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ELEN [110]
2 years ago
6

Help me solve this Step by step 1/2(y+2)+2=1/4(8y-60)-3

Mathematics
1 answer:
Shkiper50 [21]2 years ago
5 0
This is the answer step by step

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How do you find the equation of a triangles altitude using point slope formula?
forsale [732]
<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>
3 0
3 years ago
I don't get it at all could you go step by step with me
Elodia [21]
Okay, so if e=110, then so does c, because they are Alternate Interior angles. If c=110, then so does a, because they are Alternate Exterior. Angles a and b are on a straight line, which equals 180 altogether, and 180-110 is 70, so the measure of angle b is 70.

Hope this helps ya
3 0
3 years ago
Read 2 more answers
Find the length of the leg. If your answer is not an integer, leave it in simplest radical<br> form
Setler [38]

Step-by-step explanation:

{14}^{2}  = 2 {a}^{2}  \\ 2 {a}^{2}  = 196 \\  {a}^{2}  = 98 \\  a = \sqrt{98 }  =  \sqrt{49 \times 2}  \\  =  7 \sqrt{2}

7 0
3 years ago
Below are two parallel lines with a third line intersecting them.
Allushta [10]
180-48= 132 ( I think)
8 0
2 years ago
"A new bakery offers decorated sheet cakes for children’s birthday parties and other special occasions. The bakery wants the vol
Darya [45]

Answer:

w = 9 \text{ inches}\\l = 13\text{ inches}\\h = 3\text{ inches}      

Step-by-step explanation:

We are given the following in the question:

Volume of cake = 351 cubic inches

Let x inches be the width of cake.

Width of cake, w =

x\text{ inches}

Then, length of cake,l =

(x + 4)\text{ inches}

Height of cake,h =

\dfrac{x}{3}\text{ inches}

Volume of cake = Volume of cuboid

V = lwh

Putting values, we get:

351 = x(x+4)(\dfrac{x}{3})\\\\1053 = x^3 + 4x\\x^3+4x^2-1053= 0\\\\\text{For x = 9}\\(9)^3+4(9)^2-1053= 0

Thus, dimensions of cake are:

w = 9 \text{ inches}\\l = 13\text{ inches}\\h = 3\text{ inches}

3 0
3 years ago
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