(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)
… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)
… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))
… = (2 - 2√3 <em>i</em> ) / 4
… = 1/2 - √3/2 <em>i</em>
… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))
… = exp(<em>i</em> arctan(-√3))
… = exp(-<em>i</em> arctan(√3))
… = exp(-<em>iπ</em>/3)
By DeMoivre's theorem,
[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1
3(x^2+10x+5)-5(x-k)=
3x^2+30x+15-5x+5k=
3x^2+25x+15+5k
for this to be divisible by x every term must include x or get eliminated
the problematic terms are 15 and 5k
to eliminate them they must equal 0 when added:
15+5k=0
5k=-15
k=-3
so A) -3 is the solution
Answer:
25 = base
Step-by-step explanation:
I searched all of this on YT to try and help
so first we need to know the area of a Trapezoid
A = 1/2h(b + b)
86 = 1/2(18 + b)4
we dont know the base where going to put b
we also dont like fractions so where going to get rid of 2 by multiplying 2 by 2. And we do it in both ends, so where doing the same with our Area.
172 = (18 + b)4
the 4 is multipling so divide it on both ends.
43 = (18 + b)
then do the opposite operation on the 18, by subtracting 18 on both sides.
25 = b
is the base
check the work by plugging it back in
A = 1/2h(b + b)
A = 1/2 4(18+25)
A = 1/2 4(43)
A = 1/2(172)
A = 86in