Answer:
16/3 because you put a 1 under 8 since it's not a fraction hen multiple across
Step-by-step explanation:
pls give brainly
<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
------------------------------------------------------------
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>
Using the given information, we can say the following:
Width (W) = x
Length (L) = (2x - 4)
Area of Rectangle = L × W
Using this, we can formulate an equation for rectangle in question:
x(2x - 4) = 30
Expand and move everything to one side:
2x² - 4x - 30 = 0
Simplify by dividing everything on both sides by 2:
x² - 2x - 15 = 0
Factorise:
(x + 5)(x - 3) = 0
Set each factor equal to 0 and solve for x:
x + 5 = 0
x = -5 (a dimension cannot be negative so this is not the solution we want)
x - 3 = 0
x = 3 (this is the solution)
x = W = 3"
L = 2x - 4
L = 2(3) - 4
L = 2"
So, the length the rectangle is 2" and the width is 3"
Answer:
The probability that it would take more than four hours to construct a soapbox derby car = 0.1587 or 15.87
Step-by-step explanation:
Given -
Mean 
= 3 hours
Standard deviation 
= 1 hours
Let X be the no of hours to construct a soapbox derby car
the probability that it would take more than four hours to construct a soapbox derby car =
= 
= 
Put 
= 1 - 
= 1 - .8413 Using z table
= 0.1587
Answer:
y=1/2x+3.5
Step-by-step explanation:
this one was a bit trickier than the previous one, but i think that that answer is correct. i did the same thing i did to solve your last problem, solved for the slope, and then made a number line and marked the points given, drew a line through the two points, and found where the line intercepted the y axis.
