W=-1
i hope that this helps
Answer:
x=-10
Step-by-step explanation:
4.5(8-x)+36=102-2.5(3x+24) first you multiply 10 to both sides
4.5(8-x)x10+36x10=102x10-2.5(3x+24)x10
Then you have to refine the equation
45(8-x)+360=1020-25(3x+24)
Then you expand it
45(8-x)+360
=360-45x+360
Simplify
360-45x+360 -45x+720
Expand it one more time
-45x+720=-75x+420
Subtract 720 from each side
-45x+720-720=-75x+420-720
Simplify
-45x=-75x-300
Add 75x to both sides
-45x+75x=-75x-300+75x
Simplify
Divide both sides by 30
30x/30=-300/30
Then you get -10
Answer:
48
Step-by-step explanation:
using the formula 1/2 b*h
8*12=96
96/2=48
Answer:
a) Vertex: ![(h,k) = (5,3.5)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%285%2C3.5%29)
b) Vertex: ![(h,k) = (-1,-8)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%28-1%2C-8%29)
Step-by-step explanation:
First we need to realize that these equations are the equations of parabolas.
the equation of parabola are generally written as:
![y = a(x-h)^2 +k](https://tex.z-dn.net/?f=y%20%3D%20a%28x-h%29%5E2%20%2Bk)
where the vertex is the point
. <u>(note that the sign of 'h' is changed!)</u>
<u>(also note that the value of 'a' doesn't matter for finding vertex point)</u>
given this information we can now easily find out the vertex of both parabolas
a) ![y = 2(x-5)^2 + 3.5](https://tex.z-dn.net/?f=y%20%3D%202%28x-5%29%5E2%20%2B%203.5)
by comparing it with the general equation above, we can see that -5 is in the place of '-h' and +3.5 is in the place of '+k'
we can write
and solve for h.
![h=5](https://tex.z-dn.net/?f=h%3D5)
similarly,
![k=3.5](https://tex.z-dn.net/?f=k%3D3.5)
hence the vertex of this graph is ![(h,k) = (5,3.5)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%285%2C3.5%29)
b) ![y=-(x + 1)^2-8](https://tex.z-dn.net/?f=y%3D-%28x%20%2B%201%29%5E2-8)
by comparing it with the general equation above, we can see that +1 is in the place of '-h' and -8 is in the place of '+k'
we can write
and solve for h.
![h = -1](https://tex.z-dn.net/?f=h%20%3D%20-1)
similarly,
![k=-8](https://tex.z-dn.net/?f=k%3D-8)
hence the vertex of this graph is ![(h,k) = (-1,-8)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%28-1%2C-8%29)
Exterior angles are found along the outside of the figure if you extend the figure's side lengths.
The exterior angles in the image would be 4 and 5.
6 isn't an angle, and all of the other options are found on the inside of the triangle (1,2 and 3).