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The product $c_1 c_2$ in rectangular frame is [tex]\$10 e^{i(2\theta \pm \frac{pi}{3})}\$.[/tex]

Let $c_1$ and $c_2$ be the two complex numbers that frame an even triangle with $3+2i$ and $6+i$.

The dispose of between two complex numbers $a$ and $b$ is given by $|b-a|$. Since the triangle is even, the wipe out someplace in the scope of $3+2i$ and $6+i$ ought to be equivalent to the underlying venture with to the kill among $3+2i$ and $c$, conjointly make back the underlying speculation with to the take out among $6+i$ and $c$.

So, we have the following conditions:

$|6 + i - (3 + 2i)| = |c - (3 + 2i)|$

$|6 + i - (3 + 2i)| = |c - (6 + i)|$

Tackling these conditions, we get:

$|3 - i| = |c - (3 + 2i)|$

$|3 - i| = |c - 6 - i|$

Presently, let's discover the esteem of $c$:

$|c - (3 + 2i)| = |3 - i|$

[tex]\$|c - (3 + 2i)| = \sqrt{(3-0)^{2} + (-1-0)^{2} = \sqrt{10}\$[/tex]

So, [tex]\$c - (3 + 2i) = \pm \sqrt{10} e^{i\theta}\$[/tex], where [tex]\$\theta\$[/tex] is the point between the positive genuine hub and the line interfacing $3+2i$ and $c$?

Presently, let's discover the esteem of $c$ utilizing the moment condition:

$|c - (6 + i)| = |3 - i|$

[tex]\$|c - (6 + i)| = \sqrt{(3-0)^{2} + (-1-0)^{2} = \sqrt{10}\$[/tex]

So, [tex]\$c - (6 + i) = \pm \sqrt{10} e^{i\theta'}\$[/tex], where [tex]\$\theta'\$[/tex] is the point between the positive genuine hub and the line interfacing $6+i$ and $c$?

Since the triangle is equilateral, $theta$  [tex]\$\theta'\$[/tex] must vary by [tex]\$\pm[/tex] [tex]\frac{\pi}{3}\$.[/tex]

Presently, let's discover the item $c_1 c_2$:

$c_1 c_2 = (c - (3 + 2i))(c - (6 + i))$

$c_1 c_2 =[tex](\pm \sqrt{10} e^{i\theta})(\pm \sqrt{10} e^{i(\theta \pm \frac{\pi}{3})})\$[/tex]

$c_1 c_2 = [tex]10 e^{i\theta} e^{i(\theta \pm \frac{\pi}{3})}\$[/tex]

$c_1 c_2 = [tex]10 e^{i(2\theta \pm \frac{\pi}{3})}\$[/tex]

So, the item $c_1 c_2$ in rectangular frame is [tex]\$10 e^{i(2\theta \pm \frac{\pi}{3})}\$.[/tex]

Learn more about rectangular form here:

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Answer:

$-280

Step-by-step explanation:

Tiffany withdrew $20, 14 times. a withdrawal means the amount in her account would reduce.

total change in balance = 20 x 14 = 280

because it is a withdrawal, a negative sign would be attached

Answer: -280

Step-by-step explanation:

Answer:

34.6 and 145.4

Step-by-step explanation:

x+(x+110.8) = 180

2x= 180-110.8

2x= 69.2

x= 34.6

Measure of each angle:

x= 34.6

x+110.8 = 34.6 + 110.8 = 145.4

Answer:

Step-by-step explanation:

Use the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] For us that will look like this:

[tex]d=\sqrt{(6-(-3))^2+(-2-4)^2}[/tex] which simplifies to

[tex]d=\sqrt{(9)^2+(-6)^2}[/tex] and a bit more to

[tex]d=\sqrt{81+36}[/tex] so

[tex]d=\sqrt{117}[/tex]

Answer:

f

Step-by-step explanation:

Answer:

C = pi d

C = 3 × 36

C = 108

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Answer:

Total amount pay for new apartment = $4,740.75

Step-by-step explanation:

Find:

Total amount pay for new apartment

Computation:

Particular                                       Amount

Monthly rent of apartment           $1,650

Add:

Application fee [1,650 x 1.5%]      $24.75

Credit application fee                   $30

Security rent                                  $1,650

Broker's fee [1,650 x 12 x 7%]      $1,386

Total                                               $4,740.75

Total amount pay for new apartment = $4,740.75

Answer: the answer is 63,ABC

Step-by-step explanation:

Answer:

EarthQuakes

Step-by-step explanation:

I think it's b.  This is because people should be smart enough to not build near volcanos, floods with enough pressure would knock the building down no matter what, and I don't know much about landslides.  

Answer:

16

Step-by-step explanation:

Formula for volume of a rectangular prism

Volume = length * width * height

Volume = 4 * 2 * 3

Volume = 24 cubic cm

I hope this helps :)

Answer:

Step-by-step explanation:

Hi, Emily. The average rate of change can be calculated by adding all the profits together and dividing by the different profits (4 profits all together A to D) so 10,600+21,600+-21,600+-10,600= 0

0/4= 0

So we can best describe this as 0 or nothing at all as it hasnt changed from year 2 to 4.

Many Regards,

                          Abdelmumen Nakoa

A fellow 8th grader.

