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

for part of a recipe jada adds 0.35 milliliters of vanilla extract to 16.4 milliliters of milk. How many milliliters does the mixture contain??

Answers

Answer: 16.75 milliliters
Step-by-step explanation:
I believe it is 16.75 because 0.35 + 16.4 is 16.75 why is it addition decimals? Because it says How many milliliters does the mixture contain. It is talking about both combined.

Zea has a credit limit of $2,000 on her credit card. Each month, she charges about $200 and makes a payment of $125. Estimate the number of months that Zea can continue this pattern until she reaches her credit limit.

Answers

Fun fact actually really really sad fact i dont know

The number of months that Zea can continue this pattern until she reaches her credit limit will be 27 months.

What is a credit card?

A credit card is a method of payment that is given to customers so they may pay a merchant for products and services depending on the debt they have accumulated.

Zea has a credit limit of $2,000 on her credit card. Each month, she charges about $200 and makes a payment of $125.

The distinction between the installment made and the charges done will be given as,

Difference = $200 - $125

Difference = $75

Partition as far as possible by this distinction to find the number of months that Zea can proceed with this example until she contacts her credit limit.

⇒ $2,000 / $75

⇒ 26.667 ≈ 27

The number of months that Zea can continue this pattern until she reaches her credit limit will be 27 months.

More about the credit card link is given below.

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Simplify each expression. Show all work from credit.
Plz help me

Answers

Answer:

1. = 1 because any numbers to the power 0 is one

2. = 1/64

3.= b^15 base same power added up

33°
114"
33
A) right scalene
B) acute scalene
C) obtuse isosceles
D) equilateral

Answers

Answer:

b acute I think so ok but that was a weird quistoin

Find the value of JK

Answers

Answer:

10t = 7t + 15

3t = 15

t = 5

JK = 50

JK = 50 because 3T = 15, so T = 5 and 10T = 50

HELP WILL MARK BARINLIEST IF RIGHT!!!

Answers

Step-by-step explanation:

Hence the value of x is 70.14cm.

what is the ratios to 25:90

Answers

Answer:

5/18

Step-by-step explanation:

25 / 90 =5*5 / 5*18 =5/18

Mean
Vasquez read 5 books in January, 8 books in February,
4books in March, and 7 books in April. What is the
average number of books Vasquez reads per month?

Answers

In order to determine the mean:

Add all of the numbers given and then divide the sum by the total amount of numbers in the equation.

5 + 8 + 4 + 7 = 24

There are 4 numbers, so:

24 / 4 = 6

The average number of books Vasquez reads per month is 6.

heyy could you help me out with this question I have been stuck in this question??​

Answers

i think the first box is perpendicular good luck

A soup kitchen cooks up a total of 200 cups of soup. If their standard serving size is 2 1/2 cups, how many servings can they hand out, at most?

Answers

Answer: They can hand out exactly 80
Explanation: 200 divided by 2 1/2 = 80

Which equation is the inverse of y =2x^2 - 8?
A. y = + √x+8/2
B. y = +√x+8/2
C. y = + √ x/2 + 8
D. y = +√x/2 +4​

Answers

Answer:

a

Step-by-step explanation:

Find the volume. Round your answer to the nearest tenth and show your work

Line segmentAB has vertices A(−3, 4) and B(1, −2). A dilation, centered at the origin, is applied to AB⎯⎯⎯⎯⎯. The image has vertices A′(−1, 43) and B′(13, −23).

A: 1/6
B: 1/3
C: 3
D: 6

Answers

Answer:

B: 1/3

Step-by-step explanation:

It seems the coordinates given are incorrect.

It should read:

A'(-1, 4/3), B'(1/3, -2/3)

This reflects the rule:

(x, y) → (1/3x, 1/3y)

Correct choice is B

Answer:

B: 1/3

Step-by-step explanation:

(x,y) = (1/3x,1/3y)

Describe the transformation of f(x) = sin x to g(x) = sin x - 17 ?

Answers

Answer:

f(x) underwent a downward vertical translation to get g(x)

Step-by-step explanation:

here, we want to describe a transformation

Looking at the two equations, we can notice that the difference between the two is the -17

Practically, we have this difference as 17 subtracted from the second equation

what this mean is that there is a downward vertical translation of the first graph by 17 units to get the second graph

In a survey, some children were asked to choose whether they like to stay up late or get up early.
35% of the students said they prefer to get up early. 28 students prefer getting up early. How many students in total were surveyed?
students

Answers

Answer:

80 Students

Step-by-step explanation:

So I set up my problem like this(This is a way to figure a certain amount of a percent or vice versa):

35            28

____ = _____

100         x

First, you do 100 x 28= 2800

Second, do 2800 divided by 35= 80

The number in students surveyed is 80.

