4/15 should be your answer!
![\bf \begin{cases} x=1\implies &x-1=0\\ x=1\implies &x-1=0\\ x=-\frac{1}{2}\implies 2x=-1\implies &2x+1=0\\ x=2+i\implies &x-2-i=0\\ x=2-i\implies &x-2+i=0 \end{cases} \\\\\\ (x-1)(x-1)(2x+1)(x-2-i)(x-2+i)=\stackrel{original~polynomial}{0} \\\\\\ (x-1)^2(2x+1)~\stackrel{\textit{difference of squares}}{[(x-2)-(i)][(x-2)+(i)]}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Ax%3D1%5Cimplies%20%26x-1%3D0%5C%5C%0Ax%3D1%5Cimplies%20%26x-1%3D0%5C%5C%0Ax%3D-%5Cfrac%7B1%7D%7B2%7D%5Cimplies%202x%3D-1%5Cimplies%20%262x%2B1%3D0%5C%5C%0Ax%3D2%2Bi%5Cimplies%20%26x-2-i%3D0%5C%5C%0Ax%3D2-i%5Cimplies%20%26x-2%2Bi%3D0%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A%28x-1%29%28x-1%29%282x%2B1%29%28x-2-i%29%28x-2%2Bi%29%3D%5Cstackrel%7Boriginal~polynomial%7D%7B0%7D%0A%5C%5C%5C%5C%5C%5C%0A%28x-1%29%5E2%282x%2B1%29~%5Cstackrel%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%5B%28x-2%29-%28i%29%5D%5B%28x-2%29%2B%28i%29%5D%7D)
![\bf (x^2-2x+1)(2x+1)~[(x-2)^2-(i)^2] \\\\\\ (x^2-2x+1)(2x+1)~[(x^2-4x+4)-(-1)] \\\\\\ (x^2-2x+1)(2x+1)~[(x^2-4x+4)+1] \\\\\\ (x^2-2x+1)(2x+1)~[x^2-4x+5] \\\\\\ (x^2-2x+1)(2x+1)(x^2-4x+5)](https://tex.z-dn.net/?f=%5Cbf%20%28x%5E2-2x%2B1%29%282x%2B1%29~%5B%28x-2%29%5E2-%28i%29%5E2%5D%0A%5C%5C%5C%5C%5C%5C%0A%28x%5E2-2x%2B1%29%282x%2B1%29~%5B%28x%5E2-4x%2B4%29-%28-1%29%5D%0A%5C%5C%5C%5C%5C%5C%0A%28x%5E2-2x%2B1%29%282x%2B1%29~%5B%28x%5E2-4x%2B4%29%2B1%5D%0A%5C%5C%5C%5C%5C%5C%0A%28x%5E2-2x%2B1%29%282x%2B1%29~%5Bx%5E2-4x%2B5%5D%0A%5C%5C%5C%5C%5C%5C%0A%28x%5E2-2x%2B1%29%282x%2B1%29%28x%5E2-4x%2B5%29)
of course, you can always use (x-1)(x-1)(2x+1)(x²-4x+5) as well.
Answer:
1
Step-by-step explanation:
2(k + 1) = -4(k - 2)
2k + 2 = --4k+8
2k+4k=8-2
6k=6
k=6/6
k=1
Answer:
34
Step-by-step explanation:
Given that
2x - 7 = 9 ← solve for x
Add 7 to both sides
2x = 16 ( divide both sides by 2 )
x = 8
Substitute x = 8 into 5x - 6
5x - 6 = (5 × 8) - 6 = 40 - 6 = 34
Answer:

Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
We need to find the slope, m, and the y-intercept, b.
The line we need is perpendicular to the line 2x + y = 8.
<em>The slopes of perpendicular lines are negative reciprocals.</em>
We solve the given equation for y to find the slope of the given line.
2x + y = 8
y = -2x + 8
The given line has slope -2.
The negative reciprocal of -2 is 1/2.
Our line has slope, m = 1/2.
Now we have
y = 1/2 x + b
Now we use the given point, (-2, 3), for x and y, using x = -2, and y = 3, and we solve for b.
y = 1/2 x + b
3 = 1/2 * (-2) + b
3 = -1 + b
4 = b
b = 4
Now we have
y = 1/2 x + 4
Answer: 