Answer:
Step-by-step explanation:
Stephen Curry
B is incorrect because the absolute value of -1 is 1 the absolute value of anything is always positive sorry if I’m incorrect
Answer:
![\dfrac{9}{13}-\dfrac{19}{13}i](https://tex.z-dn.net/?f=%5Cdfrac%7B9%7D%7B13%7D-%5Cdfrac%7B19%7D%7B13%7Di)
Step-by-step explanation:
Remember ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
You are given the fraction ![\dfrac{3+5i}{-2+3i}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%2B5i%7D%7B-2%2B3i%7D)
First, multiply the numerator and the denominator by -2-3i:
![\dfrac{3+5i}{-2+3i}=\dfrac{(3+5i)(-2-3i)}{(-2+3i)(-2-3i)}=\dfrac{(3+5i)(-2-3i)}{(-2)^2-(3i)^2}=\dfrac{(3+5i)(-2-3i)}{4-9i^2}=\dfrac{(3+5i)(-2-3i)}{4+9}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%2B5i%7D%7B-2%2B3i%7D%3D%5Cdfrac%7B%283%2B5i%29%28-2-3i%29%7D%7B%28-2%2B3i%29%28-2-3i%29%7D%3D%5Cdfrac%7B%283%2B5i%29%28-2-3i%29%7D%7B%28-2%29%5E2-%283i%29%5E2%7D%3D%5Cdfrac%7B%283%2B5i%29%28-2-3i%29%7D%7B4-9i%5E2%7D%3D%5Cdfrac%7B%283%2B5i%29%28-2-3i%29%7D%7B4%2B9%7D)
This gives you 13 in denominator, now multiply two complex numbers in numerator:
![(3+5i)(-2-3i)=-6-9i-10i-15i^2=-6-19i+15=9-19i](https://tex.z-dn.net/?f=%283%2B5i%29%28-2-3i%29%3D-6-9i-10i-15i%5E2%3D-6-19i%2B15%3D9-19i)
Thus, the initial fraction is
![\dfrac{9-19i}{13}=\dfrac{9}{13}-\dfrac{19}{13}i](https://tex.z-dn.net/?f=%5Cdfrac%7B9-19i%7D%7B13%7D%3D%5Cdfrac%7B9%7D%7B13%7D-%5Cdfrac%7B19%7D%7B13%7Di)
Hey there!
150 = 8x + 6y
↠ 150 = 8x + 6(9)
↠ 8x + 6(9) = 150
↠ 8x + 54 = 150
SUBTRACT 54 to BOTH SIDES
8x + 54 - 54 = 150 - 54
CANCEL out: 54 - 54 because that gives you 0
KEEP: 150 - 54 because helps solve for x
↣150 - 54 = 96↢
NEW EQUATION: 8x = 96
DIVIDE 8 to BOTH SIDES
8x/8 = 96/8
CANCEL out: 8/8 because that gives you 1
KEEP: 96/8 because that gives the value of x
96/8 = x
x = 12
Answer: x = 12
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)