - L = (4, 0)
m = 0 - (-2) / 4 - (-1)
<em>m = 2/5</em>
Perpendicular, because the slopes are opposite reciprocals.
22.
M = (-2, 2) - N = (2, 2)
Horizontal line
<em>m = 0</em>
O = (3, 0) - P = (-3, 0)
Horizontal line
<em>m = 0
</em>Parallel, because the slopes are the same.
<em>
</em>23.
Angle 2 is congruent to angle 1 because of the alternate exterior angle theorem.
Angle 1 is congruent to angle 3 because of the vertical angle theorem.
Angle 2 is congruent to angle 3 because of substitution.
Line l is parallel to line m because the corresponding angles are congruent.
Hi there!
First, let's find the slope of the two points using the slope formula (y2 - y1 / x2 - x1).
S = 4 - 2 / 3 - 5
S = 2 / -2
S = -1
Next, we'll plug in the slope and a point into point-slope form (y - y1 = s(x - x1)) in order to find an equation. I will show the work using both points, which will result in two different equations.
(2,5)
y - 5 = -1(x - 2)
y - 5 = -x + 2
y = -x + 7
(4,3)
y - 3 = -1(x - 4)
y - 3 = -x + 4
y = -x + 7
The two equations came out the same! Which is completely okay, and happens sometimes.
Hope this helps!! :)
If there's anything else that you're needing help with, don't be afraid to reach out!
-6x^2+4x
my reasoning:
eliminate the opposites (5 & -5)
collect the like terms (-8x^2 & + 2x^2)
collect the like terms again (-3x &+7x)
Answer:
Quadrant III ( C )
Quadrant IV ( D )
Step-by-step explanation:
Ordered pair ( a, b )
gives a point P on the coordinate plane
( a, b ) = ( x, y )
given : b = negative ( y-axis )
a ≠ 0 ( i.e. a = negative or positive ) ( x -axis )
Therefore point P is located in the : Third and fourth quadrants
