Answer:
The standard equation of the parabola is:
![y=-\frac{3}{2}x^2+12x-18](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-18)
Step-by-step explanation:
An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.
We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.
![y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2](https://tex.z-dn.net/?f=y-y_%7Bvertex%7D%3Da%5C%2C%28x-x_%7Bvertex%7D%29%5E2%5C%5Cy-6%3Da%5C%2C%28x-4%29%5E2)
Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:
![y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}](https://tex.z-dn.net/?f=y-6%3Da%5C%2C%28x-4%29%5E2%5C%5C0-6%3Da%5C%2C%282-4%29%5E2%5C%5C-6%3Da%5C%2C4%5C%5Ca%3D-%5Cfrac%7B6%7D%7B4%7D%20%3D-%5Cfrac%7B3%7D%7B2%7D)
Then the equation of the parabola becomes:
![y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18](https://tex.z-dn.net/?f=y-6%3D-%5Cfrac%7B3%7D%7B2%7D%20%5C%2C%28x-4%29%5E2%5C%5Cy-6%3D-%5Cfrac%7B3%7D%7B2%7D%20%28x%5E2-8x%2B16%29%5C%5Cy-6%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-24%5C%5Cy%3D-%5Cfrac%7B3%7D%7B2%7Dx%5E2%2B12x-18)
Answer:
the answer is C, 369
Step-by-step explanation:
1. divide 800 by 40 which will give you 20
2. then multiply 18 by 20
3. answer is 360
the reason I did this was because if you had multiplied math, physics and chemistry by 20 it would have given you the total of 800 trials
Answer:
1) (3 - 6x)(-8) = (-8)(3) - (-8)(6x) = -24 - (-48x) = -24 + 48x = 48x - 24
2) (-12)(2x - 3) = (-12)(2x) - (-12)(3) = -24x - (-36) = -24x + 36 = 36 - 24x
3) (10 - 2x)9 = (9)(10) - (9)(2x) = 90 - 18x
4) (-5)(11x - 2) = (-5)(11x) - (-5)(2) = -55x - (-10) = -55x + 10 = 10 - 55x
5) (1 - 9x)(-10) = (-10)(1) - (-10)(9x) = -10 - (-90x) = -10 + 90x = 90x - 10
6) (-6)(x + 8) = (-6)(x) + (-6)(8) = -6x + (-48) = -6x - 48
7) (-4 + 3x)(-8) = (-8)(-4) + (-8)(3x) = 32 + (-24x) = 32 - 24x
8) (-5)(1 - 11x) = (-5)(1) - (-5)(11x) = -5 - (-55x) = -5 + 55x = 55x -5
9) (-12x + 14)(-5) = (-5)(-12x) + (-5)(14) = 60x + (-70) = 60x - 70
Step-by-step explanation:
The distributive property is a(b + c) = ab + ac
The answer would be (x+1)(x+3)