Answer:
x = 5
Step-by-step explanation:
First, break it down:
Two is eight less than twice a number
2 = 2x - 8
+8 + 8
10 = 2x
5 = x
Hope this helps :)
Answer:
why why why humm why why why why
Answer:
See below
Step-by-step explanation:
I assume you mean ![f(x) = 3(x-1)^2-4](https://tex.z-dn.net/?f=f%28x%29%20%3D%203%28x-1%29%5E2-4)
The equation is already in vertex form
where
affects how "fat" or "skinny" the parabola is and
is the vertex. Therefore, the vertex is
.
The axis of symmetry is a line where the parabola is cut into two congruent halves. This is defined as
for a parabola with a vertical axis. Hence, the axis of symmetry is
.
The minimum value is the smallest value in the range of the function. In the case of a parabola, the y-coordinate of the vertex is the minimum value. Therefore, the minimum value is
.
The interval where the function is decreasing is ![(-\infty,1)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C1%29)
The interval where the function is increasing is
A, dilation because the shape got larger. The other three options just move it around
Answer:
The animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats
![Cost = 51.275](https://tex.z-dn.net/?f=Cost%20%3D%2051.275)
Step-by-step explanation:
The given parameters can be summarized as:
![\begin{array}{cccc}{} & {x} & {y} & {Total} & {Protein} & {70} & {21} & {168} &{Fats}& {9} & {7} & {27} & {Minerals} & {7} & {1} & {14}& {Cost} & {21} & {7} & {} \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccc%7D%7B%7D%20%26%20%7Bx%7D%20%26%20%7By%7D%20%26%20%7BTotal%7D%20%26%20%7BProtein%7D%20%26%20%7B70%7D%20%26%20%7B21%7D%20%26%20%7B168%7D%20%26%7BFats%7D%26%20%7B9%7D%20%26%20%7B7%7D%20%26%20%7B27%7D%20%26%20%7BMinerals%7D%20%26%20%7B7%7D%20%26%20%7B1%7D%20%26%20%7B14%7D%26%20%7BCost%7D%20%26%20%7B21%7D%20%26%20%7B7%7D%20%26%20%7B%7D%20%5C%20%5Cend%7Barray%7D)
Where: x = Soybeans and y = Oats.
So, the system of equations are:
![70x + 21y = 168](https://tex.z-dn.net/?f=70x%20%2B%2021y%20%3D%20168)
![9x +7y = 27](https://tex.z-dn.net/?f=9x%20%2B7y%20%3D%2027)
![7x + y = 14](https://tex.z-dn.net/?f=7x%20%2B%20y%20%3D%2014)
![Cost = 21x + 7y](https://tex.z-dn.net/?f=Cost%20%3D%2021x%20%2B%207y)
The best way to solve this, is using graph
Plot the following equations on a graph, and get the points of intersection:
![70x + 21y = 168](https://tex.z-dn.net/?f=70x%20%2B%2021y%20%3D%20168)
![9x +7y = 27](https://tex.z-dn.net/?f=9x%20%2B7y%20%3D%2027)
![7x + y = 14](https://tex.z-dn.net/?f=7x%20%2B%20y%20%3D%2014)
From the attached graph, we have:
![(x_1,y_1) = (1.636,2.545)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%281.636%2C2.545%29)
![(x_2,y_2) = (1.775,1.575)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%281.775%2C1.575%29)
![(x_3,y_3) = (2.023,1.256)](https://tex.z-dn.net/?f=%28x_3%2Cy_3%29%20%3D%20%282.023%2C1.256%29)
Substitute each of the values of x's and y's in the cost function to get the minimum cost:
![Cost = 21x + 7y](https://tex.z-dn.net/?f=Cost%20%3D%2021x%20%2B%207y)
![(x_1,y_1) = (1.636,2.545)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%281.636%2C2.545%29)
![Cost = 21 * 1.636 + 7 * 2.545](https://tex.z-dn.net/?f=Cost%20%3D%2021%20%2A%201.636%20%2B%207%20%2A%202.545)
![Cost = 52.171](https://tex.z-dn.net/?f=Cost%20%3D%2052.171)
![(x_2,y_2) = (1.775,1.575)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%281.775%2C1.575%29)
![Cost = 21 * 1.775 + 7 * 1.575](https://tex.z-dn.net/?f=Cost%20%3D%2021%20%2A%201.775%20%2B%207%20%2A%201.575)
![Cost = 48.3](https://tex.z-dn.net/?f=Cost%20%3D%2048.3)
![(x_3,y_3) = (2.023,1.256)](https://tex.z-dn.net/?f=%28x_3%2Cy_3%29%20%3D%20%282.023%2C1.256%29)
![Cost = 21 * 2.023 + 7 * 1.256](https://tex.z-dn.net/?f=Cost%20%3D%2021%20%2A%202.023%20%2B%207%20%2A%201.256)
![Cost = 51.275](https://tex.z-dn.net/?f=Cost%20%3D%2051.275)
The values of x and y that gives the minimum cost is:
![(x_2,y_2) = (1.775,1.575)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%281.775%2C1.575%29)
and the minimum cost is:
![Cost = 48.3](https://tex.z-dn.net/?f=Cost%20%3D%2048.3)
Hence, the animal farm should buy 1.775 bags of soybeans and 1.575 bags of oats