Are all real numbers either rational or irrational?​

Answers

Answer 1

Answer:

Yes. All real numbers are either rational or irrational.

Step-by-step explanation:

The set of all irrational numbers is commonly defined as the set of all real numbers that are not rational.

Let [tex]\mathbb{R}[/tex] denote the set of all real numbers. Let [tex]\mathbb{Q}[/tex] denote the set of all rational numbers.

For any given real number [tex]x[/tex] ([tex]x \in \mathbb{R}[/tex],) either [tex]x\![/tex] is rational ([tex]x \in \mathbb{Q}[/tex]) or [tex]x\!\![/tex] isn't rational ([tex]\lnot (x \in \mathbb{Q})[/tex], such that [tex]x \not\in \mathbb{Q}[/tex] and thus [tex]x \in (\mathbb{R} \backslash \mathbb{Q})[/tex].)

Assume that [tex]x[/tex] isn't a rational number. By the definition of rational numbers, since [tex]x\!\![/tex] is a real number but not a rational number ([tex]x \in (\mathbb{R} \backslash \mathbb{Q})[/tex],) [tex]x\![/tex] would be an irrational number.

Therefore, either [tex]x[/tex] is rational or [tex]x\![/tex] is irrational. Every real number would either be rational or irrational.


Related Questions

I need answers to these questions

Answers

Answer is in the attached file...

A. In a complete sentence, describe the angle relationship in the diagram. B. Find the value of x

Answers

Answer:

  x = 30

Step-by-step explanation:

a) The sum of the angles along the line is 180°. That means ...

   2x° +90° +x° = 180°

__

b) Subtracting 90° and dividing by 3° gives ...

  3x° = 90°

  x = 30

Answer:

a) supplamentary angles b) X= 30

Step-by-step explanation:

A) Equal to 180 b) 90 divided by 3 gives you 30

regular price: $225.75
Precent of discount: 30%

Answers

Answer:

$156.63

Step-by-step explanation:

223.75 - (223.75 x .3) = 156.625

Evaluate the expression when b= -4 and c=6. -4c+ b​

Answers

Answer:

-4 x 6 + -4

-24 + -4

-28.. is your answer mark me brainlist bro plz

Answer:

-28

Step-by-step explanation:

-4(6)+(-4)

-24+(-4)

-28

crisps
normal price £1.43
three for the price of two
what is the total of 6 packets

Answers

Answer:

3 packs equal the price of two, therefore 1.43•2= 2.86

and 6 packs equal the price of 4, so 2.86•2= 5.72

The point (-5,0) is plotted on a coordinate plane.
What is the point of reflection when (-5,0) is reflected across the y-axis?
A-(0,5)
B-(-5,0)
C-(0,-5)
D-(5,0)

Answers

[tex]\huge\boxed{Hello! :)}[/tex]

We plot the point (-5,0) on the coordinate plane.

Then, we reflect it over the y-axis.

Remember the rule:

If a point has coordinates (x, y), and the point is reflected over the y-axis, the new point's coordinates are: (-x,y)

Let's use this rule now.

We reflect (-5,0) over the y-axis.

(-5,0)

The new point is: (5,0)

[tex]\huge\boxed{(5,0) \: is \: the \: answer. :)}[/tex]

(Option D)

[tex]\boxed{Felicitous\: Girlie\: here\: to\: help}[/tex]

What is an equation of the line that passes through the points (3,4) and (-4, -3)?

Answers

Answer:

y=x+1

Step-by-step explanation:

1) Find the slope

m=-3-4/-4-3

m=-7/-7

m=1

2) Use y=mx+c

by using the point (3,4)

4=1(3)+c

4=3+c

c=1

3) The answer

y=x+1

PLEASE, LAST POINTS! ( GIVING BRAINLIEST) TO GET BRAINLIEST ANSWER 6 and 8 PLEASE. LAST 10 POINTS!

Answers

Answer:

6; 6⁒2

10; 10⁒2

0; 3(0)+3

1; 3(1)+3

2; 3(2)+3

3; 3(3)+3

4; 3(4)+3

Step-by-step explanation:

each line is in order.

Answer:

  6. inputs: 2, 6, 10

  8. inputs: 0, 1, 2, 3, 4

Step-by-step explanation:

Use your knowledge of arithmetic facts.

6.

x = 2, 2÷2 = 1

x = 6, 6÷2 = 3

x = 10, 10÷2 = 5

__

8.

x = 0, 3×0 +3 = 3

x = 1, 3×1 +3 = 6

x = 2, 3×2 +3 = 9

x = 3, 3×3 +3 = 12

x = 4, 3×4 +3 = 15

In which quadrant does the graph of the sum of
(-3 – 5i) and (2 + 4i) lie?

Answers

Answer:

Third quadrant

Step-by-step explanation:

The complex and real parts can be added separately:

(-3 - 5i) + (2 + 4i) = -1 -i

This shows that the sum would be in the third quadrant of the complex plane as there is negative real and negative imaginary parts.

