Is the difference of a rational number and an irrational number always irrational? Explain.

Answers

Answer 1

Answer:

Step-by-step explanation:

Yes, the irrational number stays irrational.

Make the assumption that this statement is false and that a rational and an irrational can produce a rational. x is irrational. Assume that a, b, c, and d are all integers.  If you like, they can be relatively prime to each other.

a/b + x = c/d                   Subtract a/b from both sides.

x = c/d - a/b                    Now put the 2 fractions over a common denominator.

x = (c*b - d*a)/(b*d)         Investigate what you have.

b*d are two integers multiplied together. multiplication of integers is closed (the answer will be an integer).

cb and da are also integers. subtracted integers are also closed under subtraction.

But

Here's the kicker. An irrational number is one that cannot be expressed as a fraction. Sqrt(2) for example cannot be shown to be rational. There is no fraction that equals sqrt(2)

So our proof is "bogus." It cannot work. An irrational number excludes the possibility of being able to be represented by a fraction by definition.


Related Questions

Which is the value of this expression when )=-2 and k=-1?
3
jk2
0-64
Nino
O
w
o
NI -
O 64

Answers

Answer:

64

........................

PLEASE HELP ME! I am suck on this math assignment

Answers

Hey there! I'm happy to help!

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QUESTION 18

Here is how you multiply a 2×2 matrix by a column vector (just one column matrix).

[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] *\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}ax&by\\cx&dy\\\end{array}\right][/tex]

Once you get that final matrix, you add the rows which will give you a final column vector. Let's do it with this question, as we are multiplying together the matrices A and v.

[tex]\left[\begin{array}{ccc}-1&4\\2&0\\\end{array}\right] *\left[\begin{array}{ccc}8\\6\\\end{array}\right] =\left[\begin{array}{ccc}-8&24\\16&0\\\end{array}\right] =\left[\begin{array}{ccc}16\\16\\\end{array}\right][/tex]

So, your answer is [tex]\left[\begin{array}{ccc}16\\16\\\end{array}\right][/tex].

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QUESTION 14

We have this equation of an ellipse and we need to solve for y. When we have a more complex equation to solve you get rid of the things furthest from the variable you are solving for first and then you get closer and closer to it.

[tex]\frac{x^2}{25} + \frac{y^2}{16}=1[/tex]

We subtract [tex]\frac{x^2}{25}[/tex] from both sides.

[tex]\frac{y^2}{16}=1-\frac{x^2}{25}[/tex]

We multiply both sides by 16.

[tex]y^2=1-\frac{x^2}{25}*16[/tex]

We square root both sides.

[tex]y=[/tex] [tex]\sqrt{1-\frac{x^2}{25}*16[/tex]

We can take a four out of our root (because 16 is a perfect square so it can be simplified more).

y= [tex]4\sqrt{1-\frac{x^2}{25}[/tex]

And we take out 1/5 (which is the square root of 1/25).

y=± [tex]\frac{4}{5}\sqrt{1-x^2[/tex]

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QUESTION 17

We see that Sea Slugs have 3/10 matches won, so they have won 30% of their matches.

From now on, they will be winning 2/3 of their games. Let's look at the answer options.

A. If they play 15 more games, they will win 10 of them. Our total matches will be 25 (our original 10+15). So, we will have 13/25, which is equal to 52%, so this is incorrect.

B. If they play 10 more games they win 6 2/3 games (like that makes any sense) for a total of 9 2/3 games out of 20. This is about 48%, so this is incorrect.

C. If they play 40 games, they are winning fractional games again. They win 29 2/3 games out of 50 total, which is about 59%, but not quite 60. This is also incorrect.

D. If they play 45 matches, they will win 30 games. Add the original 10 and you have 40 games. Our total is 55. 40/55 is about 73%, so they have passed that 60% threshold, so this is the correct answer.

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QUESTION 16

Our question tells us that if we have two numbers x and y, and we add them, it has to be 24 or greater. By saying it can be equal to 24 or greater, we are going to be using a ≤ or ≥ sign. The opening of the arrow always faces the equal or greater quantity, and in this case it is x+y, so it will look like x+y≥24.

This eliminates answer choices B and D as they do not have the equal part on the inequality.

Product means to multiply, so it will be written as xy. It has to be less than 60, so in this case the greater quantity is 60, so the arrow will opening towards 60, so it will look like xy<60.

So, our final answer is A.

