Mathematics College

if x+y = 1, and x^2 + y^2 = -1, what is x^7 + y^13?
1) 0
2) 1
3) -2
4) 2
5) -1

Answers

Answer 1

Solve for x and y :

x + y = 1   →   y = 1 - x

x ² + y ² = -1

x ² + (1 - x)² = -1

x ² + (1 - 2x + x ²) = -1

2x ² - 2x + 1 = -1

2x ² - 2x + 2 = 0

x ² - x + 1 = 0

x ² - x + 1/4 = -3/4

(x - 1/2)² = -3/4

x - 1/2 = ±√(-3/4)

x - 1/2 = ±√3/2 i

x = 1/2 ± √3/2 i   →   x = exp(± iπ/3)

y = 1 - (1/2 ± √3/2 i )   →   y = -1/2 ± √3/2 i   →   y = exp(± 2iπ/3)

Then

x ⁷ + y ¹³ = exp(± 7iπ/3) + exp(± 26iπ/3)

… = exp(± iπ/3) + exp(± 2iπ/3)

since 7π/3 is equivalent to π/3, and 26π/3 is equivalent to 2π/3 (both modulo 2π).

In either case, we get

x ⁷ + y ¹³ = x + y = 1

so the answer is (2) 1.

Related Questions

I will give brainiest to whoever answers correctly !!

Answers

Answer:

2.4

Step-by-step explanation:

The formula you would use is: A = P(1 + rt)

P is the principal which is $270

r is the interest rate

t is the time in years but we have 11 days so 11/360

A is $19.8

let's put the values in the formula

$289.9= $270(1 + r*(11/360))

you will find the r is 2.4

A={b,l,o,u,s,e} and U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.

Answers

Answer:

????????????????????????????????????????

What loliloolollokllkabbsbsnanab

Identify the property that justifies the following statement
1. Distributive Property of Congruence

2. Symmetric Property of Congruence

3. Reflexive Property of Congruence

4. Transitive Property of Congruence

Answers

Transitive property of congruence

Answer:

Transitive property of congruence

Step-by-step explanation:

Please help fast!!!!

Answers

Answer:

BGHjf, it skf skoad 78, then mutli 0867, then you'll get your answer!! 657.

Step-by-step explanation:

Can you please help me

Answers

X = 70 and y = 35, I hope this helps
The answer is Y=35 and x=70

You are driving up a mountain. At the base of the mountain you see a sign that states the elevation above sea level is 3,720 feet at this point. You then travel a horizontal distance of 5 miles to the top of the mountain, and see another sign that states the elevation is 4,215 feet above sea level. What was the average slope of the mountain you just climbed in feet/mile?

A) 843 ft/mi
B) 744 ft/mi
C) 99 ft/mi
D) 0.0188 ft/mi

Answers

Step-by-step explanation:

Slope of the mountain

= Rise in height / Run in distance

= (4215ft - 3720ft) / 5 mi

= 495ft / 5mi

= 99ft/mi. (C)


Can someone solve this please and thank you

Answers

The answer to the question is: 3

Answer:

Step-by-step explanation:

16

what is the value of x?

Answers

Answer:

i go with 55

Step-by-step explanation:

Answer:

25°{vertically opposite angle}

hope it helps.

SOLVE FOR X, WILL GIVE BRAINLIEST

Answers

The two angles are supplementary angles and when added together equal 180 degrees.

3x -12 + x+2 = 180

Simplify:

4x -10 = 180

Add 10 to both sides

4x = 190

Divide both sides by 4

X = 190/4

X = 47.5

Which expression correctly represents "nine less than the quotient of a number and four, increased by three"?

Answers

Answer:

x/4-9+3

Step-by-step explanation:

Sarah has 23 apples she divides them into 15 places what is the fraction of the apples she has left?

Answers

8/23 is the answer ... well that is all .. brainly asks me to write at least twenty letters so that is why i typed this much out of rage ... mark it the brainly that would make me happy when i check my phone before sleeping at night
The answer is 1 5/8, because 1 times 15 is 1, which leaves 8 left.

