since the equation of the line passing through the given point is perpendicular to the given line(m2= -1/m1)
using the formula y=mx+c
y=2/3x +1
m1=2/3
m2= -1/2/3
m2= -3/2
the slope of the second line is -3/2 and it passes through the point(3,-2)
using the formula y-y1 = m(x-x1)
y-(-2)= -3/2(x-3)
y+2= -3/2(x-3)
multiply both sides by 2
2(y+2) = -3(x-3)
2y+4 = -3x+9
2y = -3x+5
y= -3/2x + 5/2
34(3-2)9x-2 = 14 would be the correct way to solve the problem!
Answer:
D)14 units
Step-by-step explanation:
Just counts how many numbers you get from point A to B. Its pretty simple.
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