Perform the indicated operation and express the result as a simplified complex number in the form a+bi. Do not put any spaces between your characters. If your answer includes a number that is not an integer type it as a decimal rounded to the nearest hundredth.
(3+4i)/(2-i)
simplifies to a+bi where:

A=

B=

Answers

Answer 1

9514 1404 393

Answer:

  0.40+2.20i

Step-by-step explanation:

To clear the denominator of its imaginary part, multiply numerator and denominator by the conjugate of the denominator.

  [tex]\dfrac{3+4i}{2-i}=\dfrac{(3+4i)(2+i)}{(2-i)(2+i)}=\dfrac{6-4+3i+8i}{4+1}=\dfrac{2+11i}{5}\\\\=\boxed{0.40+2.2i}[/tex]

_____

Additional comment

This "multiply by the conjugate" is also used to clear radicals from the denominator. It takes advantage of the factoring of the difference of squares:

  (a -b)(a +b) = a² -b²


Related Questions

how many 3/5s are in 9/10

Answers

Answer:they are only 2

Step-by-step explanation:

3/5 + 3/5 = 6/10 so you need a 6/5 + 3/5 and it will equal 9/10

Answer:

1

Step-by-step explanation:

3/5's = 6/10 and 6/10 plus 6/10 would be 12/10 so only 1 3/5's can fit.

what is the volume of the prism ?

Answers

Answer:

Your answer is 150 units!

Your answer is 150 units. hope this helps :)

which expression is equivalent to 3(x+5)-6
A) 3x-3
B)3x-1
C )3x+9
D) 15x-6

Answers

Answer:

answer C. 3x + 9

Step-by-step explanation:

3(x + 5) - 6 =

3x + 15 - 6 =

3x + (15 - 6 ) =

3x + 9

3(x+5)-6

Multiply 3 by the inside parenthesis:

3x+15-6

Subtract

3x+9

This means our answer is C) 3x+9

I hope this helps! :)

HELP ME PLEASE


whats 9+10?​

Answers

Answer:

21

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

A flower pot in the shape of a truncated cone with a height of 8 in. was formed by slicing off the tip of a cone along a plane parallel to the base.The original cone had a height of 12 in. and a volume of 810 in3. What is the volume of the tip that was sliced off?
A)30 in3B)60 in3C)90 in3EliminateD)180 in3

Answers

the correct answer is B

hope I helped

Write an equation in slope-intercept form of the line that passes through (0, 6) and (3, -3)

Answers

Answer:

y=-3x+6

Step-by-step explanation:

Using slope formula

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex](0,  6) x1, y1(3, -3) x2, y2[tex]\frac{-3-6 }{3-0}=\frac{-9}{3}=-3[/tex]

Find the exact length of the third side.

10

8

Answers

Answer: 6

Step-by-step explanation:

The typical way to solve this problem is with the Pythagorean Theorem, which states that a^2 + b^2 = c^2, where a and b are the legs of the right triangle, and c is the hypotenuse.  Unfortunately, due to a lack of a diagram, I am forced to infer.

Because the most famous Pythagorean triplet is 3, 4, 5, and 8 and 10 are multiples of the latter two terms, I can infer that the final side length is 6.

Hope it helps :) and if it is wrong, please let me know, and repost another question with the provided diagram.

I-Ready find the measure of angle RST

Answers

Answer:

Step-by-step explanation:

You need an image for problem to be solved, please repost it with a image, so it can be solved

1. Describe the three-dimensional shape that is generated by
rotating the two-dimensional shape around the axis shown.
A rectangular prism
C cylinder
B cube
D triangular prism

Answers

Answer:

Cylinder and cube are three dimensional shape

Answer:

triangular prism

rectangular prism

Step-by-step explanation:

How do you find the quotient in the equation 8÷304

Answers

Answer:

304 divided by 8 in decimal = 38

304 divided by 8 in fraction = 304/8

304 divided by 8 in percentage = 3800%

Step-by-step explanation: You just simply divide.

Rachel has 16 chocolate bars . Tracy takes 4 and asks for the remaining quarter. what would she end up with?

Answers

Answer:

Rachel ends up with 9 chocolate bars.

Step-by-step explanation:

16 - 4 = 12

quater is 1/4, so

12 / 4 = 3

12 - 3 = 9

Answer:

9 chocolate bars

Step-by-step explanation:

Rachel had 16 chocolate bars and Tracy takes (minus) 4.Now she has 12.

Tracy asks for the remaining (12) quarter. A quarter is 1/4, and a quarter of 12 is 3.