The population of City A was approximately 243,000
people, and it increased by 8% in one year. What was the
new population?

Answers

Answer:

262440

Step-by-step explanation:

12- (-5) + (-4 ) calculate

Answers

13teen is the answer because -5 plus -4 equals-9 so when you subtract a positive which is 12 that’s what you get.


Help plis plis


18. Find the sum of (x + 3) and
(- x - 4).




Help plis

Answers

Answer:

-1...................

Step-by-step explanation:

x+3-x-4

o-1

-1

Answer :

-1

Explanation:

please mark me brainliest and follow me my friend.

For a field trip 4 students rode in cars and
the rest filled nine buses. How many
students were in each bus if 472 students
were on the trip?

1a. What does the variable "x" represent?

1b. What equation represents this word problem?


1c. What is the solution to the word problem?


(Please help me with this quiz)

Answers

Step-by-step explanation:

We are solving for the number of students in each bus, so let x represent the number of students in each bus.

We have 4 + 9x = 472.

=> 9x = 468, x = 52.

Hence there are 52 students on each bus.

WILL GIVE BRAINLEST
1.1.4 Practice: Scale Drawings

Practice

Math 7 Sem 2

Points Possible:5

Name:

William Bennett

Date:



Tips for Success
Read the assignment carefully and make sure you answer each part of the question or questions.
Check your work when you're done.
Your Assignment

Jason and Adam are using a kit to build their own electronics board for a computer project. They use a scale drawing included in the instructions to help build the board.

Jason will use the scale factor to find the board's actual length and width, then multiply those dimensions to find the board's area.

Adam says he knows another way.


Answer the questions to show how Adam could find the area of the scale drawing, and then use this strategy to find the area of the electronics board.

1. What is the area of the board shown on the scale drawing? Explain how you found the area.


Write your answer in the space below.















2. How can Adam use the scale factor to find the area of the actual electronics board? Remember, he uses a different method than Jason.


Write your answer in the space below.















3. What is the area of the actual electronics board?


Write your answer in the space below.

Answers

Answer:

do we answer all of them are just one

if AB=BA= I then write the relation between matrix A and matrix B​

Answers

Answer:

If  AB = BA = I, then B is inverse of A and vice-versa.

Step-by-step explanation:

Given: AB = BA = I

To find: The relation between matrix A and B.

If AB = BA = I, then B is called the inverse matrix of A and is denoted by [tex]A^{-1}[/tex].

In that case, A is said to be invertible.

Also, if B is the inverse of A, then A is also the inverse of B.

Hence, the relation between A and B is that both are inverse of each other.

Dana works at a flower shop. One day she received a delivery of flowers and 30% of the flowers were roses. There were 240 roses. What percent of the flowers were not roses?

Answers

Answer:

800

Step-by-step explanation:

I started off with putting 240 over x and 30 over 100. Next I multiplied 240 with 100 and got 24000. Then I divided that with 30 and got 800 as my answer.

Hope this helps :)

Lydia wants to find the height of a flagpole. She measures the height of a tree and the length of the shadow it casts. The tree is 14 feet tall, and its shadow is 21 feet long. Next, Lydia measures the shadow cast by the flagpole, and finds it is 30 feet long. What is the height of the flagpole?

Answers

draw a diagram.

the two are similar bc of AAsimilarity

so 8.8 is to 4 as 22 is to x

basically the answer is 10 ft tall

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 4385 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 55.5 feet per second and Plane B is gaining altitude at 45.25 feet per second.


How many seconds will pass before the planes are at the same altitude?
seconds
What will their altitude be when they're at the same altitude?
feet

Answers

Answer:

Step-by-step explanation:

xhxj

subtract -3n^2 from -7n^2

Answers

Answer: 4n^2

Step-by-step explanation: -3n^2 - (-7n^2) = -3n^2 + 7n^2= 4n^2. When adding and subtracting the exponents stay the same only the coefficients are subtracted or added

The prism and pyramid above have the same width, length, and height. The volume of the prism is 36 cm3. What is the volume of the pyramid?

