Let
x = wristbands
y = headbands
We then have the following inequations:
2x + 3y> = 50 x> = 5 The graph that represents the solution for this system of inequations is shown in the attached image.
The set of solutions is the shaded region.
Answer:
y = 4(3)^x
Step-by-step explanation:
Here, we want to write the exponential equation
From the question, we have the equation tripling in x value every year and the original amount is 4
The exponential equation is of the form;
y = a(b)^n
In this case;
a = 4 , b = 3 and n = x
So we have the equation as;
y = 4(3)^x
Using polynomial long division, we get
3x^3+6x^2+11x
_____________
(x+2) | 3x^4-x^2+cx-2
-(3x^4+6x^3)
____________
6x^3-x^2+cx-2
- (6x^3+12x^2)
_____________
11x^2+cx-2
-(11x^2+22x)
__________
(22+c)x-2.
If you're wondering how I did the long division, what I essentially did was get the first value (at the start, it was 3x^4) and divided it by the first value of the divisor (which in x+2 was x) to get 3x^3 in our example. I then subtracted the polynomial by the whole divisor multiplied by, for example, 3x^3 and repeated the process.
For this to be a perfect factor, (x+2)*something must be equal to (22+c)x-2. Focusing on how to cancel out the 2, we have to add 2 to it. To add 2 to it, we have to multiply (x+2) by 1. However, there's a catch, which is that we subtract whatever we multiply (x+2) by, so we have to multiply it by -1 instead. We still need to cross out (22+c)x. Multiplying (x+2) by -1, we get
(-x-2) but by subtracting the whole thing from something means that we have to add -(-x-2)=x+2 to something to get 0. x+2-x-2=0, xo (22+c)x-2 must equal -x-2, meaning that (22+c)=-1 and c=-23
Answer:
126,300.
Step-by-step explanation:
