8 hundred thousands, 1 thousand, and 1 hundred, 6 tens, 3 ones
We need to find the volume of a rectangular prism with dimensions 6 ft, 10 ft, and 12 ft:
• The volume of a rectangular prism is given by the product of its dimensions.
Thus, the volume V of the room is given by:
![\begin{gathered} V=6ft\cdot10ft\cdot12ft \\ \\ V=6\cdot10\cdot12(ft\cdot ft\cdot ft) \\ \\ V=720ft^{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20V%3D6ft%5Ccdot10ft%5Ccdot12ft%20%5C%5C%20%20%5C%5C%20V%3D6%5Ccdot10%5Ccdot12%28ft%5Ccdot%20ft%5Ccdot%20ft%29%20%5C%5C%20%20%5C%5C%20V%3D720ft%5E%7B3%7D%20%5Cend%7Bgathered%7D)
Therefore, that volume is 720 cubic feet.
What? I have an idea of what your saying but i'm not positive. Can you explain better please?
Add 4x
to both sides of the equation.
a. y=4x+6
Add 5x to both sides of the equation.
b. y=5x+21
Answer:
1. (7,-9)
2. (4,0) and (10,0)
3. (3,0) and (-3,0)
4. (0,-9)
5. (-1,-32)
Step-by-step explanation:
To find the vertex use the formula
![\frac{-b}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B2a%7D)
First make the equation into a quadratic equation.
![(x-4)(x-10)\\x^{2} -10x-4x+40\\x^{2} -14x+40](https://tex.z-dn.net/?f=%28x-4%29%28x-10%29%5C%5Cx%5E%7B2%7D%20-10x-4x%2B40%5C%5Cx%5E%7B2%7D%20-14x%2B40)
Now it is in the form
![ax^{2} +bx+c=0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2Bbx%2Bc%3D0)
Now we can substitute the values
![\frac{-(-14)}{2(1)} \\\frac{14}{2} \\7](https://tex.z-dn.net/?f=%5Cfrac%7B-%28-14%29%7D%7B2%281%29%7D%20%5C%5C%5Cfrac%7B14%7D%7B2%7D%20%5C%5C7)
Now we have 7 as our x value for the vertex we can substitute for y,
![x^{2} -14x+40=y\\(7)^{2} -14(7)+40=y\\49-98+4=y\\y=-9](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-14x%2B40%3Dy%5C%5C%287%29%5E%7B2%7D%20-14%287%29%2B40%3Dy%5C%5C49-98%2B4%3Dy%5C%5Cy%3D-9)
So the vertex for 1 is (7,-9)
To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.
![x-4=0\\x=4\\\\x-10=0\\x=10](https://tex.z-dn.net/?f=x-4%3D0%5C%5Cx%3D4%5C%5C%5C%5Cx-10%3D0%5C%5Cx%3D10)
4 is slightly different but start the same,
![(x-3)(x+3)\\x^{2}+3x-3x-9\\x^{2}-9](https://tex.z-dn.net/?f=%28x-3%29%28x%2B3%29%5C%5Cx%5E%7B2%7D%2B3x-3x-9%5C%5Cx%5E%7B2%7D-9)
Here, c (9) just shows the graph move down 9, so the y intercept = 9.
5 is the same process as 1,
![2(x-3)(x+5)\\2(x^{2}+5x-3x-15)\\2(x^{2}+2x-15)\\2x^{2}+4x-30](https://tex.z-dn.net/?f=2%28x-3%29%28x%2B5%29%5C%5C2%28x%5E%7B2%7D%2B5x-3x-15%29%5C%5C2%28x%5E%7B2%7D%2B2x-15%29%5C%5C2x%5E%7B2%7D%2B4x-30)
Vertex,
![\frac{-(4)}{2(2)} \\\frac{-4}{4} \\-1](https://tex.z-dn.net/?f=%5Cfrac%7B-%284%29%7D%7B2%282%29%7D%20%5C%5C%5Cfrac%7B-4%7D%7B4%7D%20%5C%5C-1)
Substitute,
![2x^{2}+4x-30\\2(-1)^{2}+4(-1)-30\\2-4-30\\-32](https://tex.z-dn.net/?f=2x%5E%7B2%7D%2B4x-30%5C%5C2%28-1%29%5E%7B2%7D%2B4%28-1%29-30%5C%5C2-4-30%5C%5C-32)
So the vertex is (-1,-32)