First we need to simplify the numerator of the fraction
(2 - 4i)(3 + 5i)
= 6 +10i - 12i - 20i²
= 6 - 2i + 20
= 26 - 2i
So now the fraction becomes:
In order to convert the fraction to standard form, we need to multiply and divide the fraction by the conjugate of the denominator as shown below:
Answer:
(5,4)
Step-by-step explanation:
thanks to the second information we know that a certain second point of the line is (-1,0)
Now we can use a formula to find the equation of the line, that is
(y-y1)/(y2-y1) = (x-x1)/(x2-x1) where x and y 1 and 2 are the coordinates of the points.
(y+2)/2 = (x+4)/(-1+4)
y+2/2 = (x+4)/ 3
3y+6 = 2x+8
2x-3y+2 = 0
now we have to find the point that make true the equation (we have to sobstitute x and y with the coordinates of the given points)
1) -12 +15 + 2 = 0 ; 3 = 0 (wrong)
2) 6-4+2 = 0 ; 4 = 0 (wrong)
3) 8-15+2 = 0 ; -5 = 0 (wrong)
4) 10-12+2 = 0 ; 0=0 (true)
so (5,4) is the correct answer
10. (5,8)(-3,7)
slope = (7 - 8) / (-3 - 5) = -1 / -8 = 1/8
11. (5,-2)(3,-2)...since both y values are the same, this line is a horizontal line with a 0 slope.
12. (-4,7)(8,-1)
slope = (-1 - 7) / (8 - (-4) = -8 / (8 + 4) = -8/12 = - 2/3
13. (6,-3)(6,4)....since both x values are the same, this line is a vertical line with a slope that is undefined
14. -2/5
Answer:
Step-by-step explanation:
5t - 3 = 14
5t=14+3
5t=17
t=17/5
t=3.4
