The smallest value it could be is 4 and the largest value it could be is 10.
The triangle inequality theorem states that any two sides of a triangle must have a sum greater than the third side. Given the two sides we have, 7 and 4, the sum would be 11; this would mean that the missing side could be no more than 10.
If we take the unknown side and the smallest one we're given, we would have the inequality
n+4>7
Subtracting 4 from both sides we would have n>3. That means it would have to be the next integer up, which would be 4.
Set up two equations:
1st: P (for Price family) + J (for Jenkins family) = 45 hours
2nd: 20P + 35J = 1200 liters
Rewrite the first equation as P = 45 – J
Replace P in the second equation:
20(45-J) + 35J = 1200
Simplify:
900 -20J + 35J = 1200
900 +15J = 1200
Subtract 900 from both sides:
15J = 300
Divide both sides by 15:
J = 300/15
J = 20
Jenkins used theirs for 20 hours
Price used theirs for 45-20 = 25 hours.
The first one is rectangle
When x=-5, y=(1/5)*(-5)-1=-2, so the first order pair is (-5,-2)
when y=-1, -1=(1/5)x-1, (1/5)x=0, x=0, so the second ordered pair is (0, -1)