Answers

The pyramid's formula for Volume is identical to the formula for Volume of a prism, except for having a factor 1/3.

Base Area and height being the same for a pyramid and a prism, the volume of the pyramid is always one third that of the prism.

A similiar fact pertains to Cone vs Cylinder...these 3 dimensional volumes have a ratio of 1/3 to one another.

In two dimensions, there's a ratio of 1/2 between areas of triangles and rectangles having the same base & height.

PLEASE HELP PLEASE 100 POINTS PLUS BRAINLIEST
(I had the answer already but it deleted and now I can’t find it)

Answers

Step-by-step explanation:

Area of Sector

= θ/360° * πr² (degrees) or 0.5r²θ (radians)

Question 11:

(88°)/360° * π(19)² = 277.23ft².

Question 12:

(260°)/360° * π(11)² = 274.54mi².

Question 13:

0.5(6.2)²(7π/12) = 35.22km².

Question 14:

0.5(7.1)²(5π/3) = 131.97cm².

Question 15:

(215°)/360° * π(4.5)² = 37.99yd².

Question 16:

0.5(21.4)²(13π/18) = 519.54m².

here is the answers!

Area of Sector

= θ/360° * πr² (degrees) or 0.5r²θ (radians)

Question 11:

(88°)/360° * π(19)² = 277.23ft².

Question 12:

(260°)/360° * π(11)² = 274.54mi².

Question 13:

0.5(6.2)²(7π/12) = 35.22km².

Question 14:

0.5(7.1)²(5π/3) = 131.97cm².

Question 15:

(215°)/360° * π(4.5)² = 37.99yd².

Question 16:

0.5(21.4)²(13π/18) = 519.54m².

1) Jared got 18 out of 25 questions correct on a quiz. What grade did he get?​

Answers

Answer:

72 or 72/100 or 72% or whatever

Step-by-step explanation:

18/25= .72  Simple!


1) Which of these are equivalent to - ? Choose ALL that apply.

PLEASE ANSWER ASAP !!!!
*ANSWERS ON PIC*

Answers

the last 3 should be the right ones, hope thats correct
The fist one is right hope I helped you

The equation of line j is y=5/7x-9. Line k, which is parallel to line j, includes the point (-7, 1 ). What is the equation of line k ?

Answers

Answer:

math waaayys can help you

Step-by-step explanation:

Where do the lines y = 3x + 5 and y = -2x + 10 intersect?

Answers

9514 1404 393

Answer:

  (x, y) = (1, 8)

Step-by-step explanation:

A graphing calculator quickly tells you the point of intersection.

__

You can equate the y-values and solve for x.

  3x +5 = -2x +10

  5x = 5 . . . . . . . . . add 2x-5

  x = 1 . . . . . . . divide by 5

  3·1 +5 = y = 8 . . . . substitute for x in the first equation

The point of intersection is (x, y) = (1, 8).

A 40-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. If x
represents the length of the first piece, find the lengths of all three pieces.
What is the length of the first piece?
What is the length of the second piece?
What is the length of the third piece?

Answers

Answer:

The first piece is 5 inches long, while the second is 15 inches and the third one is 20 inches.

Step-by-step explanation:

To determine the length of the 3 pieces, knowing that the total of the board is 40 inches, and that the second measures 3 times more than the first and the third measures 4 times more than the first, the following equation must be performed:

X + 3X + 4X = 40

8X = 40

X = 40/8

X = 5

Therefore, the first piece is 5 inches long, while the second is 15 inches and the third 20 inches.

what is the inverse f(x)=1/5x

Answers

Answer:

F = 1/5

Step-by-step explanation:

The answer for your equation is 1/5x

Help me please! 20 POINTS Im using all of mine please help!

