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.
Answer:
8 miles
Step-by-step explanation:
24/3 = 8
The probability that the number of heads obtained from flipping the two fair coins is the same is 35/128.
Probability:
Probability means the fraction of favorable outcome and the total number of outcomes.
So it can be written as,
Probability = Favorable outcomes / Total outcomes
Given,
The coin a is flipped three times and coin b is flipped four times.
Here we need to find the probability that the number of heads obtained from flipping the two fair coins is the same.
We know that,
There are 4 ways that the same number of heads will be obtained;
0, 1, 2, or 3 heads.
The probability of both getting 0 heads is

Probability of getting 1 head,

Probability of getting 2 heads is,

And the probability of getting 3 heads is,

Therefore, the probability that the number of heads obtained from flipping the two fair coins is the same is,
=> (1/128) + (12/128) + (18/128) + (4/128)
=> 35/128.
To know more about probability here
brainly.com/question/14210034
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