How to find rational numbers between any two numbers for example like finding six rational numbers between three and four please elaborate

Answers

Answer 1

Answer:

The whole series is:

3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4

Step-by-step explanation:

Inserting Numbers Between Two Given Endpoints

Suppose we want to insert n equally-spaced numbers inside a given interval with endpoints [x,y].

To place n numbers, we need to open n+1 slots, at the end of which, a new number will be placed. The given interval is then divided into n+1 rational numbers of a value (y-x)/(n+1) each.

For example, let's add 6 rational numbers between 3 and 4. The width of the given interval is 4-3=1, and we need to place 6 numbers separated by 1/(6+1) = 1/7.

Start by the left endpoint:

3

The first number to add is 3+1/7=22/7

22/7

The second number to add is 22/7+1/7=23/7

23/7

The third number is 23/7+1/7=24/7

24/7

The next numbers follow the same pattern:

25/7

26/7

27/7

The last number is 28/7=4

4

The whole series is:

3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4

We have inserted 6 rational numbers between 3 and 4.


Related Questions

You rode 180 miles at 60 miles per hour. Let t be the time it took. Can t be 4 hours?

Answers

Answer:

t = 3 hours, therefore it cannot be 4 hours

Step-by-step explanation:

Divide the miles traveled by the rate you traveled. This will find the time it took to travel.

180/60 = 3

You drove 3 hours to travel 180 miles, therefore t cannot equal 4.

What is "fifty thousand, six hundred thirty-one" in standard form?

Answers

Answer:

50,631

Step-by-step explanation:

Answer:

55,631

Hope it helps!

Write the converse of the following conditional? If you own a Prius, then you own a car made by Toyota.

Answers

Answer:

You own a car made by Toyota if you own a Prius.

Step-by-step explanation:

If the conditional is p->q then the converse would be q->p. So basically to get the converse switch the order of the statements.

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 5. If there were
4104 total votes, how many yes votes were there?

Answers

Answer:

the residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 5 to 8. If there were 6776 no votes, what was the total number of votes?

-------

5 to 8 is the same as 5x to 8x where 8x is the number of no votes.

----

If 8x = 6776, then x = 847

Step-by-step explanation:

HOPE THIS HELPED ✨

to find the slope of the two points

Answers

Answer:

Slope is :-

[tex] \boxed{\bf \; m \; = - \cfrac{7}{5}} [/tex]

Step-by-step explanation:

Given two points :-

[tex] \sf \implies(-5,3) , (0,−4)[/tex]

To Find :-

The slope of Two points that is given.

Solution :-

[tex]\sf \implies(-5,3) , (0,−4)[/tex]

As we know that the formula of Slope is :-

[tex]\sf \implies \boxed{\sf Slope = \cfrac {y_2 - y_1}{x_2 - x_1}}[/tex]

Now, Put the values of x and y :-

Where,

[tex]{ \sf \: {y_2} = - 4}[/tex]

[tex] \sf \: x_2 = 0[/tex]

[tex] \sf \: y_1 = 3[/tex]

[tex] \sf \: x_1 = - 5[/tex]

Put the values on their respective place :-

[tex]\sf \implies \: Slope = \cfrac{ - 4 - 3}{0 - ( - 5)} [/tex]

Simplify this Fraction :-

Add -4 and -3 which is on the numerator as we know that "-" and "-" equals to "+":-

[tex]\sf \implies \: Slope = \cfrac{ - 7}{0 - ( - 5)} [/tex]

Now Add 0-(-5) on the denominator as we know that "-" and "-" equals to "+":-

[tex]\sf \implies \: Slope = \: \cfrac{ - 7}{ 5} [/tex]

Which can be rewritten as,

[tex]\sf \implies \: m = \: - \cfrac{7}{5} [/tex]

This fraction can't be cancelled. Hence, the slope of the two points is:-

[tex]\sf \implies \boxed{\sf m = \: - \cfrac{7}{5}} [/tex]

Note :- Slope can also be denoted as [tex] m [/tex].

________________________________

I hope this helps!

A boat cost $16,500 and decreases in value by 13% per year how much will the boat be worth after eight years?

Answers

Answer:

$5,415.49

Step-by-step explanation:

Cost of the boat = $16,500

Decrease in value per year = 13%

Worth of the boat in 8 years = ?

