In order to determine which subset it belongs, we must rewrite
as
All these three numbers are irrational numbers, hence their product is also irrational
<h2>
</h2><h2>belongs to the set of
irrational numbers</h2>
<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)
-------------------------------
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
-------------------------------
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
-------------------------------
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
------------------------------------------------------------
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
</span><span>
</span></span>
Answer:
(23,-4):
units
Step-by-step explanation:
We are given that M(-19,4)and P(4,0)
We have to find the ordered pair that represents MP and find the magnitude of MP.
MP=P-M
MP=(4,0)-(-19,4)=(4+19,0-4)
MP=(23,-4)
Magnitude of MP=
Magnitude of MP=
Magnitude of MP= units
Hence, .option c is true.
Answer:c.(23,-4): units
Answer:
2x^3+2x-1
Step-by-step explanation:
Set it up like a regular equation. I used:
As you can see, however, I inserted the "less than" symbol rather than the equal sign because values greater than a certain value can also equal "x". Solve it like a normal equation and you will arrive at:
<u>
</u>
This means that, as long as x is greater than 45, "6x" will be greater than "3x+135". Thus, if you bring 46 students, the Science Center will cost less.
