Answer: x=11/22
Step-by-step explanation: 2x+6=3x−12x+6=3x-1 2x+6=3x+−12x+6=3x+-1 2x+6=(3x+−12x)+(6+-1)=3x 2x+6+9x=−9x+5+9x=3x+9x 11x+6=5=12x 11x+12x=6+5 22x/22=11/22 x=11/22
Step-by-step explanation:
Below is an attachment containing the solution.
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
The distance Jada is from starting point will be found using the cosine formula:
c²=a²+b²-2abCos C
a=200, b=90, C=70°
thus plugging in our values we get:
c²=200²+90²-2×200×90×cos70
c²=40000+8100-36000(0.3420)
c²=35788
hence
c=189.1772 m'
therefore the distance Jada is from the starting point is 189.1772 m