Remaining value = 100% - 13%

= 87%

Worth of the boat in 8 years = cost of the boat × remaining value^8

= $16,500 × 87%^8

= $16,500 × 87/100^8

= $16,500 × 0.87^8

= $16,500 × 0.3282116715437121

= $5,415.49

The worth of the boat after 8 years = $5,415.49

y=−3(x+3)+4 i have no clue how to answer

Answers

Answer:

y=-3x+13

Step-by-step explanation:

y=-3x-9+4

-9+9= 0 so that cancel out

next u do

4+9=13

and thats when u drop the variables and the 13 down then it will be

y= -3x + 13

PLS HELP TT
write a paragraph proof for the following conjecture
Given m∠1 + m∠2 = m∠4
Prove: m∠3 + m∠1 + m∠2 = 180°

Answers

 m∠1 + m∠2 = m ∠4 , under the exterior angle property of a triangle which says that sum of the interior opposite angles of an exterior angle will be equal to the measure of the exterior angle .

To prove that m∠3 + m ∠1 +  m∠2 = 180° , let us use the angle sum property .

= Angle sum property = Sum of the three interior angles in a triangle will be equal to 180° .

= Since  ∠1 ,  ∠2 and  ∠3 are the interior angles of this triangle , their sum will be equal to 180° .

Hence proved that m∠1 +  m∠2 + m∠3 = 180°

∴ m∠1 +  m∠2 + m∠3 = 180° under the angle sum property of a triangle .

Hassan writes an algebraic expression with four terms. The x-term has a coefficient of 2, and the z-term has a coefficient of -1. The expression has a constant term less than zero. Which expression could he have written?

a) 2x + z + 5 - 6z^2
b) 2x- z-5 + 2z^2
c) -2 x - z- 5 + 2z^2
d) -2 x + z- 5 + 2z^2

Answers

Answer:

Hi there!

Your answer is:

B) 2x -z -5 + 2z^2

Step-by-step explanation:

xterm has 2 in front

z term has -1 in front

expression has constant term <0 (means it must be neg)

2x - 1z + (x<0)

Hope this helps

solving literal equations a-bc=d solve for a

Answers

Answer:

a=d+Bc

Step-by-step explanation:

a-bc=d

+bc

a=d+bc

17v + 3v = 20

Solve for V.

Answers

Answer:

v=1

Step-by-step explanation:

Answer:

V = 1

Hope this helped :)

how do I find measure of angles​

Answers

Answer:

you are going to need a protractor

Step-by-step explanation:

Can you help me please?

Answers

Answer:

61.5 in 41 mins 90 in one hour,

Step-by-step explanation:

i multiplied 1 1/2 by 41 and by 60

hope this helps i am very sorry if it is incorrect..

Solve the system of equations by using substitution. Give your final answer in the form of an ordered pair.



5x - 2y = 26

y + 4 = x

Answers

5x -2y = 26. We know that x = y + 4. Substitute the value of x in and you get 5y + 20 - 2y = 26 If yous simplify this you get 3y + 20 = 26
Take away 20 from both sides and you end up with 3y = 6
Now did use both sides by 3

You end up with y = 2
Now to find x you just simplify the value of y into x = y + 4. You end up with x = 2 + 4. Now you know that y = 2 and. X = 6

- sixteen divided by -two

Answers

Answer:

8

Step-by-step explanation:

Answer:

-16 divided by -2 is 8

Step-by-step explanation:

When you divide a negative from a negative you get a positive

5. Arrange the following interest rates in ascending order (least to greatest):
4.72
4 1/4
4.168
4 1/5
4 1/6
4.22

Answers

4 1/6, 4.168, 4 1/5, 4.22, 4 1/4, 4.72

The first three terms of a geometric sequence are as follows.
-7, 14, -28
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
-7, 14, -28, 00

Answers

Answer:

The next two terms of the sequence -7, 14, and -28 are 56 and - 112.

Step-by-step explanation:

-7 * -2 = 14

14 * -2 = -28

The sequence is to multiply each number by -2.

-28 * -2 = 56

56 * -2 = -112

Answer: The next two terms of the sequence -7, 14, and -28 are 56 and - 112.

Step-by-step explanation:

State if the two triangles are congruent. If they are, state how you know.

Answers

Answer:

The triangles can be congruent.

Step-by-step explanation:

They are congruent if proven by SSS: 2 sides are clearly stated that they are congruent due to the marks they have.

The last side can be congruent if the diagonals are congruent in length by proving.

They can also be congeuent due to SAS because there is gonna be alternate interior angles due to the transversal.

Definition: Ifa = b. then a - c= b - c. This is the what property of equality

Answers

Answer:

Subtraction property

Step-by-step explanation:

i drew tge question because im not doing it ion my home laptop

Answers

Answer:

Correct Choice: G. point B

Step-by-step explanation:

The Number Line

A number line is defined as a graphic representation of numbers such as fractions, integers, and whole numbers laid out evenly on a straight horizontal line.

The number line can be used for comparing and ordering numbers and also performing simple operations such as addition and subtraction.

There are four numbers located on a number line. Let's analyze each one:

A: -27/3. This division is a whole number =.9 and is correctly placed.

B: -13/2 = -6.5. Note this value was incorrectly placed at -4.5.

C: 9/2= 4.5. The number is correctly placed

D: 21/3 = 7. This number is also placed in the correct location

Correct Choice: G. point B

cual es la motaña más alta del mundo​

Answers

Answer: Mount Everest

Step-by-step explanation: dunno

which is the correct value of c for x^2-14x+c=(x-7)^2

Answers

Answer:

c = 3.5 - x

Step-by-step explanati

x^2 - 14x + c = (x - 7)^2

x^2 - 14x + c = x^2 - 7^2

x^2 - 14x + c - x^2 = x^2 - 49 - x^2

-14x + c = 49

-14x / -14 + c = 49 / -14

x + c = 3.5

x - x + c = 3.5 - x

c = 3.5 - x

Why you do not have to do any computing or math do solve 15 x 0 x (13 + 7)? Explain.

Answers

Answer:

because when you do 15*0 it =0 so anything else multiplied by 0 is 0

Step-by-step explanation:

What is the square root of 30 to two decimal places

Answers

Answer:

30.0

Step-by-step explanation:

I need help asap I'm giving the rest of my points

Answers

Answer:

a. 32. 3

Step-by-step explanation:

4x3=12

1×3=3 (3 min missing from table)

32×3=96 (32 songs miss)

8 ghosts greet each other with 'Boo!
How many times is the phrase 'Boo! being said?

Hint For three ghosts, Boo
is said 6 times For four ghosts, Boo is
said 12 times!

Answers

Answer:

im pretty sure 16 times

Step-by-step explanation:

well if you look at it there are 8 ghost's. they are going to greet each other, soo. B would say 8x7 because 8 ghost's would say boo to 7 more. soo 8x7=56                        

p.s

sorry if wrong

an Elephant at the zoo Lost 24 pounds over 6 months. The elephant lost the same amount of weight each month. Write a integer that represents the change in the elephant’s weight each month.

Answers

Answer:

4

Step-by-step explanation:

24 divided by 6 equals 4

Answer:

...

Step-by-step explanation:

10. Calculate the speed of waves in a puddle that are .15 apart and made by tapping the water
surface twice each second.

Answers

Since the waves are 0.15 apart and made by tapping the water surface twice each second the speed of waves in the puddle is 0.6 m/s

To answer the question, we need to know what a wave is

What is a wave?

A wave is a disturbance in space which carries energy from one point to another

What is the speed of a wave?

The speed of a wave v = fλ where

f = frequency and λ = wavelength

Wavelength of wave

Since the puddles are 0.15 m are and we know that this is the distance from crest to crest.

Also, the distance from crest to crest is λ/2

So, λ/2 = 0.15

λ = 2 × 0.15 m

= 0.3 m

Frequency of wave

Also, since the tapping by the water surface is done twice each second, the frequency, f = 2 times/s = 2 Hz

Speed of waves in puddle

Substituting the values of the variables into the equation, for speed, we have

v = fλ

v =  2 Hz × 0.3 m

v = 0.6 m/s

So, the speed of waves in the puddle is 0.6 m/s

Learn more about speed of wave here:

https://brainly.com/question/4054018

#SPJ1

What are the slope and y-intercept of the graph of y=−13x+1

Answers

Slope is -13 and y-intercept is +1

Answer:

Hi there!

Your answer is:

slope: -13

y-int: 1

Step-by-step explanation:

The slope is the x coefficient, rise/run

In this case, its -13/1. Which means it has a slope of -13.

The y int is the constant term.

In this case, its 1. Which means it crosses the y axis at 1

Hope this helps

Which statements about the values of 4.099 and 40.99 are true? Select all that apply. 4.099 is 110 of 40.99. 4.099 is 1100 of 40.99. 40.99 is 10 times more than 4.099. 40.99 is 100 times more than 4.099. 4.099 is 10 times more than 40.99.

Answers

Answer:

40.99 is 10 times more than 4.099

Step-by-step explanation:

Given the values :

4.099 and 40.99

4.099 is 110 of 40.99 : 110 * 40.99 = 4508.9 (false)

4.099 is 1100 of 40.99 : 1100 * 40.99 = 45089 (false)

40.99 is 10 times more than 4.099 : (10 * 4.099) = 40.99 (true)

40.99 is 100 times more than 4.099 : (100 * 4.099) = 409.9 ( false)

4.099 is 10 times more than 40.99 : (10 * 40.99) = 409.9 (false)

Answer:

the answer is c trust me

Step-by-step explanation:

Other Questions
Essay/ why online school is better please at least 5 paragraphs Buzz and Jessie are missing each other and their friend Woody. They want to meet at Woody's house which is halfway between their apartments. The distance from Buzz's apartment to Woody s house is (5x + 4) miles, while Jessie's apartment is (15x + 30) miles. How far apart do Jessie & Buzz live from each other? a polynomial function with leading term 8x ^9 has a degree of what? What are two theories about the origin of the Greeks?settlers from Anatoliasettlers from the Black Seasettlers from the Red Seasettlers from Athens What can be said about the equipment used by photographers during the Civil War?1. It was not easy to use.2. It was poorly manufactured.3. It was only sold to men.4. It was extremely heavy. The soldiers are lying askew __________ on a battlefield making it a pitiful sight. Fill in the blank A twistedB sleeping C uncomfortable Are you more likely to solve a math problem logically or miraculously _________ .A poorlyB badly C amazingly 1. The length of arectangle is three inches more than its width. It's area is 130 in^2. Find the width and length of the triangle. A sample of peptide of unknown sequence was treated with trypsin to produce the following smaller peptides: 1) Met-Val-Ser-Thr-Lys 2) Val-Ile-Trp-Thr-Leu-Met-Ile 3) Leu-Phe-Asn-Glu-Ser-Arg Another sample of the same peptide was treated with chymotrypsin and gave the following smaller peptides: 1) Asn-Glu-Ser-Arg-Val-Ile-Trp 2) Thr-Leu-Met-Ile 3) Met-Val-Ser-Thr-Lys-Leu-Phe What is the sequence of the original peptide? The density of water is ____________. Waves that make up the visible part of the electromagnetic spectrum have Which of the following best describes energy transformations in ecosystems?a.Most energy in a lower trophic level is passed to higher trophic levels.b.Heat is not a significant waste product as energy passes between trophic levels.c.Most of the energy collected by an organism is not passed on to other organisms.d.Tertiary consumers collect the most energy in an ecosystem. Why do we need to measure the weight of our decisions? What are the distinctive characteristics of the Hagia Sophia? An elevator rises steadily up a skyscraper. After 4 s it is 33 m above the ground, 2 s later it is 47 m above the ground. Which equation models its position, y, with respect to time, x? A. y-47= -7(x-2)B. y+33=7(x+4)C. y-33= -7(x-4)D. y-33=7(x-4) Renaissance instrumental How did the United States government spread its propaganda? How did the United States government portray Germany? estimate 8.2x6.7 divided by 0.46 (5a^2 + 3) (4a^2 + 3) Molecules that are ___ and ____membrane easily. pass through the cell Jeff and Brett both play basketball at the country club. Jeff is amember, so he pays $64 a month and $2 each times he plays. Brettis not a member, so he pays $10 each time he plays.a. After how many visits to the basketball court will Jeff and Brett'sbills be the same amount?