Lary works in a automobile company. They just shipped out 5 brand new cars. The total cost of these cars was $1,067,800. If they all cost the same amount,what was the price of each car ?
She your work.

Answers

You will have to divide 1,067,000 by 5.
1,067,000/5= 213,400 $ per each car

Dr. W Sweet Rides Car Rental charges a flat fee of $24 and an additional $0.35 for every mile the car is driven. Which function models the total cost, C(x), of renting a car for x miles?

Answers

Answer:

[tex]c = 0.35 x + 24[/tex]

Step-by-step explanation:

First, let's go over the information we have. We know that no matter what, Dr. W Sweet will charge a base fee of $24, and that for each additional mile, he will charge 35¢. Now let's make an equation reflecting this information:

cost = 35¢ (number of miles) + $24 (starting fee)

We can also write this like this:

[tex]c = 0.35x + 24[/tex]

If you want to test this equation, put in a value for the x variable, like so:

Value: 25 miles

[tex]c = 0.35(25) + 24 \\ c = 8.75 + 24 \\ c = 32.75[/tex]

For this situation, the cost will be $32.75. I hope this helps! If you have questions, comment on this response, I should write back reasonably quickly.

Find the value of

-12
20
36
-10

Answers

Answer:

20 is the answer.

Step-by-step explanation:

(-4)² + (-2)²=> 16 + 4=> 20

Conclusion:

Therefore, 20 is the answer.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

(-4)²+(-2)²16+420

Option B

Which of the following is a required deduction?
A. Health insurance
B. Disability insurance
C. FICA
D. State sales tax

Answers

To withhold a percentage of an employee's wages or salary and contribute an equal amount to these programs.FICA s a required deduction. Thus, option C is correct.

What is the FICA?

FICA (Federal Insurance Contributions Act) is a required deduction that includes Social Security and Medicare taxes for employees in the United States.

Health insurance and disability insurance may be offered by employers but are not required by law to be deducted from an employee's paycheck.

The current FICA tax rate is 7.65%, which includes a 6.2% Social Security tax and a 1.45% Medicare tax.

State sales tax is not a deduction from an employee's paycheck. It is a tax paid by consumers on purchases they make.

Therefore, FICA s a required deduction.

Learn more about FICA here:

https://brainly.com/question/14208089

#SPJ1

Divide 6.72 by 0.041 and round to the nearest hundredth

Answers

Answer: 163.90

Step-by-step explanation:

163.9 is the answer

If f (x) = 7+2x and g(x) =5x -2, find f (7)

Answers

Answer:f=103.444

Step-by-step explanation:

took this test and got an A++

The value of the function [tex]f(x)=7+2x[/tex]  for [tex]f(7)[/tex] is 21.

The given functions are [tex]f(x)=7+2x[/tex] and [tex]g(x)=5x-2[/tex].

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

To find [tex]f(7)[/tex], substitute [tex]x=7[/tex] in [tex]f(x)=7+2x[/tex], we get

[tex]f(7)=7+2(7)[/tex]

[tex]f(7)=21[/tex]

Therefore, the value of the function [tex]f(x)=7+2x[/tex]  for [tex]f(7)[/tex] is 21.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ4

Help help help math nath

Answers

Answer:

12

Step-by-step explanation:

plug in -7 where x is

5 - (-7) = 12

Answer:

12

Step-by-step explanation:

plug in -7 where x is

5 - (-7) = 12

It's pretty simple!

I hope this helps you

The first term of an arithmetic sequence is 4 and the tenth term is 67.
What is the common difference? Show your work or explain your answer.

Answers

Answer:

Step-by-step explanation:

Formula

tn = a1 + (n-1)* d

Givens

tn = 67 (it is the last term or the nth term

n = 10

a1 = 4

find d

Solution

67 = 4 + (10 - 1)*d

67 = 4 + 9*d               Subtract 4 from both sides

67 - 4 = 9d            

63 = 9d                      Divide by 9

63/9 = 9d/9              

7  = d

Remark: This is a fundamental application of the arithmetic sequence. You pretty much have to know how to juggle it's parts.

1 mi = 1.6 km

How many miles are in 39.2 kilometers?