Answer:

she will need to work for 55 hours to buy the phone

Step-by-step explanation:

680 - 240 = 440

that's how much more she needs

449 ÷ 8 = 55

and that's the answer

55

hope that helped

Answer:

55 hours

Step-by-step explanation:

Well first we need to set up the equation

We know she needs 680$ to buy the phone so the equation must be equal to 240

She has 240 and earns 8 dollars per hr so were finding out how many hours of work is needed to be able to buy the phone

Represent the number of hours worked by "x"

Set the equation up as

240 + 8x = 680

Add -240 to both sides of the equation to make 240 be 0 and 680 be 440

8x = 440

divide both sides of equation by 8 to get what x equals

x=55

She needs to work 55 hours

Answer:

60

Step-by-step explanation:

3+2=5

5*12=60

Respuesta:

¿El punto que colocó después del segundo corchete indica multiplicar? Si es así, aquí está la respuesta.

Explicación paso a paso:

3 + 2 = 5

5 * 12 = 60

Respuesta: 60

Answer:

angle R = 37

angle Q= 114

angle p = 29

Step-by-step explanation:

(3x+3) +(x-8) +(x) =180

5x-5=180

x=185/5

x=37

Answer: uhhhh try the first one

Step-by-step explanation:

Answer:

5/6

Step-by-step explanation:

See the steps below:)

Answer:

5/6

Step-by-step explanation:

PEMDAS

the number of yellow ball is 18

Answer:

5.656854

Step-by-step explanation:

So technically, the distance is the hypotenus of the right triangle that forms.

That means we find the square root of 32, or the hypotenuse

[tex]\sqrt{32} = 5.656854[/tex]

Look at picture below for what I mean.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

6 out of the last 15 = 6/15 = 0.4 = 40% of the people won a prize.

Multiply the 20 players by 40%:

20 x 0.4 = 8

You would expect 8 people to win.

Answer:

8

Step-by-step explanation:

Answer:

Yes, she will have $1.96 left

Step-by-step explanation:

Initial cost : $60

Discount : 25%=0.25

Calculating discount : 60 * 0.25 = 15

Calculating cost after discount : 60-15 = 45

Sales tax : 6.75%=0.0675

Calculating sales tax : 45 * 0.0675 = 3.0375≈$3.04

Calculating final cost : 45+ 3.04 = $48.04

Can she buy the printer : 50 - 48.04= $1.96

Answer : yes

Yes, she has enough money to buy the printer.  Then the balance of her account will be $ 1.9625.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.

Grace needs to buy a new printer.

The printer she wants has a price tag of $60.

She has a 25% off coupon and $50 in her bank account.

If she must pay 6.75% sales tax.

Then the price of the printer after the discount of 25% and the sales tax of 6.75% will be

Cost = $ 60 x (1 - 0.25) x 1.0675

Cost = $ 60 x 0.75 x 1.0675

Cost = $ 48.0375

Yes, she has enough money to buy the printer.

Then the balance of her account will be

Balance = $ 50 - $ 48.0375

Balance = $ 1.9625

More about the percentage link is given below.

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Answer:

Step-by-step explanation:

To solve this problem you need the function

h(t) = -16t2 + v0t + h0

where t = time

v0 is the initial velocity, which in our case is 0

h0 = initial height, which in our case is 256

h(t) = 0 since we want to know when the ball will hit the ground.

0 = -16 t2 + 256

And we can solve for t

If we rearrange the terms we see that this is a difference of 2 squares

0 = 256 - 16t2

0 = (16-4t)(16+4t)

Setting each factor = 0

16-4t=0       16+4t=4

t = 4             t = -4

The second solution is discarded as time cannot be negative.

So the ball will hit the ground in 4 seconds.

Answer:

A_16x20=320

Step-by-step explanation:

Esto se puede hacer fácilmente de 2 formas.

1) 20 se puede dividir en un múltiplo de 10 y luego multiplicar

16 x 20 =16 x 10 x 2 = 160 x 2 = 320

2) Uso de cero.

Cualquier cosa multiplicada por cero da un cero y luego multiplicar el otro número da el resultado.

16 x 20 = (16 x 2) * 10 = (32) 10 = 320

Así que separamos el cero añadiéndole un 1, lo que lo convierte en 10 y obtenemos el mismo resultado.

This can be easily done in 2 ways .

1) 20 can be broken into a multiple of 10 and then multiplied

16 x 20 =16 x10 x 2=160x 2= 320

2) Use of zero.

Anything multiplied with zero gives a zero and then multiplying the other number gives the result.

16 x 20 = (16x 2) *10= (32)10= 320

So we separated the zero by adding a 1 to it thus making it 10 and we get the same result.

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=================================================

Explanation:

Use a marker to highlight the first three digits on the left. That would be the 7, 0 and 0.

The digit just to the right of that second "0" is the digit "9". Since this 9 is larger than 5, we'll bump the 7.00 up to 7.01

The 0 in 7.01 is significant because it's between two nonzero values. So we have three sig figs here.

Answer:Each of the 17 students will need to raise 37.58 each

Step-by-step explanation:

Total amount needed to be raised =857.11

Amount of money already raised =218.25,

Amount of money required to complete the amount  needed to be raised =857.11 -218.25=638.86

Since there are 17 students to raise the money, Each student will raise

638.86/17=37.58

Each of the 17 students will need to raise 37.58 each  to complete the money

Given:

The matrix is [tex][-8][/tex].

To find:

The determinant of given matrix, i.e, [tex]|-8|[/tex].

Solution:

If a matrix is A of order [tex]1\times 1[/tex], then the value of the determinant of that matrix is equal to the element of that matrix.

For example: Let A be the matrix of order [tex]1\times 1[/tex].

[tex]A=[a][/tex]

Then,

[tex]|A|=a[/tex]

The given matrix is [tex][-8][/tex]. So, the  determinant of given matrix, i.e, [tex]|-8|[/tex], is

[tex]|-8|=-8[/tex]

Therefore, the value of determinant of given matrix is -8.