among all fractions $x$ that have a positive integer numerator and denominator and satisfy $$\frac{9}{11} \le x \le \frac{11}{13},$$ which fraction has the smallest denominator?

Answers

Answer 1

The fraction that has the smallest denominator is [tex]\frac{9}{11} < =\frac{5}{6} < =\frac{11}{13}[/tex]

Notice that the fractions seem to have the form  n / [ n + 2]    where n is an integer

Suppose that there exists a fraction such that

9/11 < n / [n + 2]  < 11/13

We can split this into two inequalities

Looking at the inequality on the left....we have

9[n + 2] < 11n    

9n + 18 < 11n

18 < 2n

9 < n    or

n > 9

Looking at the inequality on the right.... we have

13(n) < 11[n + 2]

13n < 11n + 22

2n < 22

n < 11

This implies that

9 < n < 11

So...n = 10 is the only integer that satisfies this

And n + 2 = 12

So....the fraction is 10/12  = 5/6  

Learn more about fractions here:https://brainly.com/question/78672

#SPJ4


Related Questions

[tex]\sqrt[3]{11}[/tex]

Answers

Answer:

2.22

Step-by-step explanation:

[tex]\sqrt[3]{11} =2.223980091[/tex]

Rounded to hundredths: 2.22

Jamie is twice as old as Natalie now. Give years ago the sum of their ages was 26. How old is each person now?

Answers

answer:

8. 67 and 17. 36

step-by-step explanation:

hi there!

to find out the age of both girls, i believe that we should divide the number 26 by 3 because jamie is twice as old as natalie meaning ( natalie ) is younger

26/3

= 8. 67

meaning 8.67 is how old natalie is/was

add 8.68 to itself once and you will get jamie's age!

8. 67 + 8. 67

= 17. 34

meaning 17. 34 is how old jamie is/was

sorry if i misread the question or made it a little confusing! but i do hope that this ends up helping you! :)

(Write the equation) Thank you if you answer it <3

Answers

Answer:

10 - 2 = (x + 6)

Explanation:

The Sum Of x And 6 Is Two Less Than Ten.

The Sum Of x And 6: x + 6

Two Less Than Ten: 10 - 2

Put The Two Terms Together10 - 2 = (x + 6)
answer is: 10-2=(x+6)

Multiple Response. Select all the equations that have exactly one solution.

A. 3x + 1 = -3x + 7
B. 3x + 1 = x + 1
C. 3x + 1 = 3x + 7
D. 3x + 1 = 1/2 (1x + 1)
E. 3x + 3 = 3(x+1)

Answers

Answer:

A, B, D

Step-by-step explanation:

How do I find tips and discounts?​

Answers

Well, there are many apps and websites such as Honey to help you. You can also find then on newspapers and magazines where you can find coupons for discounts. And you can find tips in places like BRAINLY like I am doing now.

Charlie is saving for a new computer desk. The table costs $70. So far, she has already saved $35/ Write an equation to show how much more does she need to save to buy the desk. *Let x represent the amount of money that needs to be saved

Answers

Answer:

x + 35 = 70

   -35    -35

–––––––––––

     x = 35

Step-by-step explanation:

35 + 35 = 70

:))

Without doing any calculations, compare Expression A to Expression B.

A (34 + 25) ÷ 14

B 34 + 25

Answers

Answer:

A < B

Step-by-step explanation:

well lets see, they are both adding 34 and 25

But in a, they are dividing, and because dividing usually makes the number smaller, B is larger

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Expression A is less than expression B

Step-by-step explanation: Connexus  

A line has a slope of 0 and passes through the point (-4, 3). What is its equation in slope-intercept form.​

Answers

Answer:

y = 3

Step-by-step explanation:

We already know the slope, all we need to do is find the y-intercept.

You have to plug the coordinates into the equation, y = 0x + b

y = 0x + b

3 = 0(-4) +b

3 = 0 + b

3 = b

The equation is y = 3

0.25% of 42 is what number

Answers

Answer:

0.105

Step-by-step explanation:

0.25/100 x 42 = 0.105

Answer: The answer is 0.105

i need help btw i am in middle school

Answers

Answer: J

Step-by-step explanation: It is very cool you are in middle schopol

Help please :)) Ignore the writing i was attempting to figure it out

Answers

Answer:

The answer is C. I hope this helps and is the paper red? That's cool. Anyways have a nice day!!

Step-by-step explanation:

Answer:

I think its is D but i'm not 100% sure

The senior classes at Portland High School and Biddeford High School planned separate
trips to New York City. The senior class at Portland High School rented and filled 1 van
and 6 buses with 372 students. Biddeford High School rented and filled 4 vans and 12
buses with 780 students. Each van and each bus carried the same number of students. How
many students can a van carry? How many students can a bus carry?

Answers

I believe it would be 47

The fractuon 3/5 is found between which pair of fractions on a number line?

Answers

Answer: It's kinda simple, 2/5 and 4/5

Just add 1 to the numerator of the original fraction, and there's where you get 4/5. Then subtract 1 from the original fraction, and that's where you get 2/5!

please help 15pts and will give brainlist!!

Answers

Answer:

1st ans

(x+15)=135(alternate angle)

x=135-15

x=120

2nd ans

(8x-4)=92(corresponding angle)

8x=92+4

x=96/8

x=12

3rd ans

(x+1)=51(vertically opposite angle)

x=51-1

x=50

STION 4
Write the following ratio in its simplest form:
64:18​

Answers

The ratio 64:18 can be expressed in its simplest form as 32:9

Data;

6418

What is Ratio?

Ratio of a value is a relationship between two or more values indicating the number of times a value is present in the other.

To find the smallest ratio between 64:18, all we have to do is simply divide them to the smallest possible value

[tex]64:18=\frac{64}{18} =\frac{32}{9}[/tex]

The ratio 64:18 can be expressed in its simplest form as 32:9

Learn more on ratio here;

https://brainly.com/question/7620723

Simplify the following equation

Answers

Answer:

3x - 2

Step-by-step explanation:

Answer:

3x−2

Heart if this helped!

HELP!! 4 questions !!! easy points!! 25 points!! please answer quick!

Answers

Step-by-step explanation:

(i) From the graph value of x varies -3 to 3 i.e.

[tex]-3\leq x\leq 3[/tex]

and domain in the input values which function can take

So, option (d) is correct.

(ii) option (d) is correct as it represent the function [tex]y=x[/tex]. While all the other function does not satisfy the given conditions.

(iii) [tex](-14,-15), (-9,-10)[/tex] are the parts of solution pair.

(iv) Option (c) and (d) represents the function as each element of the first set has a unique image in the second set.

explain how finding the square root of a number is different from finding the cube root

Answers

U could searc9 it up and it will help u

please help this is confusing me:(

Answers

Answer :
-8 miles per min
He travels 3.25min

-8 x 3.5= -26

He traveled 26 miles in 3.25

I hope this helped

jack typed 45 words in 1 minute. how many minutes will it take jack to type 990 words

Answers

Answer:

22 minutes

Step-by-step explanation:

990/45=22

Answer:

it will take 22 minutes

i just multiplied 45 and 22 and got 990

Do anyone know this problem?

Answers

Answer:

me kown it

Step-by-step explanation:

Help please and thank you

Answers

Answer:

1000

Step-by-step explanation:

well just round it to the nearest thousand

45 is the answer :)
hope this helps


A construction crew is made up of 18 men; the rest are women. If 75% of
the crew are men, how many people are in the crew altogether?
24
22
28
20

Answers

Answer:

24

Step-by-step explanation:

I just took this test and got an A

Have a great day!

Answer:

22

Step-by-step explanation:

22 because I did it already

Can someone help me with this. Will Mark brainliest.

Answers

False hope that helps

Answer:

False

Step-by-step explanation:

because all four sides of a rectangle don't have to be equal. However, the sets of rectangles and rhombuses do intersect, and their intersection is the set of squares—all squares are both a rectangle and a rhombus.

:))

A house that costs $125,400 appreciates at a rate of 3% each year. What is the value of the
home after 3 years.
a.$137027.97
b.$275503.80
c.$114449.19
d.$3385800

Answers

Answer:

The value after three years is $137,027.97

Step-by-step explanation:

Here, we want to get the value of the home after 3 years

Generally, we have the exponential formula as follows;

y = P(1 + r)^t

where P is the original cost which is $124,400

r is the rate of increase which is 3% = 3/100 = 0.03

t is the time which is 3 years

Substituting these values;

y = 125400(1 + 0.03)^3 = $137,027.97

Someone who can help me?​

Answers

Answer:

4 days

Step-by-step explanation:

$0.09 × 100 = 9

$62.47 × 4 = 249.88

249.88 + 9 = 258.88

If you roll a d6, what is the chance of rolling a 4?

Answers

Answer:

1/6

Step-by-step explanation:

They are asking for 1 section out of 6 so it is 1/6.

Can I please have Brainliest?

I need help FAST pleaseeeee

Answers

Answer:

20 i think

Step-by-step explanation:

help asap! 30 pts and brainliest!
given the data represented in the bar graph which month represents 10% of the birthdays for the students surveyed?
a. july
b. june
c. may
d. september
thank you!

Answers

Answer:

July

Step-by-step explanation:

Took terst

16/g,when g=4

Please answer

Answers

Answer:

4

Step-by-step explanation:

Other Questions
How has the poet used personification in poem Sea Fever by John Masefield? The leader of palenque known for his lengthy reign and numerous public works projects was:____.a. pacal the great b. moctezuma i c. moctezuma ii d. huayna capac What will be the best way to store his frozen fish? . Which of the following empires had already declined hundreds of years before the arrival of the Europeans? Which of the following best identifies the early speech stage in which a child speaks using mostly nouns and verbs?a. two- word stageb. babbling stagec. one-word staged. telegraphic speeche. grammar Someone help me with this please! An increase in the quantity of resources available O a moves the economy to a new point down along a given PPF. O b moves the economy to a new point up along a given PPF. O C shifts the PPF rightward. O d shifts the PPF leftward. What Colour represents protection? What is a 7 lines poem called? What is Orwell's point in Animal Farm? Complete the following table. The ratio of soccer balls to basketballs at Andrews school is shown on the ratio table. What number completes the ratio table to make an equivalent ratio? [Type your answer as a number.]soccer balls 30 ?basket balls 25 5 Select the correct answer. Why is this statement not a hypothesis? sunflowers require soil and plenty of sunlight and water to grow and thrive. A. It is a well-known fact. B. It is a proven theory. C. It is not falsifiable. D. It is difficult to test. What impact on religion did the Ottoman Empire have in Eastern Europe? If 0.05 = 2a + 5b and 0.2 = 8a + 2b are two normal equations, find the parameters a and b. Which of the following had control of Oregon in the 1820s and 1830s? What type of word is luxury? What Spanish island is the best? Hannah drove 450 miles to her brother's house at an average speed of 60 miles per hour. How long did she take? whcich is the is most deendent on long standing historical principles predating the us