Answer:
As you know, a year has around 365 + 1/4 days.
This means that in two years, we have:
365 + 356 + 1/4 + 1/4 = 730 + 1/2
and so on.
adding this up, when we have 4 years we have a full day extra, this is:
1460 + 1
When we divide 1461 by 4, we have 365 with a surpass of 1.
The rule used to keep the calendar in sync with this extra day is adding an extra day to each fourth year.
So each fourth year, we have an extra day in Februray (the Februray 29th), this is called a bisiest year.
The "math rule" used to know if a year is leap or not is:
if a year is not divisible by 4, then it is a common year
else if the year is not divisible by 100 then it is a leap year,
else if the year is not divisible by 400, then it is a common year
if not, the year is a leap year.
Where "year" represents the number of the year.
<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
</span><span>
</span></span>
2.5*36=90 inches
Alex need 90 inches of fabric to make a costume for homecoming.