Gerry visited a farm and saw a total of 87 chickens and pigs. If there were a total of 248 legs between all of these animals, how many animals were chickens and how many were pigs?
(System of Equations word problem)

Answers

There are 18 or 20 pigs if two had 1 missing leg

Step by Step explanation

Multiply the chickens by 2 or adding it by the same number since chickens have 2 legs

87

+87

-------

174

After, minus 174 from 248

That is 74

Divide by 4

Other Questions
Find the highest common factor of 55 and 605 What is the biggest obstacle to traveling by boat on the Congo River?A. the many cataractsB. the unusual path of the Congo RiverC. shallow areas due to droughtD. the river's narrow width which one of my two poems do you like better?lately it feels like the world is ending.in a way stranger than the "normal" that's perceived.but we get to live here, where there are opportunities.Ask yourself this, and tell me if you agree.In a world that is deceived, are people meant to be happy?but it's all about YOUR perspective on thingsSo for now...I choose to escape reality and hopefully end up somewhere I'm happy to be.ORThe moment you realize youre not paying attentionis the moment you've escaped realityit is an achievement we all want and needbecause nature is there when no one else will beSo feel the soft grass and hear the trains go by,the birds will stop chirping and fog corrodes the sky and we will all wonderwhat else we could've done to survive How will you remember the slopes of the horizontal and vertical lines? can someone write 4-6 sentences about how poverty effects child mortality thank you!!!!!!!!! The sum of three consecutive odd integers is 87. What are the integers?A.31, 33, 35B.30, 29, 28C.31, 30, 29D.31, 29, 27 Cindy goes into the ER with a broken leg, and her doctor orders an X-ray. At the X-ray, Cinis wearing a medical scrub uniform. The X-ray technician places a lead vest on Cindy andleg for the image. The X-ray technician then goes into another room and takes the image.radiographic safety measures that were taken for Cindy and the technician?Cindy was protected by the position of her leg, and the technician was protected by theO Cindy was protected by the technician going in another room, and the technician wasCindy was protected by the lead shield, and the technician was protected by going in aCindy was protected by lying down and the technician was protected by the medical se Is the belief that some acts are always right or always wrong so what would this mean? Help plzSharon and Kay went to a craft show with theirgranddaughters. Sharon bought 1 adult ticket and 2child tickets and spent $28. Kay brought 2 adult ticketsand 3 child tickets and spent $48. Use 'x' to representadult tickets and "y" to represent children tickets. Special Right Triangles Need help dont understand this. place solve anyoneplease answer my questions How do whales bones act like steeping stones i dont really understand social studies like that.? so, can someone help me please o>o Complete the sentences by matching the names of trees to the appropriate blanks. to do this, drag the names on the left into the appropriate blanks in the sentences on the right. match the words in the left column to the appropriate blanks in the sentences on the right. terms may be used more than once. make certain you have filled every blank with a term before clicking submit. 1. deciduous trees lose their leaves seasonally and include trees such as maple and elm. 2. conifer leaves are generally thin and needle-like, while seeds are contained in cones. conifers include cedar and pine. 3. evergreens are plants that maintain their leaves in all seasons and include trees such as cedar, elm, and pine. 4. hardwoods reproduce using flowers and have broad leaves; hardwoods include trees such as maple, , and cedar. elm returned you filled in 2 of 10 blanks incorrectly. mango trees are tropical broad leaf plants that maintain their leaves all year long. no credit lost. try again. please help and show work if you can How much space is there between particles of frozen water? the gravitational force between two objects depends on the distance between the objects and each object? Given: 8(x-1)=5x-35; Prove: x=-9 Please help ill give you 5 stars.I need to do a annotation of Dalton Sherman's speech called Believe.1.Read/listen to the speech, who is the speaker and why do they want to share this information.2.Examine the title, headings, sub-headings, bold and italicized words. Write a brief statement of what you can infer.3.In a phrase, write who or what the text/speech is about?4.What is the central idea of this text/speech? One sentence.