Answer: They sold 68 tickets at the door
688-920= -2x= -232
2x=232/2=116
184-116=68
It is true since you’re multiplying the same number on both the sides
Answer:
![y=-2\,(x+3)^2-3](https://tex.z-dn.net/?f=y%3D-2%5C%2C%28x%2B3%29%5E2-3)
Step-by-step explanation:
Notice that they are asking you to write the equation of the parabola in vertex form, that is using the coordinates of the vertex
in the expression:
![y-y_v=a\,(x-x_v)^2\\y=a\,(x-x_v)^2+y_v](https://tex.z-dn.net/?f=y-y_v%3Da%5C%2C%28x-x_v%29%5E2%5C%5Cy%3Da%5C%2C%28x-x_v%29%5E2%2By_v)
we can start by directly replacing the given vertex coordinates (-3, -3) in the expression, and then using the extra info on the point the parabola goes through in order to find the parameter
:
![y=a\,(x-x_v)^2+y_v\\y=a\,(x+3)^2+(-3)\\y=a\,(x+3)^2-3\\-5=a\,(-2+3)^2-3\\-5=a\,(1)-3\\a=-5+3\\a=-2](https://tex.z-dn.net/?f=y%3Da%5C%2C%28x-x_v%29%5E2%2By_v%5C%5Cy%3Da%5C%2C%28x%2B3%29%5E2%2B%28-3%29%5C%5Cy%3Da%5C%2C%28x%2B3%29%5E2-3%5C%5C-5%3Da%5C%2C%28-2%2B3%29%5E2-3%5C%5C-5%3Da%5C%2C%281%29-3%5C%5Ca%3D-5%2B3%5C%5Ca%3D-2)
So, now we can write the full expression for the parabola:
![y=a\,(x+3)^2-3\\y=-2\,(x+3)^2-3](https://tex.z-dn.net/?f=y%3Da%5C%2C%28x%2B3%29%5E2-3%5C%5Cy%3D-2%5C%2C%28x%2B3%29%5E2-3)
Answer:
The width of the drawer is ![15\ in](https://tex.z-dn.net/?f=15%5C%20in)
Step-by-step explanation:
we know that
The volume of the drawer is equal to
![V=LWH](https://tex.z-dn.net/?f=V%3DLWH)
we have
![L=15\ in](https://tex.z-dn.net/?f=L%3D15%5C%20in)
-----> the deep of the drawer
![V=1,125\ in^{3}](https://tex.z-dn.net/?f=V%3D1%2C125%5C%20in%5E%7B3%7D)
substitute the given values in the formula and solve for W
![1,125=(15)(W)(5)](https://tex.z-dn.net/?f=1%2C125%3D%2815%29%28W%29%285%29)
![1,125=(75)(W)](https://tex.z-dn.net/?f=1%2C125%3D%2875%29%28W%29)
![W=1,125/(75)](https://tex.z-dn.net/?f=W%3D1%2C125%2F%2875%29)
![W=15\ in](https://tex.z-dn.net/?f=W%3D15%5C%20in)