The equation of a curve is y = x³ + 4x. Show that the value of y increases when x increases. ² is a decreasing function.​

Answers

Answer 1

We will see that f'(x) > 0, which means that f(x) is an increasing function.

How to prove that the function is increasing?

For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.

Here we have the cubic function:

f(x) = x³ + 4x

If we differentiate this, we get:

f'(x) = df(x)/dx = 3x² + 4.

And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.

If you want to learn more about cubic functions:

https://brainly.com/question/20896994

#SPJ1


Related Questions

Drag the expressions into the boxes to correctly complete the table. Polynomial Not a polynomial

Answers

The answer to the given question is as below:-

Polynomials:-

x³-7x²+9x-5x⁴-20

x⁵-5x⁴+4x³+2x-1

3x²-5x⁴+2x-12

Non-polynomial:-

x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1

[tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]

[tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]

What are polynomials?

A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.

So the table will be formed as:-

Polynomials:-                            Non-polynomial:-        

x³-7x²+9x-5x⁴-20                     x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1        

x⁵-5x⁴+4x³+2x-1                        [tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]

3x²-5x⁴+2x-12                           [tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]

Therefore the polynomials and non-polynomials are shown in the table above.

To know more about polynomials follow

https://brainly.com/question/2833285

#SPJ1

Help for college scholarships! Must be a paragraph.

How has your family background affected the way you see the world?

Answers

Family background refers to the culture and tradition of the family into which a person is born.

What is family background?

Family background refers to the culture and tradition of the family into which a person is born. it is worthy of note that most of this family traditions are unspoken yet are firmly entrenched in the psyche of individual as he/she grows.

My family is strictly conservative having  had a Southern Baptist orientation. My dad believes deeply in  religion and a moralist and perfectionist.

As a  result of this, I find myself always grappling with the unfortunate disorder in the world; always trying to bring order to my world as much as I can.

Learn more about family background:https://brainly.com/question/7105836

#SPJ1

PLEASE HELP!!!!!! WHATS THE ANSWER

Answers

Answer:

3

Step-by-step explanation:

pls mark brainliest

Two adjacent rooms are rectangles, both of length 13 feet by 10 feet. Jerry wants to change the carpets in both rooms. How many square feet should he order?

Answers

Answer:

  260 square feet

Step-by-step explanation:

The area of a rectangle is given by the formula ...

  A = LW

The area of two same-size rectangular rooms will be double the area of one of them.

__

room area

Each room has an area of ...

  A = LW = (13 ft)(10 ft) = 130 ft²

carpet order

The order for carpet must be for 2 times the area of one room:

  carpet order = 2 × 130 ft² = 260 ft²

Jerry should order 260 square feet of carpet.

What is the future value of a 5-year annuity due with annual payments of $ 2,535 , evaluated at a 14.18 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.

Answers

Answer:

  $19,201.09

Step-by-step explanation:

The future value of the annuity due can be found using any of a number of apps, calculators, or spreadsheets. It can also be found using the formula ...

  A = P(1 +r)((1 +r)^n -1)/r

where P is the annual payment, r is the annual interest rate, and compounding is yearly for n years.

  A = 2535(1.1418)(1.1418^5 -1)/0.1418 ≈ 19,201.09

The value will be $19,201.09.

Deion has 62 m of fencing to build a four-sided fence around a rectangular plot of
land. The area of the land is 228 square meters. Solve for the dimensions (length and
width) of the field?

Answers

The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length of the field and y represent the width of the field, hence:

Deion has 62 m of fencing:

2(x + y) = 62

x + y = 31

y = 31 - x     (1)

The area of the land is 228 square meters. hence:

xy = 228

x(31 - x) = 228

x² - 31x + 228 = 0  

x = 12 or x = 19

when x = 12; y = 31 - 12 = 19

when x = 19; y = 31 - 19 = 12

The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1


d=√(-4-42.78)^2 + (3-44.78)^2

Answers

The expression is equal to 3sqrt(517)/5

Gravano Engineering co has the following items appearing in its statement of financial position at the year end:
What is the total for:
1. Non-current assets?
2. Current assets?
          Trade payables                             39000
2)     Cash at bank     14,000
3).  Motor vans           25000 4)Inventories             7000           
  5)  Bank overdraft                                  13,000              6)Property                                              96,000             
7)Trade receivables                              43,000             
8)Plant and equipment                        26,000             

9)Trademarks                                        28,000 10.   Fixtures and fittings             17,000 11.   Mortgage on property         45,000​

Answers

Based on the items appearing in Gravano Engineering's Statement of Financial Position at the year-end, the totals for the following are:

1. Non-current Assets = $192,000

2. Current Assets = $64,000

What is a Statement of Financial Position?

