Identify the quotient in the form of a + bi.
1 + 6 divided by
−3 + 2i

Answers

Answer 1

The quotient of the expression in form of a + bi is 9/13 - 20/13i

Rationalizing complex expressions

Given the following expressions

1+6i/-3+2i

Rationalizing the given rational complex number, we will have;

= 1+6i/-3+2i * -3-2i/-3-2i

= (1+6i)(-3-2i)/9+4
= -3-2i-18i-12i²/13

Simplify the result to have:

= -3+12-20i/13
= 9-20i/13

Express in the form a + bi

9/13 - 20/13i

Hence the quotient of the expression in form of a + bi is 9/13 - 20/13i

Learn more on complex number here: https://brainly.com/question/10662770


Related Questions

Use the given information about angles ABC and DBC to solve for x and the measures of each of the angles. ABC andDBC are supplementary angles. mABC = 3x + 19 and mDBC = 7x - 9. Solve for x and the measures ofABC andDBC. Complete your work in the space provided. Include your calculations and the steps necessary to solve for the measures ofABC andDBC.

Answers

Answer:

Below in bold.

Step-by-step explanation:

Supplementary angles add up to 180 dgrees, so we have the equation:

3x + 19 + 7x - 9 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

x = 17.

So m <ABC = 3(17) + 19 = 70 degrees

and m < DBC = 7(17) - 9 = 110 degrees.

Answer:

3x + 19+7x-9=180

10x+10=180

10x=180-10

10x=170

x =17

The entire graph of the function f is shown in the figure below.

Write the domain and range of f using interval notation.

Answers

Answer:

no idea

is the answer

if you like my answer please like comment and mark me as brilliant

Tory is going to the fair with four of her friends. The entrance fee per person is $7.50. They plan to go together on all the rides. The cost of each ride is $3.00. Write an expression to represent the cost of the group to go to the fair for any number of rides.

Answers

Answer:

$37.5+$3r

Step-by-step explanation:

We can assume that the number of rides is r. Since each ride is $3.00, all rides are $3r ($3xr).

We also know that there are FIVE people going to the fair, with Tory being one and each of her friends. Since the entrance fee is 7.50, we can do 7.50x5 which is $37.5.

Then, you can add it which is $37.5+$3r

Mandy paints four square walls that are ten feet on each side. Which expression represents the total square footage that Mandy painted?

4 × 102
42 × 10
4 × 10 × 2
102 + 4

Answers

Answer:

C. 4 × 10 × 2

Step-by-step explanation:

There are four walls that are ten feet on each side.

You would take 4 (number of walls) × 10 (number of feet in length), and because there are 2 sides of the walls, you would take that × 2.

Therefore, your answer is 4 × 10 ×2

what is the distance of 53 yards square

Answers

Answer:

477 square foot

Step-by-step explanation:

cause yea

Sadie is saving for a new car. Below is the total amount of money in her savings account on the last day of each month. show all steps to find the mean amount of money Sadie saves each month. Round your answers to the nearest cent.

Are physical activities becoming safer or more dangerous

Answers

The mean amount of money Sadie saves each month is $10,724.29.

What is the mean amount of money saved each month?

Mean is a measure of central tendency that is used to determine the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(10150 + 102211 + 10424 + 10769 + 11155 + 11477) / 7 =  $10,724.29.

To learn more about mean, please check: https://brainly.com/question/25842202

Landry is going to wrap a birthday present for his mom. He needs to know how much wrapping paper he needs to wrap the present with no overlap.

volume
or
surface area​

Answers

Answer:

  surface area

Step-by-step explanation:

Wrapping paper covers the surface of an object.

To know how much paper he needs, Landry will need to determine the surface area of the present.

Is 5/2 to the right of number 1 on number line?

Answers

Answer:

Yes;

Step-by-step explanation:

5/2 = 2 1/2

2 1/2 > 1

Yes, 5/2 is to the right of 1 on a number line.

Yes it would be to the right of number one


Explanation:the fraction 5/2 represents 2 and a half thus since numbers greater than one are to the right of the number line 5/2 is to the right

Help pls!!!!!!!!!! :<<<<

Answers

The answer to this question is D 2/4

Which of these inequalities means that
18 is greater than three times a number?

Answers

hello!

Let's write this verbal phrase as an inequality.

First of all, let the number be n.

"three times n" can be written like so:-

[tex]\pmb{3n}[/tex]

Now, 18 is greater than 3n:-

[tex]\pmb{18 > 3n}[/tex]

Which means 3n is less than 18:-

[tex]\bigstar{\boxed{\pmb{3n < 18}}}[/tex]

note:-

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

The amount of work to move a chair to the living room is equal to 10 joules. How much work would it be to move the same chair using a simple machine?