I agree with him 80 students

Tywaun wants to know how much candy his container can hold. The
container is 20 centimetres tall, 10 centimetres long and 10 centimetres
wide. What is the container's volume?

Answers

Answer:

100 pieces maybe?

Step-by-step explanation:

please help first image pleaseeeeee............................................

Answers

I think the answer is 2 for the math , not sure mark brainliest pls

Answer:

1:2

Step-by-step explanation:

What is the solution to the system graphed below? How do you know?

Answers

Answer:

(1,7)

Step-by-step explanation:

It is where the line intersects. coordinates x axis 1, coordinates y axis 7.

473hours to days and hours​

Answers

Answer:

19 days and 17 hours

Step-by-step explanation:

4.6 isosceles and Equilateral Triangles

Answers

Step-by-step explanation:

3).20⁰

4).60⁰

180-70+70_180-140__20

PLZ HELPPPP ILL GIVE BRAINLIEST

Answers

Answer:

(A).

Step-by-step explanation:

yo my boy look at the problem first because that was so easy

Tonya drives for 5 hours at 55 mph. How far does she go?

Answers

I believe it’s 275 because you would multiply 5 by 55

Which of the following shows the extraneous solution to the logarithmic equation log7(3x^3+x)-log7(x)=2?

Answers

Answer:

x=4

Step-by-step explanation:

on edge

The extraneous solution to the logarithmic equation log₇(3x²+x)-log₇x=2 is x=16

What is logarithm?

When you raise a number with an exponent, there comes a result.

Lets say you get[tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We are given the function as;

log₇(3x²+x)-log₇x=2

Domian: 3x²+x>0

x(3x+1)>0

x∈(-∞,-1/3)U(0,∞)

Hence, x∈(0,∞), Thus x∈(0,∞)

In this problem we use the following formula:

 [tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\x=16[/tex]

Learn more about logarithm here:

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President Jackson favored state banks over the Second Bank of the United States because he
believed
A.
the Constitution called for a series of state banks.
B.
state banks should issue a uniform national currency.
C.
the Bank could not control the nation's loans.
D.
the Bank had too much power over the nation's economy.

Answers

I believe it’s D! Good luck!

Simply (2x^5)^2(4x^3)

Answers

The answer is 16x^13

Cecilia is saving money to buy a bicycle. She started with $75 and saves $10 each week from her allowance. Which equation represents how much money, y, Cecilia has at the end of x weeks? O A. y = 75x + 10 o B. y = 10x + 75 O C. x = 75y + 10 O D. X = 10y + 75​

Answers

Answer:

y = 10x + 75 If not then

X = 10y + 75

250 is 1.5cm. How thick is 400 pages

Answers

Answer: 2.4 cm

Step-by-step explanation:

1.5 divided by 250 gives that each page is .006cm. 400 times .006 is 2.4cm

Okay, I and my mom do not know how to do this- please help-
Distribution Skill
3 (-5y²- 3)

Help p-p

Answers

3(-5y^2-3)
=-15y^2-9

Answer:

Step-by-step explanation:

this is the start of your mad algebra skilz.. it does take constant practice, like anything you want to get better at :)  keep trying

this is called  "Distribution" and is used often

3(-5[tex]y^{2}[/tex] -3)

-15[tex]y^{2}[/tex] +9

if you need more explanation just put your questions at the comments of this problem ... i'll see them   :)

Anyone else having to do school work during spring break because edgenuty sucks?

Answers

no I’m not on spring break hahaha

2. In Ella's math class, there are 12 girls and 15 boys. Which of the following is the ratio of boys to girls in Ella's math class?
A 12/27
B 12/15
C15/12
D27/12​

Answers

Answer:

C. 15/12

Step-by-step explanation:

15 boys and 12 girls

Answer:

b

Step-by-step explanation:

12/15

What is the straight-line distance between (-2, -7) and (-4, -9) on a coordinate graph?

Answers

Answer:

yeah, the selected is correct

Step-by-step explanation:

distance is...

2 and 2 square root

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