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4 years ago

Simplify the complex number. Express your answer in a + bi form and include each step necessary in simplifying.

/tex.z-dn.net/?f=%20%5Cfrac%7B3-2i%7D%7B1%2B4i%7D%20" id="TexFormula1" title=" \frac{3-2i}{1+4i} " alt=" \frac{3-2i}{1+4i} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

insens350 [35]4 years ago

3 0

$\dfrac{x+iy}{u+iv}\times\dfrac{u-iv}{u-iv}=\dfrac{(x+iy)(u-iv)}{u^2-(iv)^2}$
$=\dfrac{xu-i^2yv+iyu-ixv}{u^2+v^2}$
$=\underbrace{\dfrac{xu+yv}{u^2+v^2}}_a+i\underbrace{\dfrac{yu-xv}{u^2+v^2}}_b$

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Solve by elimination 3x+2y=19 -9x+8y=-29

Alja [10]

Step-by-step explanation:

(3x + 2y =19)(3)

-9x + 8y =-29

9x + 6y = 57 NOTE: we cross here 9x in first

-9x + 8y = -29 we cross here - 9x in second

Since 9x and - 9x are opposite

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6y +8y = 57 - 29

14y = 28

Y=28/14

Y=2

Replace y in second equation of this system:

-9x + 8y = - 29

-9x +8(2)= - 29

-9x + 16 = - 29

-9x = -29 - 16

-9x = - 45

X= -45/-9

X=5

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3 years ago

What is the slope of the graph of y=−8x+15 ?

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See the file attached (photo) above - That is the graph for (-(8*x))+15

Graph the line using the slope and y-intercept, or two points.

Slope: −8

y-intercept: (0,15)

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3 years ago

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3 years ago

1. What is the sum of the probabilities in a discrete probability distribution? Why?

ycow [4]

Answer:

Sum of probabilities in a discrete probability distribution is 1.

Step-by-step explanation:

The sum of the probabilities in a probability distribution is always 1.

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Each probability in the distribution must be of a value between 0 and 1.

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3 years ago

Match the one-to-one functions with their inverse functions.

Nady [450]

The inverse of a function is obtained by making x the subject of the formular of the function.

Given the function
$f(x)= \frac{x}{8} -7$
the inverse of the function is obtained as follows:
$y= \frac{x}{8} -7 \\ \\ y+7=\frac{x}{8} \\ \\ x=8(y+7) \\ \\ \bold{f^{-1}(x)=8(x+7)}$

Given the function
[tex[f(x)=x+7[/tex]
the inverse of the function is obtained as follows:
$y=x+7 \\ \\ x=y-7 \\ \\ \bold{f^{-1}(x)=x-7}$

Given the function
$f(x)=1- \frac{x}{3}$
the inverse of the function is obtained as follows:
$y=1- \frac{x}{3} \\ \\ -\frac{x}{3} =y-1 \\ \\ x=-3(y-1) \\ \\ \bold{f^{-1}(x)=-3(x-1)}$

Given the function
$f(x)=20-0.25x$
the inverse of the function is obtained as follows:
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