Explain why the product of a non-0 rational number and an irrational number is irrational?

Answers

Answer 1

Answer:

An irrational number is a number that can not be written as the quotient of two integer numbers.

Then if we have:

A = a rational number

B = a irrational number.

Then we can write:

A = x/y

Then the product of A and B can be written as:

A*B = (x/y)*B

Now, let's assume that this product is a rational number, then the product can be written as the quotient between two integer numbers.

(x/y)*B = (m/n)

If we isolate B, we get:

B = (m/n)*(y/x)

We can rewrite this as:

B = (m*y)/(n*x)

Where m, n, y, and x are integer numbers, then:

m*y is an integer

n*x is an integer.

Then B can be written as the quotient of two integer numbers, but this contradicts the initial hypothesis where we assumed that B was an irrational number.

Then the product of an irrational number and a rational number different than zero is always an irrational number.

We need to add the fact that the rational number is different than zero because if:

B is an irrational number

And we multiply it by zero, we get:

B*0 = 0

Then the product of an irrational number and zero is zero, which is a rational number.


Related Questions

Find a, b and c giving reasons for each answer.
2)
3)
1)
55
b
С
b
b
110°
с
a
a
С
120°
5)
6)
25 °
4)
115
a
10°
ab

Answers

Answer/Step-by-step explanation:

1.

✔️a = 180 - 110 (consecutive angles are supplementary)

a = 70°

✔️b = a (corresponding angles are congruent)

b = 70°

✔️c = 110° (alternate interior angles are congruent)

2.

✔️a = 180 - 120 (linear pair)

a = 60°

✔️b = a (corresponding angles are congruent)

b = 60°

✔️c = a (alternate interior angles are congruent)

c = 60°

3.

✔️a = 55° (corresponding angles are congruent)

✔️b = 55° (Vertical angles are congruent)

✔️c = 180 - 55 = 125° (linear pair)

4.

✔️a = 115° (corresponding angles are congruent)

✔️b = 180 - a (linear pair)

b = 180 - 115

b = 65°

✔️c = b (vertical angles are congruent)

c = 65°

5.

✔️a = 180 - 25 = 155° (supplementary angles)

✔️b = 25° (corresponding angles)

✔️c = 25° (vertical angles)

6.

✔️a = 180 - 10 = 170° (linear pair)

✔️b = a (corresponding angles are congruent)

b = 170°

✔️c = 10° (corresponding angles are congruent)


What must be true about the coordinates of any point that lies in the third quadrant?

Answers

Answer:

(-, -)

Step-by-step explanation:

The x value is negative and the y value is also negative

help please! ill mark you brainliest!

Answers

Answer:

80 degrees

Step-by-step explanation:

angle c=50

this is an isoceles triangle in which both base angles are same

so, angle e=50

now we will use angle sum.property which states that the sum of all the interior angles of a triangle is equal to 180

so, 50+50+angle d=180

100 + angle d = 180

angle d =180-100

angle d = 80 degrees

I don't know to much about this can you help me on it.

Answers

I think that DE is the answer (Intermediate = largest/longest?)

Length corresponds with the magnitude of the angle

I need help please fast

Answers

Step-by-step explanation:

[tex]6p \geqslant - 42 \\ p \geqslant - 7[/tex]

find x, then find each angle

Answers

Answer:

x=8

Step-by-step explanation:

23x=184

x=8

-0.2(x-20)=44-x Please i really need help. and please add an explanation if u want to.

Answers

Answer: x = 50

Step-by-step explanation:

-0.2(x - 20) = 44 - x

-0.2x + 4 = 44 - x (distribute the -0.2)

  + x                + x

-----------------------------------------------------

0.8x + 4 = 44

        - 4    - 4

-------------------------------------------------------

0.8x = 40 (divide by 0.8)

x = 50

Calculate the value of y to the nearest hundredth.

Answers

Answer:

y ≈ 9.24

Step-by-step explanation:

Using the cosine ratio in the right triangle.

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{8}{y}[/tex] ( multiply both sides by y )

y × cos30° = 8 ( divide both sides by cos30° )

y = [tex]\frac{8}{cos30}[/tex] ≈ 9.24 ( to the nearest hundredth )

Help me I don’t know how to do this

Answers

Answer:

hmm

Step-by-step explanation:

Standard Form of a linear equation. Match the phrase with the equivalent term
Ax + By = C

equation
line
point
x-intercept
y-intercept

Which one is correct I’ll mark Brainlest

Answers

Answer:

pretty sure its equation, if its wrong im sorry!