A Statement of Financial Position is a financial statement that shows an entity's assets, liabilities, and equity.

Assets are items owned by an individual or entity that generate current, future, or potential economic benefits.

Liabilities are financial obligations that an individual or entity owes creditors.

Equity is the difference between assets and liabilities, which refers to the financial benefits accruing to the stockholders.

Data and Calculations:

1. Trade payables                                    $39,000

2. Cash at bank                                         14,000

3. Motor vans                                           25,000

4. Inventories                                             7,000

5. Bank overdraft                                     13,000

6. Property                                              96,000            

7. Trade receivables                              43,000            

8. Plant and equipment                        26,000            

9. Trademarks                                        28,000

10.   Fixtures and fittings                        17,000

11.   Mortgage on property                   45,000​

Current Assets:

2. Cash at bank                                          14,000

4. Inventories                                              7,000

7. Trade receivables                                43,000            

Total current assets =                           $64,000

Non-Current Assets:

3. Motor vans                                          25,000

6. Property                                              96,000                      

8. Plant and equipment                         26,000            

9. Trademarks                                        28,000

10.   Fixtures and fittings                         17,000

Total non-current assets =                $192,000

Thus, the total non-current assets are $192,000 and the current assets total $64,000.

Learn more about current and non-current assets at https://brainly.com/question/24147620

#SPJ1

Based on probability and if it is appropriate for a decision to be left up to chance, choose every situation that is both statistically fair and morally fair.
Situation #1 A high school student is deciding whether to first clean his room or do his homework. He decides by picking a tile at random from a bag of lettered tiles. If he picks a consonant he will clean his room, and if he picks a vowel he will do his homework.
Situation #2 There are four candidates eligible for a vacancy at a company. Ignoring qualifications and experience, the recruitment manager decides which candidate to hire by writing their names on pieces of paper, shuffling the papers, and drawing one at random.
Situation #3 Five cousins are deciding which board game to play. They each write their preferred game on a different section of a spinner that has five equally-sized sections. They spin the spinner and will play the game written on the section where the spinner lands.
Situation #4 To determine who can choose the spot for a picnic, Kate picks a tile at random from a collection of five tiles, numbered 2 through 6. Kate chooses the spot if she picks a prime number, and Charles chooses if Kate picks a composite number.
Situation #5 Five roommates all want to attend an event, but they only have four invites. To decide who will attend, they shuffle a set of five cards consisting of four aces and a king. Each roommate is randomly dealt a card. The ones dealt an ace will attend the event.
Reset Next

Answers

The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5

How to categorize the situations?

For a situation to be fair, the probability of every outcome must be equal.

We can now analyze each option using the above highlight

Situation 1

Alphabets = 26Probability of vowel = 5/26Probability of consonant = 21/26

The probabilities of vowels and consonant are not equal.

Hence, this situation is not fair

Situation 2

People = 4

P(Each) = 1/4

The probability of each participant is equal in the above scenario i.e. 1/4

Hence, this situation is fair

Situation 3

People = 5P(Each) = 1/5

The probability of each cousin is equal in the above scenario i.e. 1/5

Hence, this situation is fair

Situation 4

Numbers = 5 i.e. 2 to 6P(Prime) = 3/5P(Composite) = 4/6

The probabilities of prime and composite numbers are not equal.

Hence, this situation is not fair

Situation 5

Roommates = 5Cards = 5Aces = 4P(Each) = 1/5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

Read more about probability at:

brainly.com/question/251701

#SPJ1

Select the correct answer from each drop-down menu. y = f(x) = (1/2) ^ 5 Consider the function The value of f(- 7) is The value of f(5) rounded to the nearest ten thousandth, is

Answers

The values of the functions are:

1. y = f(-7) = 128

2. y = f(5) = 0.0313

How to Find the Value of a Function?

We can evaluate a function by substituting the given value into the equation of the function, then simplify.

