The answer is p v q and some other one, I haven't done logic in 2 years already, so I don't know the other one. BUT, if p is true, then p v q HAS to be true because if one of the statements, p or q, is true, then p v q is true. For or statements to be true, at least one of the statements included has to be true.
Answer:
This is proved with the help of slope.
Step-by-step explanation:
Given Mr. Johnson is working on constructing a square table for his classroom. He positioned his design on a coordinate grid, as shown. Mr. Johnson will need to put a brace through each diagonal of the table in order to secure the table's stability.
Now, if Johnson use more than one brace then we have to prove that the braces will intersect at a right angle.
From the figure we have to prove the diagonals AC and BD are at right angle. To prove above we have to find the slopes of both diagonals.



As we know, In a coordinate plane, the slopes of perpendicular lines are opposite reciprocals of each other i.e their product is equals to -1.
⇒ AC and BD are perpendicular
⇒ Braces which put through each diagonal intersect at right angle and the table will stable.
Answer:
8
Step-by-step explanation:
Isolate and solve for C

Answer:
30 inches
Step-by-step explanation:
Assuming the lengths are measured when B lies between A and C on a line, the segment addition theorem applies:
AC = AB +BC
42 = AB + 12 . . . . . fill in the given numbers
30 = AB . . . . . . . . . subtract 12
The length of AB is 30 inches.
Answer:
1. y = - 4 x + 5
2. x = -8
Step-by-step explanation:
1. (-1,9) (1,1)
y = mx + b
m = (y-y') / (x-x') = (1-9) / (1-(-1)) = -8 / 2 = - 4
b = y - mx = 9 - (-4) x (-1) = 5
equation: y = - 4 x + 5
check: (1,1) y=1 = (-4) x 1 + 5 = 1
2. Vertical line through (-8,6) is a line perpendicular to x axis
x = -8