Answers

Answer:

24.35775

Step-by-step explanation:

Ty for points xd

Answer:

24.35 miles

Step-by-step explanation:

just divide 39.2 by 1.6

3’2x (8-5)
6’2+(4x3)
42-(14-12)

Answers

Answer:

1. 27

2. 48

3. 40

Step-by-step explanation:

3 to the power of 2 is 9 (3×3)

9×3=27. (8-5=3)

6 to the power of 2 is 36 (6×6)

36+12=48. (4×3=12)

42-2=40

Evaluate the expression when b=5 and y=-2. b-8y ​

Answers

Substitute the numbers in place of the variables. (5)-8(-2)—> 5+16–>21. Answer is 21. Can I get brainliest?
ubstitute the variables with the numbers. 5+16->21 = (5)-8(-2). The correct answer is 21.

whats the rate of change

Answers

The line needs to start at the 0 it can’t be off the 0

How many meters are in 28% of 15 km?
Explanation Please with proportions.
I will reward the brainiest

Answers

Answer:

4200

Step-by-step explanation:

Answer: 4,200 meters

Step-by-step explanation:

[tex]\frac{28}{100} * 15 = 4.2 km = 4200 m[/tex]

5. Randall wants to buy a pizza. He can
select from 4 different sizes (s,m,Ixl), three
types of crust (pan, thin, hand toss), and
two toppines (cheese or pepperoni). How
many different outcomes of pizza can
Randall order?

Answers

Answer: 18 outcomes

Step-by-step explanation:

For the small:

pan+cheese

or

pan+pepperoni

or

thin + cheese

or

thin + pepporoni

or

hand + cheese

or

hand + pepperoni

which is 6 outcomes

then 6x3(because of the sizes) is 18.

Need help ASAP!!! Use the function below to find the stuff in the picture!!!

Answers

f(x) = 3^x, f(-2)
Substitute
f(-2) = 3^ -2
= 1/9
Therefore it’s b

Answer: B. 1/9

Step-by-step explanation:

Plug in -2 to the ^x

f(x) = 3^-2

3^-2 = 0.111111111111

0.1111111111 = 1/9

Correct me if I am incorrect.

Ok here’s another question

Answers

Answer:

20 necklaces

Step-by-step explanation:

If Elizebeth is starting off w/10 necklaces we can find on the graph that $10 buys an additional 10 necklaces. Now knowing that information we can add 10 necklaces to our original necklaces and get 20 necklaces. We can also find that our unit rate of change is 10 dollars : 10 necklaces or 1 dollar : 1 necklace. Knowing this can help us solve future problems like how many necklaces can Elizebeth get for x dollars.

Part G Compare this activity tracker & with the calorie calculator you used in part A. Imagine that a company hires you to make an online tool that uses the best features of each calculator to give users an accurate sense of their physical activity and energy expenditure. What features would you use from each calculator? How would your calculator work?

Answers

Answer:

The physical activity calculator helps calculate minutes of activity and breaks down the types of activities performed every week. The calorie calculator doesn’t keep track of all activities. However, it calculates calorie expenditure. A new calculator might be a combination of the two calculators. It’d be a two-step process. People would be able to enter their age, gender, weight, height, and any medical factors so that they can ensure that their calorie calculations are accurate. Then, they’d be able to track the calories expended each day for a week by adding their activities for the whole day, from sitting to exercising. This information would give them an accurate portrayal of calorie expenditure and estimated caloric requirement.

exact answer

Step-by-step explanation:

Answer:

by seeing how the things they are doing and effecting them and then calulating them to add them up so i can see the amount of thier activity caused them to decrease or increase themselfs

Step-by-step explanation:

own explaination just incase teacher does suspect the answer

to be copied :)

Write the equation of the line graphed below in the form y = mx + b​

Answers

Answer:

y= -1/4x + 2

Step-by-step explanation:

so basicly find the slope first which is "m"

to do that do rise/run or do y2-y1/x2-x1

rise over un in this case is -1/4

slope is negative so its -1/4 = m

that find y intercept which is "b"

in this case its 2

then put it in formula

y=mx+b

y= -1/4x + 2

What is the length of side b?








Thank u

Answers

My guess is length of side B would be 12. This is my estimation, I remember a bit on how to do these but since it’s a triangle, I’m thinking the sides are going to be 1/2 of the base. In this case, the base is 24, so the sides should be 12.

Please answer this ASAP
Solve for x.
2x−4=6−3x

A: x= -0.4
B: x= 2
C: x= -2
D: x= 0.4

Answers

Answer:

x = 2

Step-by-step explanation:

First, let's write out our equation:

[tex]2x-4=6-3x[/tex]

I want to isolate x on one side, so first, I'll add 4 to both sides to remove the -4 from next to 2x:

[tex]2x-4+4=6-3x+4\\2x=-3x + 10[/tex]

Notice that I combined like terms with the -4 and 4 (to get 0) and the 6 and 4 on the right side (to get 10). Next, I'll add 3x to both sides:

[tex]2x + 3x = -3x + 3x + 10[/tex]

And then I'll add like terms:

[tex]5x=10[/tex]

Now, all we have to do is divide both sides by 5:

[tex]5x/5=10/5\\x=2[/tex]

And there's our answer. Hopefully that's helpful! :)

Domain and Range of a linear function

Answers

Answer:

domain is the lenght of the road (in miles)

range is the number of days

Step-by-step explanation:

domain is the input because there building the road that is the input because the number of days is the output (range) because that is what happens from working on the roads (the input) what come out is the days they worked on the road

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