Each side of a regular hexagon has a length of 2 ft 3 in. Find the perimeter of the regular hexagon

Answers

Answer:

gdghdhsxjsjsj

Step-by-step explanation:

jcjcjcjcjjcjcjcjcjc

Answer:

t is a regular hexagon of side 2′. So it can be divided into 6 triangles equal in all respects.The sum of all interior angle of hexagon =(n-2)*180 = (6–2)180 =720 deg. each interior angle =720/6 =120 deg.Side of the triangle divides this angle into two equal halves each = 60 deg.when two base angles of each triangle are 60 and 60 third angle will also become 60 making it as equilateral triangle. N ow the area of hexagon =6*the area of each equilateral triangle of base 2 ft.=6*1/2*2*h. h is the altitude of the triangle=2/2*tan 60 = rt3 =1.732 .NOW area of hexagon =6*1.732 = 10.392 sq.ft

Mark got 487 questions wrong out of 9374 questions. What is his grade?

Answers

Answer:

5%

Step-by-step explanation:

487/9374=0.05

0.05 would translate to 5%

Hope this helps! :)

Answer:

F (5%)

Step-by-step explanation:

To find the percentage of questions he got correct:

487/9374=0.051....

So, assuming an F is less than 50%, he got an F.

ok whoever helps me is da best so plz :) 50 points

Answers

Answer:

A(-2/3)

B(-1/6)

C(1/2)

D(4/3)

Step-by-step explanation:

There are 6 tics in each section.

That means each tic is 1/6

A(-4/6) -> (-2/3)

B(-1/6)

C(3/6) -> (1/2)

D(8/6) -> (4/3)

PLEASE HELP ME I NEED HELP RIGHT AWAY AND YOU MUST EXPLAIN!!!

A box contains fiction and nonfiction books. There are 22 fiction books in the box, which is 55% of the total number of books in the box. What is the total number of books in the box?

thank you for helping

Answers

Answer:

So it's either 12.1

Step-by-step explanation:

So you must multiply them to get the answer cause it tells how much fiction books are in there, and It 55% of the total so to find the total you must multiply them.  

But if you have a percent you have to make that into a decimal. So 55% will be 55/100 so that's .55, so all you have to do now is multiply them.

Answer: 40 books

Step-by-step explanation:

First divide 22/55 then multiply the product by 100.

22/55= 0.4

0.4*100=40

Hope this helps u Emilee :)

what is 5^(−3)×2^(−1)​

Answers

The answer to this question is 0.004

Isaac is painting a 1.5-foot by 2-foot by 4-foot storage box with weather-resistant paint. Since the box is to be used on the patio, all of the exterior sides, including the
top and bottom, must be painted. What is the total surface area that Isaac will paint?

Answers

Answer:

34

Step-by-step explanation:

Please help. my grade in math is terrible all i want is help please.
Charmaine buys candy that costs $5 per pound. She will spend less than $45 on candy. What are the possible numbers of pounds she will buy?
Use P for the number of pounds Charmaine will buy.
Write your answer as an inequality solved for P.

Answers

Answer:

8 pounds

Step-by-step explanation:

x = number of pounds

5x<40

x<40/5

so she can buy X<8 pounds

PLEASEEEE HELP !!!!!!!!!!!!!!!!! Abanoub is using a machine to drill for oil that is 535 feet under the ground. The drill he is using is drilling at a rate of -35 feet per hour. How long did it take him to reach the oil? a 15.28 Hours b - 15.28 Hours c 18,725 Hours d -18,725 Hours

Answers

Answer:

a) 15.28 hours

Step-by-step explanation:

535/-35

≈-15.28

but time is always positive so it would take him 15.28 hours

Please help and please don't answer just for the points I'll report you

Answers

Answer:

Length of sandbox (3w + 1) = 9.1 m

Width of sandbox = 2.7 m

Step-by-step explanation:

[tex]w(3w + 1) = {5}^{2} \\ \\ 3 {w}^{2} + w = 25 \\ \\ 3 {w}^{2} + w - 25 = 0 \\ \\ equating \: it \: with \\ \\ a {x}^{2} + bx + c = 0 \\ \\ a = 3 \\ b = 1 \\ c = - 25 \\ \\ {b}^{2} - 4ac \\ = {1}^{2} - 4 \times 3( - 25) \\ \\ = 1 + 300 \\ \\ = 301 \\ \\ w = \frac{ - 1 \pm \sqrt{301} }{2 \times 3} \\ \\ w = \frac{ - 1 \pm 17.3493516 }{6} \\ \\ w = \frac{ - 1 \pm 17.3493516 }{6} \\ \\ considering \: only \: + ve \: sign \\ \\ w = \frac{ - 1 + 17.3493516 }{6} \\ \\ w = \frac{16.3493516 }{6} \\ \\ w = 2.72489193 \\ \\ w = 2.7 \: m[/tex]

3w + 1 = 3*2.7 + 1 = 8.1 + 1 = 9.1 m

please help me on this cause I'm confused ​

Answers

Answer:

h = 2.7 m

Step-by-step explanation:

The larger triangle and the smaller triangle are similar so ratios of corresponding sides are equal, that is

[tex]\frac{6}{6+12}[/tex] = [tex]\frac{0.9}{h}[/tex] , that is

[tex]\frac{6}{18}[/tex] = [tex]\frac{0.9}{h}[/tex] ( cross- multiply )

6h = 16.2 ( divide both sides by 6 )

h = 2.7 m

what does x represent in the equation 3x+1=10​

Answers

Answer:

3

Step-by-step explanation:

3x+1=10 subtract 1 to both sides

3x+1-1=10-1

3x=9 divide both sides by three

3x/3=9/3

x=3

HELP ME PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

Answers

Answer: I already answered this question already

Step-by-step explanation:

independent- x or hours

dependent- y or money earned

y=8x

Are linear inequality graphs different from linear equations graphs

Answers

Answer:

The only difference between the two equations is that, a linear equation gives a line graph whereas a linear inequality shows the area of the coordinate plane that satisfies the inequality. A linear inequality graph usually uses a borderline to divide the coordinate plane into two regions.

