<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> )
<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> ) × (-1 + <em>i</em> ) / (-1 + <em>i</em> )
<em>z</em> = (3<em>i</em> × (-1 + <em>i</em> )) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3<em>i</em> + 3<em>i</em> ²) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3 - 3<em>i </em>) / (1 - (-1))
<em>z</em> = (-3 - 3<em>i </em>) / 2
Note that this number lies in the third quadrant of the complex plane, where both Re(<em>z</em>) and Im(<em>z</em>) are negative. But arctan only returns angles between -<em>π</em>/2 and <em>π</em>/2. So we have
arg(<em>z</em>) = arctan((-3/2)/(-3/2)) - <em>π</em>
arg(<em>z</em>) = arctan(1) - <em>π</em>
arg(<em>z</em>) = <em>π</em>/4 - <em>π</em>
arg(<em>z</em>) = -3<em>π</em>/4
where I'm taking arg(<em>z</em>) to have a range of -<em>π</em> < arg(<em>z</em>) ≤ <em>π</em>.
Answer:
A(...; 7)
x =-1/5
B(8; ...)
y = 48
The slope is 5
Step-by-step explanation:
y−5x=8
A(...; 7)
We know that y=7, we need to find x
7 - 5x = 8
Subtract 7 from each side
7-7 -5x = 8-7
-5x =1
Divide by -5
-5x/-5 = 1/-5
x =-1/5
B(8; ...)
We know x = 8 we need to find y
y−5x=8
y - 5(8) = 8
y - 40 =8
Add 40 to each side
y-40+40 = 8+40
y = 48
Now we need to find the slope
y - 5x =8
Add 5x to each side
y -5x+5x = 5x+8
y = 5x+8
This is in the form y = mx+b where m is the slope
The slope is 5
<h3>
Answer: Choice B. f(x) = 100 - 68x</h3>
Work Shown:
Solve for y. Then replace y with f(x).
Effectively this involves adding 1000 to both sides and subtracting 680x from both sides, afterward we divide both sides by 10 to isolate y.
Answer: 90
Step-by-step explanation:
45.5-.5=45
45^2=90
Answer:
You get a total of two hours of parking.
Step-by-step explanation:
First, you subtract the base fee of $3.50, which gives you $18.00. Then you subtract as many sevens there are in 18, which is two. And then your answer is shown, as two. Hope this helps!