That leaves Rachel with 9, because 12 - 3 is 9.

identify the like terms of 3x, chose all the apply
3y
5x
3xy
-2x
3
7y
x

Answers

Answer:

5x, -2x, and x

Step-by-step explanation:

Like terms share the same variable and powers. This means that the options with 'x' as an variable would be the like terms of 3x.

5x , -2x  , and x are like terms because they share the same variable, 'x'.

Hope this helps.

Jessica's curtain company is making curtains for a local hotel. She wants each curtain to be 24 inches long. At the fabric store, fabric is sold by the foot. If Jessica's curtain company wants to make 79 curtains, how many feet of fabric will she need? 1 inch = 1 twelfth foot

Answers

Answer:

158 feet

Step-by-step explanation:

24 inches = 2 feet

79 x 2 = 158

what is the pattern you notice when dividing 10,100,1000

Answers

Answer:

Step-by-step explanation:

Image result for what is the pattern you notice when dividing 10,100,1000

When dividing by ten, move the decimal point one place to the left. Place value is the value of a digit based on its location in the number. When dividing by 100, move the decimal place two places to the left. And, remember, if there's no decimal point, assume that the decimal falls at the end of the number.

Answer:

when you divide those numbers the place value shifts by 1.

Step-by-step explanation:

1000.0 to 100.00 to 10.000 to 1.0000 to .10000

what is equivalent to |14-20|

Answers

Answer:

7/10

Step-by-step explanation:

Which number sentence is true?
A. -4.25 > -2 4/5
B. 6/11 > 6.11
C. 7/8 > -0.78
D. 14/8 > 8.1

Answers

Answer: C. Is true 7/8>-0.78

How many solutions does 3(x + 5) - 3 = 2(3x + 1) - 3x have? Show your work.
2noop
no
ordon
dos
SOLUTION I don’t want the answer I just wanna know how to solve it cause I’m bad at math

Answers

Answer:

No solution

Step-by-step explanation:

1.Simplify

3(x+5)-3 = 2(3x+1) -3x

3x+15-3=6x+2-3x

2.Simplify

3x+12=3x+2

3. Combine like terms

3x-3x+12-2=3x-3x+-2

10 does not equal 0

No solution

Answer:

[tex]\boxed{\boxed{\sf No\:Solution}}[/tex]

Step-by-step explanation:

[tex]\sf 3\left(x+5\right)-3=2\left(3x+1\right)-3x[/tex]

Expand: Apply distributive property:

[tex]\sf 3(x+5)-3[/tex]

[tex]\sf 3x+15-3[/tex] [tex]\sf 3x+12[/tex]

[tex]\sf 2(3x+1)[/tex]

[tex]\sf 3x+2[/tex]

[tex]\sf 3x+12=3x+2[/tex]

Subtract 12 from both sides:

[tex]\sf 3x+12-12=3x+2-12[/tex]

[tex]\sf 3x=3x-10[/tex]

Subtract 3x from both sides:

[tex]\sf 3x-3x=3x-10-3x[/tex]

[tex]\sf 0=-10[/tex]

Sides are not equal, so therefore there is no Solution.

___________________________________________

Fiona earns $10 for mowing each lawn and $5 per hour for her work. Write an inequality to show how many lawns she needs to mow in order to earn at least $135.

Answers

Answer: [tex]\geq[/tex] 9 lawns, assuming Fiona spends 1 hour per lawn.

Step-by-step explanation:

Let Y = the amount earned from mowing a lawn.  Let z be the number of hours worked on that lawn.

Y = $10 + $5(z)

We need to know the number of hours, z, for any particular lawn to be able to make this a valid equation.  Not having that, we really can't set up a valid equation.  

But let's assume z=1 for each and every lawn and see what we'd have.

Y = $10 + $5

Y = $15/lawn.

Fiona needs at least $135 for her Broadway ticket.

Let L be the number of lawns mowed.  We need:

L*($15/lawn) [tex]\geq[/tex] $135

L  [tex]\geq[/tex] 9 lawns

Find the equation of this line. i’m really confused and i really need help.

Answers

Y=-2/5+1 ?I think this is right


A backpacking club can average 2 1/2 miles per hour. At that
rate, how long will it take for a hike of 8 3/4 miles?

Answers

Answer:

3.5 hours

Step-by-step explanation:

8.75/2.5=3.5

Answer:

3.5 miles

Step-by-step explanation:

The midpoint of DF is E(-5, 4). If the coordinates of Fare (-4, 2), What are the coordinates of D?