Answers

The work done by the machine is the product of force and distance

The amount of work done by the machine is 10 joules

How to determine the amount of work?

The amount of work done is calculated using:

W = Fd

Where:

F represents the forced represents the distance

The distance moved to the living room is the same when you move the chair or a machine does is the same.

Also, if the force applied in moving the chair remains unchanged, the amount of work done would be the same.

Hence, the amount of work done by the machine is 10 joules

Read more about work done at:

https://brainly.com/question/18762601

Evaluate lim x²-1 x/x^2+3x-4​

Answers

Nandyan na po

Step-by-step explanation:

I hope I help

GIVING BRAINLIEST!

2pi8^2 + 2pi8*8=?

the answer should be 150, show the steps

Answers

Answer:

256π

Step-by-step explanation:

2π(8²) + 2π(8)(8) <== exponents first

2π(64) + 2π(64) <== multiply

128π + 128π <== add

256π <== final answer

Note: 8 * 8 can also be written as 8²

Hope this helps!

Answer:

256π

Step-by-step explanation:

4π(8²) =   4π(64)=  804.2477193

804.2477193/π = 256π

Jacob can swim the 400-meter distance in 6.4 minutes now.How many more meters per minutes will Jacob need to swim to reach is goal?Explain how you found your answer.

Answers

Answer:

62.5 meters per minutes

Step-by-step explanation:

12y – 2x = 12
slope intercept form

Answers

Answer:

Step-by-step explanation:

12y = 2x + 12

y = 2/12x + 12/12

y = 1/6x + 1

The slope intercept form is y = (1/6)x + 1.

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

12y - 2x = 12

The slope intercept form is y = mx + c.

So,

12y - 2x = 12

Add 2x on both sides.

12y = 12 + 2x

12y = 2x + 12

Divide both sides with 12.

y = (2/12)x + (12/12)

y = (1/6)x + 1

Thus,

The slope intercept form is y = (1/6)x + 1.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ2

equivalent (x+ 4)(2r - 1)

Answers

Answer:

Step-by-step explanation:

r (2 x + 8) - x - 4

(2 r - 1) x + 8 r - 4

Suppose that you have been hired at an annual salary of $16,000 and expect to receive annual increase of 3%. What will your salary be when you begin your sixth year?

Answers

well, at the beginning of the 6th year, you've been there for 5 whole years, so you've gotten 5 increases hmmm

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &16000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &5\\ \end{cases} \\\\\\ A=16000(1 + 0.03)^{5}\implies A=16000(1.03)^5\implies A\approx 18548.39[/tex]

Question - I need more ----- inside of my life

Answers

Answer:

Hi, this is not really a question it is a statement but if you really need help with math then you can provide an actual question.

Step-by-step explanation:

Answer:

Then you must improve to get more things in your life

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

180- (55) = ACB 125
Angles on a straight line =180
ACE and 90° adjacent on a straight line so they add up to 125

What is the equation for the graph shown?

Answers

Answer:

[tex]y = \frac{2}{3}x + 4[/tex]

Step-by-step explanation:

The rule for graphs is:

[tex]y = mx + c[/tex]

Where [tex]m[/tex] is the gradient and [tex]c[/tex] is the y-intercept (where the line crosses the y-axis)

We can work out c by looking at our graph.

Our line crosses the y-axis at (0, 4). So... [tex]c=4[/tex]

To work out our gradient of a straight line (which is what we have)

We use the formula:

[tex]m = \frac{\triangle y}{\triangle x}[/tex]

The triangle [tex]\triangle[/tex] just means the "change in" the coordinates between any two points.

To calculate the change in y, we can pick any two points on our line!

Let's go for (0, 4) and (-6, 0)

To work out the gradient:

[tex]m = \frac{\triangle y}{\triangle x} = \frac{0 - 4}{-6 - 0} = \frac{-4}{-6} = \frac{4}{6} = \frac{2}{3}[/tex]

Using our formula

[tex]y = mx + c[/tex]
[tex]y = \frac{2}{3}x + 4[/tex]

integrate the following by parts |x^2 e^2x dx​

Answers

Answer:

The answer is shown in the picture. you basically have to do integration by parts 2 times to get final answer.

The circumference of circles

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's find the circumference of given circle ~

Circumference :

[tex]\qquad \tt  \dashrightarrow \: \pi{d}^{}[/tex]

where, d = diameter

Now, let's calculate it ~

[tex]\qquad \tt  \dashrightarrow \: c = 4×\pi{}^{}[/tex]

[tex]\qquad \tt  \dashrightarrow \: c = 4\pi\: \: in[/tex]

That's the answer I terms of π, but we can also plug in the approximate value of pi as 3.14

[tex]\qquad \tt  \dashrightarrow \: c = 4 \times 3.14{}^{}  \\\qquad \tt  \dashrightarrow \: c = 12.56\: \: in\\\qquad\tt \dashrightarrow \: c \approx 12.6\: \: in[/tex]

Help picture below problem 9

Answers

Answer:

sometimes...

