Answer:
Step-by-step explanation:
![\because \: f(x) = (2x - 1)(x + 4) \\ \therefore \:f(x) = 2x(x + 4) - 1(x + 4) \\ \therefore \:f(x) = 2x ^{2} + 8x - x - 4 \\ \therefore \:f(x) = 2x ^{2} + 7x - 4 \\](https://tex.z-dn.net/?f=%20%5Cbecause%20%5C%3A%20f%28x%29%20%3D%20%282x%20-%201%29%28x%20%2B%204%29%20%5C%5C%20%20%5Ctherefore%20%5C%3Af%28x%29%20%3D%20%202x%28x%20%2B%204%29%20%20-%201%28x%20%2B%204%29%20%5C%5C%20%5Ctherefore%20%5C%3Af%28x%29%20%3D%20%202x%20%5E%7B2%7D%20%20%2B%208x%20-%20%20%20x%20%20-%20%204%20%5C%5C%20%5Ctherefore%20%5C%3Af%28x%29%20%3D%20%202x%20%5E%7B2%7D%20%20%2B%207x%20%20-%20%204%20%5C%5C%20)
Answer:
B.) 5, -1
Step-by-step explanation:
Formula:
ax^2+bx=c
Shift the equation and set it equal to 0 by subtracting c.
ax^2+bx+c=0
So, in this case:
x^2-4x=5
Shift the equation:
x^2-4x-5=0
a= 1
b= -4
c= -5
Now, to figure out the zeros of an equation like this:
You need to find two numbers that multiply to c (-5), but also add to b (-4).
These numbers are 5 and -1
So, the zeros of the equation are 5 and -1.
Step-by-step explanation:
2x-5=2x-6. First you collect like terms
2x-2x=-6+5
0=-1
This statement is false 0≠-1
Answer:
x = 125 ft and y = 250/3 ft
Step-by-step explanation:
Let assume that,
x be the length of the northern part of the fence (parallel to the north wall)
y be the length of the western and eastern pieces of the fence
As well as farmer has $4000 to spend hence we can write,
8x + 8y + 4y = 4000
8x + 12y = 4000
Hence we can say that,
from the above equation we can write
![y=\frac{4000}{12} -\frac{2x}{3}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4000%7D%7B12%7D%20-%5Cfrac%7B2x%7D%7B3%7D)
We know that area
A=xy.
![A(x) =\frac{500x}{3}-\frac{2x^2}{3}](https://tex.z-dn.net/?f=A%28x%29%20%3D%5Cfrac%7B500x%7D%7B3%7D-%5Cfrac%7B2x%5E2%7D%7B3%7D)
we can write
![A'(x) = \frac{500}{3} -\frac{4x}{3}](https://tex.z-dn.net/?f=A%27%28x%29%20%3D%20%5Cfrac%7B500%7D%7B3%7D%20-%5Cfrac%7B4x%7D%7B3%7D)
equating it 0 we get
![A'(x) = \frac{500}{3} -\frac{4x}{3}=0](https://tex.z-dn.net/?f=A%27%28x%29%20%3D%20%5Cfrac%7B500%7D%7B3%7D%20-%5Cfrac%7B4x%7D%7B3%7D%3D0)
![x=125](https://tex.z-dn.net/?f=x%3D125)
Also,
![A"(x) = -\frac{4}{3}](https://tex.z-dn.net/?f=A%22%28x%29%20%3D%20-%5Cfrac%7B4%7D%7B3%7D)
which is less than zero.
we can see that A''(x) is always less than 0 hence using second derivative test we can say that x = 125 is a maximum point.
now, solving for y we get ![y= \frac{250}{3}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B250%7D%7B3%7D)
Hence we can say that dimensions for the plot that would enclose the most area is,
x = 125 ft and y = 250/3 ft