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3 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]3 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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Use the graph to estimate the selling price for a 4-year old car.

muminat

Answer:

The Correct answer would be option D, $16,000.

Step-by-step explanation:

Look at the bottom section of the graph, that is labled

"Age (in years)" at the number 4 line (representing the 4 year old car), and find the nearest dot on that line of the graph, it goes directly to 16,000.

8 0

3 years ago

7x=5+5x x equals what

dybincka [34]

7x=5+5x

x=5/2

It could also be 2 1/2

3 0

3 years ago

Whoops i forgot to read the lesson :P 30 points

andriy [413]

Step-by-step explanation:

I'll do 2.

Alright,Alex let say we have factored a quadratic into two binomial, for example

$(5x + 3)(6x - 4)$

If we set both of those equal to zero

$(5x + 3)(6x + 4) = 0$

We can used the zero product property in this case to find the roots of the quadratic equation.

This means that

$if \: ab = 0 \: then \: a = 0 \: and \: b = 0$

This means we set each binomal equal to zero to find it root.

$5x + 3 = 0$

$5x = - 3$

$x = - \frac{3}{5}$

$6x + 4 = 0$

$6x = - 4$

$x = - \frac{2}{3}$

So our roots are negative 3/5 and negative 2/3 using zero product property

6 0

3 years ago

4(5x + 9)^2 – 33 = -21

ozzi

Answer:

x = sqrt(3)/5 - 9/5 or x = -9/5 - sqrt(3)/5

Step-by-step explanation by completing the square:

Solve for x over the real numbers:

4 (5 x + 9)^2 - 33 = -21

Add 33 to both sides:

4 (5 x + 9)^2 = 12

Divide both sides by 4:

(5 x + 9)^2 = 3

Take the square root of both sides:

5 x + 9 = sqrt(3) or 5 x + 9 = -sqrt(3)

Subtract 9 from both sides:

5 x = sqrt(3) - 9 or 5 x + 9 = -sqrt(3)

Divide both sides by 5:

x = sqrt(3)/5 - 9/5 or 5 x + 9 = -sqrt(3)

Subtract 9 from both sides:

x = sqrt(3)/5 - 9/5 or 5 x = -9 - sqrt(3)

Divide both sides by 5:

Answer: x = sqrt(3)/5 - 9/5 or x = -9/5 - sqrt(3)/5

7 0

4 years ago

Read 2 more answers

Given an equilateral triangle that has an area of 1959 cm2. What is the length of its sides?

Nina [5.8K]

Equilateral
equi means equal
lateral means sides

all sides are equal
triangle has 3 sides

perimiter=side1+side2+side3
side1=side2=side3

area=1/2 times base times height
base=side
draw a line down the middle of te tiangle so you get 2 right triangles side by side
1/2base is one leg
base is hypotonuse
height is unknown
equilateral means that it is a 30-60-90 triangle with hypotonuse equal to 2x, height=x√3, bottom is x
1/2 times base times height=1959
1/2 times x times x√3=1959
multiply both sides by 2
(x^2)√3=3918
divide both sides by √3
x^2=3918/√3
square root both sides
x=47.5611
side=hypotonuse=2x
2x=2*47.5611
side=95.12222

legnth of each side is $2\sqrt{ \frac{3918}{ \sqrt{3} } }$ cm or about 95.12222 cm

7 0

3 years ago