<span><span><span>1. An altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Find the equations of the altitudes of the triangle with vertices (4, 5),(-4, 1) and (2, -5). Do this by solving a system of two of two of the altitude equations and showing that the intersection point also belongs to the third line. </span>
(Scroll Down for Answer!)</span><span>Answer by </span>jim_thompson5910(34047) (Show Source):You can put this solution on YOUR website!
<span>If we plot the points and connect them, we get this triangle:
Let point
A=(xA,yA)
B=(xB,yB)
C=(xC,yC)
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Let's find the equation of the segment AB
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through AB is
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Let's find the equation of the segment BC
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through BC is
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Let's find the equation of the segment CA
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through CA is
So we have these equations of the lines that make up the triangle
So to find the equation of the line that is perpendicular to that goes through the point C(2,-5), simply negate and invert the slope to get
Now plug the slope and the point (2,-5) into
Solve for y and simplify
So the altitude for vertex C is
Now to find the equation of the line that is perpendicular to that goes through the point A(4,5), simply negate and invert the slope to get
Now plug the slope and the point (2,-5) into
Solve for y and simplify
So the altitude for vertex A is
Now to find the equation of the line that is perpendicular to that goes through the point B(-4,1), simply negate and invert the slope to get
Now plug the slope and the point (-4,1) into
Solve for y and simplify
So the altitude for vertex B is
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Now let's solve the system
Plug in into the first equation
Add 2x to both sides and subtract 2 from both sides
Divide both sides by 3 to isolate x
Now plug this into
So the orthocenter is (-2/3,1/3)
So if we plug in into the third equation , we get
So the orthocenter lies on the third altitude
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Answer:
a) y = 6x - 3
b) 1/3y = 2x -1
The first thing you need to do is isolate (y) in the second equation
3 x (1/3y) = 3 x (2x - 1)
y =6x - 3
After isolating (y) in equation b they end up being the same.
Graphing:
In order to graph this, you have to make the first point at (0, -3) since this is the Y-intercept of the equation.
In order to graph the other points, you must move 6 units up and 1 unit to the right. Or vise versa If you need a visual I'll gladly link one.
Answer:
x = 7000
y = 5600
(7000, 5600)
Step-by-step explanation:
To solve the system of equations means to find the point of intersection (graphically). You are finding what value of 'x' and what value of 'y' fits both equations.
x = y + 1400
0.08x + 0.05y = 840
We can solve using the method <u>substitution</u>, where you replace a variable in one equation with an equivalent expression.
<u>Since "x" is y + 1400, we can replace "x" in the second equation.</u>
0.08x + 0.05y = 840
0.08(y + 1400) + 0.05y = 840
Distribute over brackets by multiplying 0.08 with y, then 0.08 with 1400.
0.08y + 112 + 0.05y = 840 Collect like terms (with "y" variable)
112 + 0.13y = 840
Now isolate "y" in the simplified equation.
112 - 112 + 0.13y = 840 - 112 Subtract 112 from both sides
0.13y = 728
0.13y/0.13 = 728/0.13 Divide both sides by 0.13
y = 5600 Solved for y
We can substitute "y" with 5600 in any other equation that has "x".
x = y + 1400
x = 5600 + 1400 Add
x = 7000 Solved for x
You may express the answer as a coordinate, or an ordered pair (x, y).
The solution is (7000, 5600).
Answer:
B and F
Step-by-step explanation:
The simple golden rule that we need to know here is
<em><u>"The probability of any event is always between 0 and 1 inclusive"</u></em>
<em><u /></em>
If an event has a probability of p(x), we can say:
Also, probability is ALWAYS POSITIVE.
Thus,
A) OK because 33.3% is 0.333, which is between 0 and 1
B) NOT OK, because probability isn't negative
C) 0.0002 is in between 0 and 1, so possible
D) 0 probability means it can't happen, so that's okay as well
E) this is a fraction with numerator less than denominator, which means its between 0 and 1, so OK
F) this fraction's numerator is greater than denominator, so it's greater than 1. Probability can't be greater than 1, so NOT OK
Out of these B and F cannot represent the probability of an event
Answer:
2nd option
Step-by-step explanation:
Graph both equations and find the point where they both intersect. In this case, it's (4,2).