Answers

Answer:

(-6,6)

Step-by-step explanation:

Please help and please no links..thanks ¯\_(ツ)_/¯

Answers

Answer:

[tex]\frac{c}{4} +5 = 7[/tex]

Step-by-step explanation:

The wording, "the quotient of a number and 4," can be displayed as c/4. C would be our variable for the number because the question asks specifically for it. 5 more would demonstrate that we're adding 5 more to our equation. Which would result in c/4 + 5. However, since it equals 7, just add that portion to create the following equation:

[tex]\frac{c}{4} +5 = 7[/tex]

Answer:

c / 4 + 5 = 7

Hope this helps!

Step-by-step explanation:

5 + ( more )  than the quotient ( division ) of a number and ( + ) 4 is ( = ) 7

5 + c / 4 = 7

c / 4 + 5 = 7

A nurse spent 83% of a 12-h shirt caring for patients. How many hours were devoted to patient care?

Answers

Answer:

9.96

Step-by-step explanation:

12 * .83

Answer:

10 hours

Step-by-step explanation:

83% of 12 hours = 0.83 * 12 hours = 10 hours

14. Choose the best description of the polynomial:
5y2 + 4y + 24.
A. 5th degree Trinomial
B. 3rd degree Binomial
C. 2nd degree Trinomial
D
4th degree Binomial

Answers

C as there are only 3 terms tip- (count how many symbols). And the highest power it goes to is 2 so it’s 5y squared. Hope this helps :)

How do I find x in this ?

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The Correct choice is ~

[tex]x = 450[/tex]

Refer to attachment for solution ~

I need help on Tales mathemathics below on image

Answers

Answer:

x=5

Step-by-step explanation:

i'm assuming the upper left expression is x-1 and that the 3 horizontal lines are parallel

the three horizontal lines seem to be parallel, so we have (x-1)/6 = 6/(x+4). cross multiply to get (x-1)(x+4) = 36, or x^2 +3x - 4 = 36. subtract 36 from both sides to get x^2 + 3x -40 = 0, factor or use the quadratic formula to get (x+8)(x-5)=0, so x=-8 or x=5, since we are looking for a length x can't equal -8, so x=5,

Hello! Please answer this ASAP. Thanks!

Answers

Answer:

x=3

Step-by-step explanation:

Twenty divided by four is five. You would divide fifteen by five to get three. so X=3.

A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor. He grabs the only red peg on the circumference of the wheel, which is 1.5 m above the floor (the peg is) and pushes it downward. The peg reaches a min height of 0.25 m and a max height of 2.75 m above the floor. Sketch two cycles of the graph representing the height above the ground as a function of the total distance moved. Then determine the equation of the sine function

Answers

The spin of the wheel by the contestant is an illustration of a sine function whose equation is [tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]

The wheel is 1.5 m above the floor, and the peg reaches a maximum height of 2.75 m.

So, the amplitude is:

[tex]\mathbf{A = 1.5 - 2.75}[/tex]

[tex]\mathbf{A = -1.25}[/tex]

The vertical shift is the minimum height of the peg.

So, we have:

[tex]\mathbf{D = 0.25}[/tex]

The period (T) equals one circumference.

So, we have:

[tex]\mathbf{T = (max-min)\pi}[/tex]

This gives

[tex]\mathbf{T = (2.75-0.25)\pi}[/tex]

[tex]\mathbf{T = 2.5\pi}[/tex]

The frequency (B) is then calculated as:

[tex]\mathbf{B = \frac{2\pi}{T}}[/tex]

This gives

[tex]\mathbf{B = \frac{2\pi}{2.5\pi}}[/tex]

Divide

[tex]\mathbf{B = 0.8}[/tex]

A sine function is represented as:

[tex]\mathbf{y =A sin(B(x + C)) + D}[/tex]

Substitute the calculated values

[tex]\mathbf{y =-1.25 sin(0.8(x + C)) + 0.25}[/tex]

The horizontal shift (C) is 0.

So, the function becomes

[tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]

See attachment for the graph of the equation

Read more sine function at:

https://brainly.com/question/11904902

3/12 + 7/12 =

A) 5/6
B) 10/24
C) 5/24
D) 1/6​

Answers

3+7=10

10/12
simplified (divide by 2) it’s
5/6

the answer is A

Answer:

A. 5/6

Step-by-step explanation:

Since our denominators match, we can add the numerators.

3 + 7 = 10

So 10/12 the answer but simplified would give 5/6

Ravi Makes lemonade by mixing lemon juice and water for every 1 cup of lemon juice he uses 4 cups of water.

Answers

Answer:1/4

Step-by-step explanation:

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