A) I included a graph, look below.
B)
Input the y in x = y + 3.
x = (-4x - 3) + 3
x = -4x + 0
Add 4x to both sides.
5x = 0
Divide both sides by 5.
x = 0
Input that x value in y = -4x - 3
y = -4(0) - 3
y = 0 - 3
y = -3
(0, -3)
C)
Convert both equations to Standard Form.
x = y + 3
Subtract y from both sides.
x - y = 3
y = -4x - 3
Add 4x to both sides.
4x + y = -3
Add the equations together.
4x + y = -3
x - y = 3
equals
5x = 0
Divide both sides by 5.
x = 0
Input that into one of the original equations.
0 = y + 3
Subtract 3 from both sides.
-3 = y
(0, -3)
You can use the pythagoras theorem.
20^2=5^2+x^2
x^2=400-25
x^2=375
x = 19.36
20-19.36=0.64 feet
The answer is 0.64 feet :)
Answers:
1) Given
2) angle 2 ** see note below
3) angle 3 ** see note below
4) converse of alternate exterior angle theorem
note: you can swap the answers for 2 and 3 and it doesn't matter
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Explanations:
1) This is given so we just simply state "given". It seems silly to repeat what is given, but this is how you start any geometry proof.
2 & 3) The answers here are angle 2 and angle 3 because they are both interior angles (on the inside of the parallel lines m and L) and they are on alternate sides of the transversal line q. So they are both alternate interior angles and are congruent due to line L parallel to line m (alternate interior angle theorem)
4) If you have a pair of parallel lines, then the alternate exterior angle theorem says that alternate exterior angles are congruent. Going in reverse, the converse of this theorem says that having a pair of congruent alternate exterior angles (angle 1, angle 2) leads to the lines being parallel (p and q).
Answer: I will answer this but I need a bit more detail :)
Step-by-step explanation: