is the sum of two rational numbers always rational

Answers

Answer 1

Answer:

in short, Yes they are always rational.

here's why...

E.g. suppose [tex]\frac{c}{d}[/tex] and [tex]\frac{a}{b}[/tex] are fractions, that means that a,b,c,d are all integers, and b and d are not zero. finding the sum the numerator, and denominator would also have to be integers. the denominator of the sum can't be zero since the denominators of the fractions were not zero, and would give [tex]\frac{ad+bc}{bd}[/tex] and since they are bound by addition (sum means addition) they must also be rational since eit would equal a bigger integer than initially had

Step-by-step explanation:


Related Questions

just do one if u want

Answers

Answer:

whats the question i can't really see it

Step-by-step explanation:

Mr. Green orders some cookies from a local youth group. Using his order form shown below, complete the last column to find the total to be paid. Quantity Description Unit Price Total of Line 1 Krispy Kosmos $2.89 $ 2 Chewy Chocos $3.19 $ 1 Gooey Globs 2.99 $ Total $ 5.2% tax $ Total to be paid $ a. $9.54 b. $12.26 c. $12.90 d. $18.64 Please select the best answer from the choices provided A B C D

Answers

From the computation done, it can be denoted that the total price that will be paid will be $12.90.

1 Krispy Kosmos at $2.89 = $2.89

2 Chewy Chocos at $3.19 each = 2 × $3.19 = $6.38

1 Gooey Globs at $2.99 = $2.99

Total = $2.89 + $6.38 + $2.99 = $12.26

We'll then add the sales tax of 5.2%, therefore, the total value will be:

= $12.26 + (5.2% × $12.26)

= $12.26 + $0.638

= $12.90

In conclusion, the correct option is $12.90.

Learn more about prices on:

https://brainly.com/question/1293276

Answer:

C

Step-by-step explanation:

Edg 2022

What is the radical form of the expression 4 3/2

Answers

The last option. The top part of the fraction becomes s the exponent of the number inside the root. And the bottom part of the fraction is on top part of the root symbol. With square roots you don’t write the number 2. That’s why there is no number in the last option because that means it is square root (2)

A local business charges $20 to set up their sweatshirt printing machine with the design and $9.75 in materials per sweatshirt to print.

1. Write an equation for the average cost A(x) of printing x sweatshirts through this company.

2. Describe what happens to the average cost per sweatshirts as more and more are printed.​

Answers

IM SURE ITS DEFINITELY NOT BUT POSSIBLE 19

Anne pays cash for a Tv. The store owner gives her a 10% discount. She pays $702. How much was the price of the Tv before a discount?

Answers

Answer:

$780

Step-by-step explanation:

P = Original Price

P (100% - 10%) = $702

P (90%) = $702

(P (.9)) / .9 = $702 / .9

P = $780

Check answer:

$780 (90%) = $702

What happens to the value of the expression 20 + a, a as a increases?

Answers

Answer:

With the increase of the value of a ,the value of the expression 20+a will also increase.

Step-by-step explanation:

Is 24 the correct LCD to use for subtracting 6 3/4 - 1 2/6 ? Why or why not?

In your own words, describe how to find the GCF for a set of numbers. Use the numbers 24 and 32 as an example.

Subtract and reduce to lowest terms: 9/10 - 3/10.

PLEASE HELP ASAP

Answers

Answer:

Step-by-step explanation:

A

No 24 is not the best number to use for the LCD, although it will work. 12 is much better because it is smaller.

B

Factor each number into it's primes.

24 = 2*2*2*3

32 = 2*2*2*2*2

The highest common factor is 2*2*2 = 8

C

9/10 - 3/10 = 6/10 The denominator remains the same. The numerators get subtracted.

6/10 = 3/5 Two goes into both numerator and denominator of the answer. Therefore you can divide both 6 an 10 by 2

HELP PLEASE FOR BRAINLIST!!!!!!!!!!!!

Answers

Answer:

a(x) and d(x)

hope that helps, have a good day!

dont forget my brainliest.

Step-by-step explanation:

100 points!!!!!!!!!!!!

Answers

Answer:

a)

Step-by-step explanation:

Answer: pretty sure it's d but I could be wrong

Step-by-stepStep-by-step explanation:

can some one help me on this

Answers

28 divided by 4 = 7
so do 7 * 5 which is 35 so they make 35 cookies in 5 seconds

Darren got 42 out of 56 questions correct on a test. What percent of the questions did he get correct?

Answers

Answer:

75%

42/56 =  42/56

Convert to decimal form:

42÷56 = 0.75

= 75%

Can you mark as brainliest if its right?

Answer:

75%

Step-by-step explanation:

42/56 = 0.75 = 75%

The price,
P of tickets at a movie theater since it opened in 2001 can be modeled by the linear equation shown, where t is the number of years since 2001. P = 8.75 + 0.35t
What is the meaning of the P
-intercept in this scenario?


the price of a ticket in
2001
the price of a ticket in 2001

the increase in ticket price per year
the increase in ticket price per year

the total number of years the theater has been open
the total number of years the theater has been open

the difference in the price of a ticket in
2001
and the price in
2011

Answers

Answer:

B

Step-by-step explanation:

You have to look at the second term to be sure of the meaning of t - 15n

What the given term says is that the total number of tickets sold (p) will decrease by 15 times the number of increases that there are.

The other term says that the cost of 1 ticket will increase that each ticket will increase by 2 dollars for each change in the ticket prices providing that change is 2 dollars.

C is out of the question. The information talks about 2 dollars per increase which is the first term.

A is not quite correct. It implies there is exactly 1 ticket increase. The crorect answer is the ticket increases can be a number of times (n)

The answer is B

[tex](-\frac{3n}{18n^{2} } )^{-18} * (-6n)^{-15}[/tex]

Answers

[tex]\left( - \dfrac{3n}{18n^2}\right)^{-18} \times(-6n)^{-15}\\\\\\= \left(-\dfrac{1}{6n} \right)^{-18} \times \dfrac{1}{(-6n)^{15}}\\\\\\=\left[(-6n)^{-1}\right]^{-18} \times \dfrac 1{(-6n)^{15}}\\\\\\=(-6n)^{18} \times \dfrac 1{(-6n)^{15}}\\\\=(-6n)^{18-15} \\\\=(-6n)^3\\\\=-216n^3[/tex]

what is the expressions of ײ-3y when x = -5 and y=(2-)

Answers

[tex]\huge \bf༆ Answer ༄[/tex]

Plug the values of x and y in the given expression ~

[tex] \sf {x}^{2} - 3y[/tex]

[tex] \sf( - 5) {}^{2} - (3 \times 2)[/tex]

[tex] \sf25 - 6[/tex]

[tex] \sf19[/tex]

The equivalent value is 19

The answer is 19 hope this helped.

80 people exercise in the morning at Planet Fitness. 100 people
exerflncise in the afternoon. What is the percent of increase in the
number of people exercising at Planet Fitness in the afternoon?

Answers

Answer: it has a 20% increase

The car travels 60 km from city A to city B passed at speed x. On the way back, the speed was increased by 12 km / h. What is the initial speed if the car has traveled for a total of 10 hours?​

Answers

Answer:

54 km/h

Step-by-step explanation:

use s=½(u+v)t

600=½(x+x+12)10

600=½(2x+12)10

600=(2x+12)5

600=10x+60

540=10x

x=54 km/h

I think this is how to do it, I'm so sorry if I do it wrong!

Un padre preocupado por motivar a su hijo en Matemáticas, se compromete a darle 1 euro por problema bien hecho, mientras que, si esta mal, el hijo le devolverá 0,5 euros. Después de realizar 60 problemas, el hijo ganó 30 euros. ¿Cuántos problemas resolvió correctamente?

Answers

Answer:

good morning I have any questions or need anything from the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer to the answer

The son solved 40 problems correctly out of the 60 problems he attempted.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's denote the number of problems the son solved correctly by "x".

According to the problem, for each correct problem, the son earns 1 euro, and for each incorrect problem, he loses 0.5 euros.

Now,

Total earnings = 1 euro (x) - 0.5 euros (60 - x)

Simplifying this expression.

Total earnings = 1.5x - 30

We are given that the son won 30 euros in total, so we can set up the equation:

30 = 1.5x - 30

Solving for x.

1.5x = 60

x = 40

Therefore,

The son solved 40 problems correctly out of the 60 problems he attempted.

Learn more about expressions here:

https://brainly.com/question/3118662


#SPJ2

The complete question.

A father concerned about motivating his son in Mathematics agrees to give him 1 euro for a problem well done, while if it is wrong, the son will return 0.5 euros. After doing 60 problems, the son won 30 euros. How many problems did you solve correctly?

HELP PLS ! How many solutions does the following system of equations have?

Answers

Answer:

A - infinite

Step-by-step explanation:

The 2 lines are on top of each other making any point on either line a solution.

Hope that helps

The formula to find the area of a triangle is A = { bh where b=base and h=height. Rearrange the
equation to highlight b, the base of the triangle, in terms of the area and height.

Answers

Answer:

A=B+H

Step-by-step explanation:

I rearange the letters and also I put a plus singe

Write in point-slope form an equation of the line that passes through the point (1,9) with a slope of -2

Y-_=_(x-_)

Answers

Answer:

y - 9 = - 2(x - 1)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Here m = - 2 and (a, b ) = (1, 9 ) , then

y - 9 = - 2(x - 1) ← is the equation of the line

Rebah and her twin brother are planning a birthday party at Pizza Pete's. There is a S64.75 charge to reserve a party room plus $4.95 per person charge for lunch
Explain how to find the greatest number of people that can attend the party for $175.00. Show your work, and state the number of people.
QUICKKK PLZZ

Answers

Answer:

22 people

Step-by-step explanation:

Step 1: I first subtracted $64.75 from $175.00 so that I knew how much would be leftover after the charge of the room, because you can't count that cost. When I did this, I got $110.25. So then I knew how much was paid other then for the room.

Step 2: I then divided $110.25 by $4.95, so I would get the amount of people who went to the party, since each person costs $4.95. When I divided, I got 22.

So that would be my answer. I hope that helps. :)

Jenna works a job where her pay varies directly with the number of hours she has worked. In one week, she worked 35 hours and made $274.75. How many hours would she need to work in order to earn $337.55?

Answers

274.75/35= $7.85 per hour
337.55/7.85= 43 hours

Caleb decreases a number by 6 and then multiplies it by 2. He gets the same answer as
when he subtracts 8 from the original number. What is the number?
please answer!!

Answers

Answer: 4

Step-by-step explanation: If Caleb starts with 4 and subtracts 6, he'll get -2. -2 times 2, equals -4. If he starts with 4 and subtracts 8, he'll again end up with -4, meaning the original number is 4!

4-6= (-2)

-2*2= (-4)

4-8= (-4)

what is x/-4 = -20 how do i sole for x

Answers

Answer:

x = 80

Step-by-step explanation:

Reverse your division by using multiplication:

x/-4 = -20

-4 x -20 = 80

What is the equation of the line that is parallel to the
given line and passes through the point (-3,2)

Answers

Answer:

Step-by-step explanation:

A parallel line will have the same slope as the reference line.  In this case, I don't see the "given line" as promised in the question.  If it does appear, and it looks like y = 5x + 3, for example, the slope is 5 and the new line will have the same slope.

If this slope is correct, we can start the equation for the parallel line that goes through point (-3,2) by starting with:y = 5x + bWe need a value of b that forces the line to go through point (-3,2).  We can do that by using the given point in the equation and solving for b:y = 5x + b2 = 5(-3) + bb = 17The parallel line to y=5x+3 isy = 5x + 17See attachment.

An arts academy requires there to be 4 teachers for every 100 students and 5 tutors for every 60 students. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has 144 standents​?

Answers

Answer: 25 students per teacher and 12 students per tutor. They need 2.4 tutors for the school

Who can help me on this? NEED OF HELP!

