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.
Answer:
answer is no solution (filler)
The answer is either 
or 
To solve: Let's solve your equation step-by-step.
5x2+5x−x2−x=2004
Step 1: Simplify both sides of the equation.
4x2+4x=2004
Step 2: Subtract 2004 from both sides.
4x2+4x−2004=2004−2004
4x2+4x−2004=0
Step 3: Use quadratic formula with a=4, b=4, c=-2004.
x=
−b±√b2−4ac
/2a
x=
−4±√32080
/8
or
Let "x" represent the weight of the toppings. We know that we can have any number of toppings. This means that one may ask for no toppings at all too.
Now, we have been told that "S" is the weight of the special sundae in kilograms. This definitely included the "mandatory" 2 kilograms of ice cream. Therefore, S will be at-least equal to 2.
Thus, the inequality that describes S, the weight of the special sundae in kilograms at Ping's Ice Cream Palace is given as:
kilograms.
It can be seen that as x increases, S increases too and if an order does not want any toppings in it then the weight of the special sundae will be a minimum of 2 kg which is the weight of the ice cream.
