Answer:
see below
Step-by-step explanation:
Since RT bisects QRS
1/2 QRS = TRS
1/2 ( 9x+214) = -9x+53
Multiply each side by 2
9x +214 = -18x+ 106
Add 18x from each side
9x +214+18x = 106
27x +214 = 106
Subtract 214 from each side
27x = 106-214
27x =-108
Divide by 27
27x/27 = -108/27
x = -4
TRS = -9x+53
=-9 *-4 +53
= 36+ 53
=89
<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:
33.08 m
Step-by-step explanation:
angle of ∆ = 131.6 - 90 = 41.6
=> x² = 8²+3²-2(8)(3)cos 41.6°
= 64+9-48(0.75)
= 73 - 36
= 37
x = √37 = 6.08 m
perimeter = (3×8)+3+6.08 = 33.08 m
The answer is D it shrinks to 35