Step-by-step explanation:

Your profile picture lol

Answer:

Trust me his/her answer are correct.....

Pllssss hellpppppppppp plssss

Answers

Answer:

Step-by-step explanation:

WE KNOW THAT THE SUM OF THE ANGLES IN A TRIANGLE=180

9g+2g+7g=180

18g=180

g=180/18

g=10

The answer is 10 tell me if I am wrong

Solve by graphing

|1x - 1| = |2x - 5|

Answers

Answer:

x=4 or x=2

Step-by-step explanation:

What is the slope of a line that goes through the points (10, -2) and (5,-5)? m =
Y1-Y2
11-12

Answers

Answer:

m = 3/5

Step-by-step explanation:

use the formula so m = -5 - -2 / 5 - 10 , so m = -5+2 / -5

m = -3/-5 so m = 3/5

Evaluate the expression when c=6 and d=5.
d+ 8c

Answers

Answer:

53

Step-by-step explanation:

when c=6 and d=5 we want to substitute the variables with the numbers in the equation so we'll have

(5) + 8(6)

after evaluating we come up with the answer 53

Ashely found 2 boxes of sugar in the kitchen. The green boxe is 1.26 kg and the red box is 1.026 kg. Which box contains more sugar?

Answers

Answer:

The green box by 0.234kg of sugar

Step-by-step explanation:

Given data

The green box weight= 1.26 kg

The red box weight=  1.026 kg

comparing the two values

the green box contains 0.234kg more sugar

=1.26-1.026

=0.234kg

Help ASAP! Thanks
Find the lateral area of this cone.
Leave your answer in terms of pi
15cm
8cm

Answers

Answer: i think its 17

Step-by-step explanation:

Draw a vertical y-axis on the left-hand side of your graph and label it. Then draw a horizontal x-axis at the bottom of your graph. Then label the coordinates of each corner of the sign on your graph. Draw line a on your graph. What is the slope of line a?

Answers

Answer: 20

Step-by-step explanation:

Other Questions
A tree is an example of an object that contains chemical energyTrue or false please help Which of the following occurs when a small group of individuals leaves a populationand establishes a new one in a geographically isolated region?A. Genetic drift B. Natural selection C. Non-random mating D. Gene flow Can someone please tell me if this is right or what the right answer is pleaseeeeee why aren't scientific theories just called facts? find the gcf 27y^3z and 45x^2y The cerebellum is part of the____? Help! I will mark brainliest Which statement about Niels Bohr's atomic model is true?O Higher orbits have lower energies.Each orbit has a specific energy level.Electrons can exist in any energy level.O Orbits close to the nucleus have no energy.Hurry. In the context of this text, why do people succeed? What qualities help a person succeed? Cite evidence from the text and consider your own experiences in your answer.i have no idea what to say help i only have 20 mins left Education Persuasion AssignmentPretend that you are a Roman teenager. What is something that you'd like to ask your parents for, but you think they'll need some convincing to say yes? Perhaps you want to have a friend spend the night on Friday or you'd like to go to the Forum for the first time. Let's practice your rhetorical skills. In a letter to your parents, outline the pros and cons of letting you have your way, and be sure to conclude with why they should be persuaded to support your choice. 2. How would you find therate of change in a table.You would divide whatOver-what?... I REALLY NEED HELP !!Write an essay to explain factors that influence teenage decision making. Use the information from the passage in your essay Which of the following is a true statement about the population of the United States between 2000 and 2010? The population of the state of North Dakota decreased by 25 percent. The population of the state of North Dakota decreased by 515 percent. The population of the state of North Dakota increased by 05 percent. The population of the state of North Dakota increased by more than 25 percent. A chemist needs to know the mass of a sample of to significant digits. He puts the sample on a digital scale. This is what the scale shows: 0 0 0 7 6 . 3 gIf this measurement is precise enough for the chemist, round it to significant digits.Otherwise, press the "No solution" button. what is the area of circle whose diameter is 32 inches? use =3.14 What is the extremely hot layer that is made almost entirely of solid iron?outer coremantlecrustinner core help quickly please! i'll mark brainliest Rules are formally expressed asO a code of conduct.consequences.O a code of ethics.O a conflict of interest. Which structures are included in the peripheral nervous system? A group of students is setting up a test to see whether earthworms, like those shown in the photo, prefer rough or smooth surfaces