Step-by-step explanation:

mark me brainliest

A parallelogram is sometimes a rectangle.

A) sometimes

Explanation:

because the vertices join the adjacent sides at 90° angles and it has two sets of parallel sides and two pairs of opposite sides that are congruent. (a rectangle has all of the properties of a parallelogram.)

Write the following in words in international system with comas:
34407615​

Answers

Answer:

34,407,615

Explanation : 34 millions 407 thousands 615

Given m n, find the value of x.
(7X-10)9
(6x-5)°

Answers

Answer:

x = 15

Step-by-step explanation:

Since m and n are parallel to the line t.

Then (7x - 10) + (6x - 5) = 180° supplementary angles for a linear pair.

(7x - 10) + (6x - 5) = 180°

13x -15 = 180°

13x = 195°

x = 15

Plug x into the angles to solve for angle.

(7x - 10)

(7*15 - 10) = 105 - 10 = 95°

(6x - 5) =

(6*15 - 5) = 90 - 5 = 85°

[50 points]
P(AB) = P(An B)/P(B)

Freshmen
Sophomores
Juniors
Seniors
Boys
3
1
4
2
Girls
7
9
5
1
P(Boy|Sophomore) =

Answers

Answer:

[tex]\sf \dfrac{1}{10}[/tex]

Step-by-step explanation:

From the table:

Total number of Sophomores = 10Total number of students = 37Total number of Boys who are Sophomores = 1

[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]

[tex]\sf \implies P(Sophomore)=\dfrac{10}{37}[/tex]

[tex]\sf \implies P(Boy \cap Sophomore)=\dfrac{1}{37}[/tex]

[tex]\begin{aligned}\sf P(Boy | Sophomore) & = \sf\dfrac{P(Boy \cap Sophomore)}{P(Sophomore)}\\\\ & = \sf \dfrac{1}{37} \div \dfrac{10}{37}\\\\ & = \sf\dfrac{1}{37} \times\dfrac{37}{10}\\\\ & = \sf\dfrac{1}{10}\end{aligned}[/tex]

Answer:

1/10

Explanation:

Given Boy Sophomores: 1

Given Total Boy: 3 + 1 + 4 + 2 = 10

So

⇒  P(Boy|Sophomore)  

⇒  Boy Sophomore/Total Boy

⇒  1/10

show work. A 2​-ft wide circular track for a camera dolly is set up for a movie scene. The two rails of the track form concentric circles. The radius of the inner circle is 59 ft. How much farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one​ turn?

Answers

Step-by-step explanation:

oh that is again something you can nicely envision :

the inner circle has a radius of 59 ft.

so, because of the 2 ft wide track the outer circle has a radius of 59+2 = 61 ft.

the circumference of a circle is

2×pi×r

the answer to the question is simply the difference bergen the 2 circumference values.

inner circle :

2×pi×59 = 118pi

outer circle :

2×pi×61 = 122pi

the difference is

122pi - 118pi = 4pi = 12.56637061... ft ≈ 12.6 ft

the wheel on the outer track travels about 12.6 ft farther than a wheel on the inner track in one full turn.

These diagrams show the dimensions of two different windows. Which of the following statements are true? Choose all that apply.
Window A
3 ft
8 ft
Window
B
4 ft
6 ft
O A. The windows have the same area.
B. The perimeter of Window A is less than the perimeter of Window B.
C. The perimeter of Window B is 20 feet.
OD. The area of Window A is 22 square feet.

Answers

A, and C is the answer

Enter a recursive rule for the geometric sequence.
3, - 12, 48, - 192, ..

Answers

Start at 3 and multiply by -4 each time.

A rectangle has a length of 10 cm and a width of 7 cm. What is its perimeter?
44 cm
70 cm
34 cm
17 cm

Answers

Answer:

34 cm

Step-by-step explanation:

Keep in mind that the perimeter of a rectangle is the sum of the measures of its sides. This means that the sum of the longer sides and the shorter sides is the perimeter of the rectangle.

Let "L" represent the longer side (length) of the rectangle and "S" represent the shorter side (width) of the rectangle.

⇒ Perimeter of rectangle = L + S + L + S

⇒ Perimeter of rectangle = 2(L) + 2(S)

⇒ Perimeter of rectangle = 2(L + S)

Now, let's substitute the length and the width in the perimeter and simplify.

⇒ Perimeter of rectangle = 2(10 + 7)                                                [L = 10; S = 7]

⇒ Perimeter of rectangle = 2(17)

Perimeter of rectangle = 34 cm

Answer: 70 cm

Step-by-step explanation: 10 x 7 = 70

hope this helps

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