Given the function, y = f(x) = (1/2) ^ x

1. Find the value of f(-7):

y = f(-7) = (1/2)^-7

y = f(-7) = 2^7

y = f(-7) = 128

2. 1. Find the value of f(5):

y = f(5) = (1/2)^5

y = f(5) = 0.0313

Learn more about functions on:

https://brainly.com/question/10439235

#SPJ1

-6x +3>-39

sombody pls do this problem

Answers

Answer:

x>-7

Step-by-step explanation:

Answer:

x>-7

It wont always be easy, but always try to do what ' s right!

   In a world of worriers, be the warrior!

        When nothing goes right, go left.

suppose y varies inversely as x and y=12 when x=6 find y if x=8

Answers

Answer:

y = 9

Step-by-step explanation:

given that y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the condition y = 12 when x = 6

12 = [tex]\frac{k}{6}[/tex] ← multiply both sides by 6 to clear the fraction

72 = k

y = [tex]\frac{72}{x}[/tex] ← equation of variation

when x = 8 , then

y = [tex]\frac{72}{8}[/tex] = 9

In which scenario can you reverse the dependent and independent variables while keeping the interpretation of the slope meaningful?

A.
As the amount of snowfall increases, the number of shovels sold increases.

B.
As number of hours spent watching TV increases, the amount spent on electricity increases.

C.
As the radius of a circle increases, circumference of the circle increases.

D.
As foot size increases, sock size increases.

Answers

Answer:

C. As the radius of a circle increases, circumference of the circle increases.

Which statements describe one of the transformations performed on f(x) = x^2 to create g(x) = (x - 2)^2 + 5? Choose all that apply.

A. A translation of 5 units up

B. A translation of 2 units to the right

C. A translation of 2 units to the left

D. A translation of 5 units down

Answers

A and B
you’re welcome

Question 2 A birthday cake in the shape of the right-circular cylinder of radius 15cm and thickness 10cm is cut into smaller pieces. One of the piece is shown. 15 cm 30° 10 cm a) What is the volume of this piece to the nearestcm³? (2 marks)​

Answers

The volume of a piece of the cake will be 588.75 cm³.

The complete question is attached below.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A birthday cake in the shape of the right-circular cylinder of radius 15 cm and thickness 10 cm is cut into smaller pieces.

One of the piece is shown.

Then the volume of piece of the cake will be

V = (30 / 360) x π x 15² × 10

V = 588.75 cm³

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ1

CAN SOMEONE HELP ME PLEASE? I’LL GIVE YOU FREE EASY POINTS IF YOU GIVE ME THE RIGHT ANSWER.. NO WRONG ANSWERS PLS!!

Answers

see the attachment..........

4. Evaluate e^-2 to one decimal place
A) 0.7
B) -1.4
C) 0.1
D) 1.4

Answers

C 0.1 .. I just did it !!!

solve for x in the following equations

Answers

Answer:

2.

[tex]x = \frac{11}{4} = 2 \frac{3}{4} = 2.75[/tex]

3.

[tex]x = \frac{5}{2} = 2 \frac{1}{2} = 2.5[/tex]

4.

[tex]x = \frac{3}{7} ≈0.428571429[/tex]

Which is the graph of y = [X] - 2?​

Answers

Answer:

Top right graph

Step-by-step explanation:

Graph is in attached image.

Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5+ 1.25x
X=the number of weeks that have passed
Y = the height of the plant
How tall will with plant be after 7 weeks?

Answers

After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a line of best fit:

y = 2.5 + 1.25x

Plug x = 7 weeks

y = 2.5 + 1.25(7)

y = 11.25 units

Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.

Learn more about the line of best fit here:

brainly.com/question/14279419

#SPJ1

If a sample proportion is 0.65, which range of possible values best describes
an estimate for the population parameter?
O A. (0.5, 0.89)
• B. (0.5, 0.8)
• C. (0.65, 0.7)
• D. (0.6, 0.69)

Answers

The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8)

How to estimate proportion?

The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8).

When we are talking about population parameters, we also have to look at the way of estimating the population, we have to add two extremes and divide by 2.

Thus, the correct one is;

(0.5 + 0.8)/2 = 0.65

Read more about Population parameter at; https://brainly.com/question/2292917

#SPJ1

where do banks get the money to lend to consumers

Answers

Answer:

Depositors

Step-by-step explanation:

Answer:

Banks get the money from the people that deposit their money at the bank for a low interest rate and lend to the customers with a high interest rate.

Argelis had þhe following containers of paint leftover, 1/2 gallon, 3/4 quarts and 1/4 gallon. How many quarts of paint does argelis have left

Answers

3.75 quarts of paint does Argelis have left with her.

What is Gallons?

A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces.

Here, we know that,

1 gallons = 4 quarts

so, 1/2 gallons = 1/2 X 4 = 2 quarts.

and 1/4 gallons = 1/4 X 4 = 1 quarts.

Now, total paint left with Argelis = 1/2 gallons + 3/4 quarts + 1/4 gallons

                                                     =  2 quarts + 3/4 quarts + 1 quarts

                                                    = 3 quarts + 3/4 quarts

                                                    = 15/4 quarts or 3.75 quarts

Thus, 3.75 quarts of paint does Argelis have left with her.

Learn more about Gallons from:

https://brainly.com/question/9917229

#SPJ1

Please show your work! I'll give you brainliest as well as a 5 star rating, thanks!

Answers

Answer:

281.3

Step-by-step explanation:

If the shapes are similar then the linear scale factor is :

15÷20 = 0.75

The area scale factor will be 0.75²

The area scale factor is 0.5625

500 × 0.5625 = Area of shaded rectangle

Area of shaded rectangle = 281.25

To the nearest tenth = 281.3

Hope you understood and brainliest please

Answer:

[tex]281.3 m^{2}[/tex]

Step-by-step explanation:

I've done this before I have the work attached below in a screenshot. Sorry that it's not much but I hope it helps!

Please feel free to comment, give feedback, ask questions, and correct me if I am wrong!

Have a great day

:)

Based on past experience, a building contractor sets the
probability of winning a contract at 0.10. The contract is
worth $75,000 and the cost to prepare the contract proposal
is $10000. What is the expected value of the contract
proposal?

A. $2500
B. $22600
C. $22600
D. $2500

Answers

Based on the cost of the contract and the probability to win it, the total expected value of the contract proposal is -$2500.

How to calculate the expected value of a contract proposal?

The general formula to calculate the expected value is:

Expected value: possibility of winnind the contract x the amount when winning - possibility of loing the contract x possible loss

Possibility of winning the contract= 0.10Possibility of losing the contract = 0.90Gain: $65000Loss: $10000

What is the expected value of the contract?Expected value: 0.10 x 65000 - 0.90 x 10000Expected value: 6500 - 9000Expected value: -$2500

Learn more about contract in: https://brainly.com/question/2669219

#SPJ1

Suppose that 950 couples each have a baby find the mean and standard deviation for the number of boys in the 950 babies

Answers

The mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

How to determine the mean and the standard deviation?

From the complete question, we have:

P(boy)= 0.5

Sample size = 950

The mean is then calculated as:

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 950 * 0.5[/tex]

Evaluate

[tex]\bar x = 475[/tex]

The standard deviation is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

This gives

[tex]\sigma = \sqrt{950 * 0.5(1 - 0.5)[/tex]

Evaluate

[tex]\sigma = 15.41[/tex]

Hence, the mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

Read more about mean and standard deviation at:

https://brainly.com/question/4079902

#SPJ1

writing equations from graphs pixel art graph

Answers

Answer:

y= -2/3x - 4

Step-by-step explanation:

the 2/3 comes from going up 2 spaces and over left 3 spaces. the b is negative 4 because of where it falls. the line is negative because of the direction it is in.

Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill Two years ago she has been at the hospital for twice as long How long has each been at r=the hospital

Answers

Answer:

Hoang has been at the hospital for 12 years while Bill has worked for 7 years.

Step-by-step explanation:

Let the years Hoang has worked as a nurse equal h and let the years Bill has worked as a nurse equal b.

Since Hoang has worked 5 years longer, h is five more than b:

h = b + 5

Now we move onto the situation 2 years ago. 2 years ago, Hoang had worked at the hospital two less than h or h-2 years while Bill has worked for b-2 which is two years less than b. We are also told that at the time, Hoang worked twice as longs, so

h - 2 = 2(b - 2)

This can be simplified:

h - 2 = 2b - 4

h = 2b - 2

We can use substitution. Since h = b + 5 and h = 2b - 2,

b + 5 = 2b - 2

b = 7

Therefore, since Hoang has worked five more years, h = 12. So, Hoang has been at the hospital for 12 years while Bill has worked for 7 years.