Answers

Answer:

25+25 = 50

sum means +

Integers are positive and negative numbers, no decimals or fractions though

Question is on the picture ​

Answers

Answer:

B. 30/65 and experimental

Step-by-step explanation:

30/65 is your answer

4/9 7/21 change to percent

Answers

Answer:

Hi there, your answers here are 44% and 33%.

To convert 4/9 to a percent, first we can write it as a decimal - 0.44444444444. To get this decimal, we divide 4 by 9. Then, we multiply this decimal by 100 to get 44.4444444444, or roughly 44%.

To convert 7/21 to a percent, first we can write it as a decimal - 0.33333333333. To get this decimal, we divide 7 by 21. Then, we multiply this decimal by 100 to get 33.3333333333, or roughly 33%.

Find the slope of the line that passes through 9,7 and 6,15

Answers

[tex]\huge \bf༆ Answer ༄[/tex]

Let's find the slope considering the points (9 , 7) and (6 , 15)

[tex] \sf \dfrac{y2 - y1}{x2 - x1} [/tex]

[tex] \sf \dfrac{15 - 7}{6 - 9} [/tex]

[tex] \sf \dfrac{8}{ - 3} [/tex]

[tex] - \dfrac{8}{3} [/tex]

Other Questions
which list shows the plot elements in the correct order? -8.5x +0.43 = -2.97The solution is x = In your own words, describe how to find the GCF for a set of numbers. Use the numbers 24 and 32 as an example. (PLS HELP ILL GIVE 50 points and brainlest also no links please, thanks) Pronoms UNLIMITED ATTEMPTS LEFT LATE DUE November 16th 11:59 PM Compltez chaque phrase avec le bon pronom d'objet indirect ou le bon pronom disjoint. 1. Vous ne envoyez pas de cadeau? ( votre frre) 2. Je montre l'appartement. (aux amis) 3. Alexis et Thibaud donnent les indications pour aller chez eux. ( nous) 4. Ma soeur, elle ne prte jamais ses vtements. (ner/ moi) 5. Vous posez des questions. ( vous) 6. TO tlphones ( tes enfants / yourself) 7. Nous ne parlons pas. ( cette fille) 8. Je demande pourquoi tu es fatigu aujourd'hui. ( toi) SAVE PLEASE HELP WHAT IS THE DOMAIN AND RANGE OF THIS GRAPH PLS HELP ME ASAPDO NOT use any links (-1, 16), (-13, 6)Write an equation in slope-intercept form.help Cuntos son cuatro ms sesenta y seis? 30 POINTS! "A triangle with the side lengths of these numbers CAN exist: 9, 3, and ____? Questionrefer to attachment nonsense will get report The trachea, the bronchial tree, and the lungs are part of which tract? Which process is absent in animal cells?making proteinschemical reactionsrespirationphotosynthesis based on your answer in part A what role does gravity play in the separation of the liquids shown Find the slope of the graphed line.ASAP 100 POINTS TO WHOEVER ANSWERS FIRST and brainiest.Which describes the introduction to the essay? 1. It has two paragraphs: one for the thesis and one for the background. 2. It has a wide focus: one that includes a variety of theories. 3. It states a contradiction: one that the conclusion corrects. 4. It states the main point: one that is not fully answered in the essay.Please answer Quickly 2 evidence ( embedded quote with citation) for does the influence of gravity extend out forever in space exploration Find the perimeter of the figure. Complete the recursive formula of the arithmetic sequence -15, -11, -7, -3,...15,11,7,3,...minus, 15, comma, minus, 11, comma, minus, 7, comma, minus, 3, comma, point, point, point. c(1)=c(1)=c, left parenthesis, 1, right parenthesis, equals c(n)=c(n-1)+c(n)=c(n1)+c, left parenthesis, n, right parenthesis, equals, c, left parenthesis, n, minus, 1, right parenthesis, plus 1. What impact did Napoleonic Europe have on neighboring countries of France? Which of the following is a government retirement program that offers a tax incentive?A. Roth IRAB. Opt- out program C. A 529 planD. Contribution matching