Answer:
given you are asked to simplify
Step-by-step explanation:
You have to multiply the numerator and denominator by the denominator's conjugate.
The conjugate of a+bi is a-bi.
When you multiply conjugates, you just have to multiply first and last.
(a+bi)(a-bi)
a^2-abi+abi-b^2i^2
a^2+0 -b^2(-1)
a^2+-b^2(-1)
a^2+b^2
See no need to use the whole foil method; the middle terms cancel.
So we are multiplying top and bottom of your fraction by (-3+4i):
So you will have to use the complete foil method for the numerator. Let's do that:
(-3+5i)(-3+4i)
First: (-3)(-3)=9
Outer:: (-3)(4i)=-12i
Inner: (5i)(-3)=-15i
Last: (5i)(4i)=20i^2=20(-1)=-20
--------------------------------------------Combine like terms:
9-20-12i-15i
Simplify:
-11-27i
Now the bottom (-3-4i)(-3+4i):
F(OI)L (we are skipping OI)
First:-3(-3)=9
Last: -4i(4i)=-16i^2=-16(-1)=16
---------------------------------------------Combine like terms:
9+16=25
So our answer is ![\frac{-11-27i}{25}{/tex] unless you want to seprate the fraction too:[tex]\frac{-11}{25}+\frac{-27}{25}i](https://tex.z-dn.net/?f=%5Cfrac%7B-11-27i%7D%7B25%7D%7B%2Ftex%5D%20unless%20you%20want%20to%20seprate%20the%20fraction%20too%3A%3C%2Fp%3E%3Cp%3E%5Btex%5D%5Cfrac%7B-11%7D%7B25%7D%2B%5Cfrac%7B-27%7D%7B25%7Di)
Answer:
5 weeks
Step-by-step explanation:
32
21
week 1 over ^
34
26
week 2 over^
36
31
week 3 over ^
38
36
week 4 over ^
40
41
week 5 over ^
Answer:
D
Step-by-step explanation:
This should be easy one unless you're making silly mistake like forgetting to take reciprocal of 
lets do it:
÷ first: we take the reciprocal of 3/2x now its
* 
now just multiply top and bottom by using distributive method
this is your answer.
Answer:
The length of diagonal BD is 11·(1 + √3)
The length of diagonal AC = 22
Step-by-step explanation:
The given data are;
Quadrilateral ABCD = A kite
The length of segment AD = 22
The measure of ∠DAE = 60°
The measure of ∠BCEE = 45°
Whereby, triangle ΔADE = A right triangle, and DE is the perpendicular bisector of AC, by trigonometric ratio, we have;
AE = EC
DE = 22 × sin(60°) = 11·√3
AE = 22 × cos(60°) = 11
∴ AE = EC = 11
BE = EC × tan(∠BCE) = 11 × tan(45°) = 11
The length of the diagonal BD = BE + DE (By segment addition property)
∴ BD = 11 + 11·√3 = 11·(1 + √3)
The length of diagonal BD = 11·(1 + √3)
The length of diagonal AC = AE + EC
∴ AC + 11 + 11 = 22
The length of diagonal AC = 22.
