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

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

Solve by graphing

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

Answers

Answer:

x=4 or x=2

Step-by-step explanation:

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:

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

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 )

I need help please fast

Answers

Step-by-step explanation:

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

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

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

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.....

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

find x, then find each angle

Answers

Answer:

x=8

Step-by-step explanation:

23x=184

x=8

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:

-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

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

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

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.

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

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)

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!

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:

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

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 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 me I don’t know how to do this

Answers

Answer:

hmm

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

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)

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

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

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