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: -42
Step-by-step explanation: 2*2 matrices are easy to find the determinant with. Its just ad-bc, so (5*-2)-(4*8), which is -42
Answer:
x = 0.72
Step-by-step explanation:
Given
3.8x = 2.736 ( divide both sides by 3.8 )
x = 0.72
The metric table goes: millimeters, centimeters, decimeters, meters, dekameters, hectometers, kilometers. To move up the table, move the decimal point one to the left. To go from millimeters to centimeters, your answer would be 8,340,000.0, which is 8,340,000. However, you want kilometers. This would be 83.4 kilometers. Hope this helps!
Answer: Cluster Sampling
Step-by-step explanation:
In cluster sampling, researcher divides the population into groups ,which are called clusters. Then random sample of clusters are chosen ,and researcher conduct study to collect data about the population.
Here each bus is considered a cluster ,because busses are selected at random ,this sampling would be an example of cluster type of sampling.
