The orthocenter is the point where the three altitudes meet.
sketch the graph and you will see that AB is a horizontal line, the altitude is a vertical line through the point (1,3), so the equation of this altitude is x=1
next, find another altitude. I'll use the altitude of BC.
the slope of BC is (6-3)/(4-1)=1, so the slope of the altitude, which is perpendicular to BC going through the point A (0,6), is -1, the equation of the altitude of BC is y=-x+6
the system of equation : x=1
y=-x+6
has a solution (1, 5)
the solution is where the two lines meet, the meeting point is the orthocenter.
Double check by find the equation for other altitude:
slope of AC: (3-6)/(1-0)=-3
slope of altitude of AC: 1/3
equation of altitude of AC: y=(1/3)x+b
the altitude of AC goes through point B (4,6), so we can find out b by plug x=4, y=6 in the equation: 6=(1/3)*4+b, b=14/3
y=(1/3)x+14/3
Is (1,5) also a solution to this equation? Plug x=1 in the equation, we get y=5, so yes, (1,5) is a point on the third altitude.
Popcorn would be 7.98. Drinks would be 5.25. Togather they would be 13.23.
Answer: 180 is the sum of the tringles
Step-by-step explanation:
2x+7x+11x=180
20x=180
x=9
Now you should put the the value of x to get the angles
2x=2x9=18
7x=7x9=63
11x=11x9=99
Now to double check add all of them together
99+18+63=180
Hoped I helped!
A=p(1+r)^t
13400=10000(1+r)^6
Solve to find the interest rate
r=((13,400÷10,000)^(1÷6)−1)×100
r=4.99%=5%