Find it and give me a step by step explanation thank you

Answers

Answer:

50.13

Step-by-step explanation:

We can easily find the area of our square, so to get that over with, 6*6=36. Now, for our circle, a full circle would be A=pi*r^2, but we only have half a circle. That means our equation will be A= 1/2(pi*r^2). We have our diameter, but we need our radius. Radius is just half the diameter, so 6/2=3. Now, we multiply. 3^3 is 9, and 9*3.14 is 28.26. All we have to do now is divide that by 2. If we do that, we get 14.13. The area of the semi-circle is 14.13. But we still have to add it to the area of the square, which will be our final step. 36+14.13=50.13, which is your area.

Hope this helps!

Answer the question below please

Answers

The correct answer is : of those planning to not to go on vacation, more of them are women.

The correct answer is (C)

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event

Given:  total people asked =145

The first option is not correct because plan to go on vacation women are more than men.

The second option is also incorrect because more women were asked than men.

The third option is correct because out of planning who were not going any vacation, women are more than of men.

The fourth option is incorrect because More men plan to go on vacation.

Learn more about probability here:

https://brainly.com/question/11234923

#SPJ1

Other Questions
why is the density of population low in Karnali province?the population is low in Karnali province because the cities are thinly populated and other place in hilly and mountains are thinly populated and low oxygen In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number. A) 6 B) 7 C) 8 D) 9 Who are the market participants in the foreign exchange market? Explain how each participant contributes to market activities. The vapour pressure of water 12.3kPa at 300K. Calculate the vapour pressure of 1 molal solution of a non-volatile solute in it. please help... The triangle represents a cross section from a 3D prism. Draw or describe the 3D prism that produced this cross section. Given that 24w = 14ten .Find the unknown base Angel is training for a weight-lifting competition. It is his first one, so he does not expect to win. He is just interested in seeing if he likes it. At the same time, he wants to be competitive. He has decided to work out with a trainer for the last few weeks and is figuring out where to fit that into his schedule. Should he plan on daily workouts? I think its B. no, even intense training required rest days. PLEASE HURRY!!Please no links. Which is the most accurate critique of "The Tell-Tale Heart?The author develops the central idea by giving examples.The author builds the suspense by using a series of analogies.The author builds the suspense by revealing a personal anecdote.The author develops the central idea by delaying answers to questions. What was an argument of Northern Whigs?A. Congressshould debate and resolve the issue of slavery.B. Economic development would get rid of the need for slavery.C. Slavery was taking away jobs that should be held by immigrants.D. Slavery should be limited to the new territories. Research the issue of genetically modified foods, and then write an essay to be read by your peers in which you argue either for or against their use. Support your position with evidence.someone please write the essay ill give you Brainliest Write a letter to your friend telling him or her how you saved a child from danger Read the paragraph.Both chocolate and commercial cola drinks are popular around the world. The main ingredient in chocolate comes from the beans of the cacao tree, and the flavoring for many cola drinks originally came from the nuts of the kola tree. Although they grow in different parts of the world, the cacao tree and the kola tree are part of the same plant family.Which paragraph pattern is being used?ITRTRITIITIR The table shown below lists the time, in days, that it takes fora package to be delivered based on its mode of transport andwhether it is international or domestic. Some additionalinformation is provided.1. The cost per package by air is $100; by train, $50; bytruck, $10; and by boat, $20.2. Fragile packages cannot be transported by air.3. Shipping fragile packages costs an extra $20.4. Shipping international packages costs an extra $30.Tim needs to transport a fragile package, and he needs it toarrive as soon as possible. He is shipping domestic. Which ofthe following shipping methods should he use? Using online and mobile banking apps to schedule automatic transfers of money into your savings account can help you _____. everfi Determine whether each triangle with sides of given length is a right triangle. justify your answer 7 yd, 5 yd, 9 yd10 ft, 24ft, 26 ft Which sentence uses parentheses correctly? my mom (cooked) beans and potatoes for dinner. she wondered why (she was so tired) after the run. the students were shocked (to see their teacher) at the grocery store. robert is driving with his parents to brooklyn (his hometown) tomorrow morning. can someone help me with this worksheet please!!!! Find the y-value when x = -5 for the equation y = -3x Which of the following regions of the United States saw the most rapidpopulation increase during the 1950s?OA. New EnglandOB. Deep SouthC. SouthwestD. Midwest