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QUESTION 12

You can only multiply matrices if the number of columns in the first matrix is equal to the number of rows in the second. So basically the two interior numbers have to be the same (a,b) and (b,c). So, if we follow this, we get these answers:

2×2 times 2×1 YES

2×1 times 2×2= NO

3×3 times 3×1= YES

3×1 times 3×3= NO

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Have a wonderful day and keep on learning! :D

1
The post office is 1= miles west of Vincent's house. The
3
2
library is 15 miles west of the post office. How far is it from
5
Vincent's house to the library? Simplify the answer if
possible.
library is 1

Answers

Use Pythagorean Theorem

1 squared + 15 squared = x squared

1 + 225 = x squared

x squared = 226

x = about 15 miles

solve for all values of x by factoring

Answers

Answer:

x = -4 and x = -6

Step-by-step explanation:

x² + 10x + 20 = -4

x² + 10x + 20 + 4 =0

x²+ 10x + 24 = 0........p = 24, s = 10 , factors = 4,6

( x² + 4x) ( + 6x + 24)= 0

x ( x + 4) + 6( x + 4)= 0

( x + 4) ( x + 6 )= 0

x + 4 = 0. or x + 6 = 0

x = -4. or x = -6

Answer:

-4, -6

Step-by-step explanation:

brainliest is appreciated

working and explaining is in the photo

The perimeter of an equilateral triangle can be represented by 6x+36. Which of the following expressions represents the length of one of the sides of the triangle?
A. 3(2x+12)
B. 2x+12
C. 6x+33
D. 3x+18

Please help quick!!

Answers

Answer:

2x + 12

Step-by-step explanation:

6x + 36 / 3 =

(6x)/3 + (36)/3 = 2x + 12

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Kira’s monthly gym bill is $50 plus $15 per class. She signs up for at least one
class each month. Write a linear function to represent Kira’s gym cost. What do the domain and range of the function represent?

Answers

Using a linear equation, it is found that:

The linear function is: [tex]C(n) = 50 + 15n[/tex]

The domain of the function is: [tex]D_C = [0,\infty)[/tex]

The range of the function is: [tex]R_C = [50,\infty)[/tex]

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The linear equation for her monthly bill, considering she goes to n classes, has the following format:

[tex]C(n) = C_f + an[/tex]

In which

[tex]C_f[/tex] is the fixed cost.a is the cost per class.

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

Monthly bill of $50 plus $15 per class means that: [tex]C_f = 50, a = 15[/tex].

Thus, the linear function is:

[tex]C(n) = 50 + 15n[/tex]

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

The domain is the input, that is, n, the number of classes she can go. It is of 0 or greater, thus: [tex]D_C = [0,\infty)[/tex].The range is the output, that is, C, the possible costs, which ranges from 50(0 classes), to infinity, and thus: [tex]R_C = [50,\infty)[/tex].

A similar problem is given at https://brainly.com/question/10891721

The time in seconds, t, it takes for a specific object being dropped from a particular height in feet above sea level, h, to reach the ground can be found by the radical function t equals one fourth times radical h period At what height should you drop an object in order for it to reach the ground in 12 seconds?

Answers

Dropping the object from a height is an illustration of an object in free fall. The object should be dropped at 2304 feet above the sea level.

Given that:

[tex]t = \frac 14 \sqrt h[/tex]

The height is calculated as follows:

[tex]t = \frac 14 \sqrt h[/tex]

Multiply both sides by 4

[tex]4t = \sqrt h[/tex]

Square both sides

[tex]16t^2 = h[/tex]

Rewrite as:

[tex]h = 16t^2[/tex]

The object reaches the ground in 12 seconds.

So: [tex]t = 12[/tex]

This gives:

[tex]h = 16 \times 12^2[/tex]

[tex]h = 2304[/tex]

Hence, the object should be dropped at 2304 feet above the sea level.

Read more about free falls at:

https://brainly.com/question/10579318

6a2 +9a3 – 16a
A. What is the name of this polynomial?
(Please help me name it)

Answers

Answer:

Step-by-step explanation:

Trinomial

what is x in 0x<3 i though you couldn't divide anything with 0

Answers

Step-by-step explanation:

0x<3

x>3/0

x>∞

x is undefined.

0-11-→
In 1905 the population was about 83,822,000 people. One hundred years later the population was about 288,368,000
people. If you are going to find the difference between the populations, would it be an estimate or exact answer?
estimate
exact

Answers

Answer:

Estimate: about 20000000 people

Exact: 288368000-83822000 = 204546000 people

12.36 divided by six

Answers

i think 2.06 ???????
12.36 divided by 6 = 2.06

The length of a rectangle is 9 inches more than the width. The perimeter is 34 inches. Find the length

Answers

Answer:

length = 13 inches

Step-by-step explanation:

let the length be x

hence, the width = x-9

perimeter = 2(x+x-9) = 34

2(2x-9) = 34

4x- 18 = 34

4x = 52

x = 13

You Want Quick Answer, Yes ? It’s 25!!!

what is value of the "2" in 32,405

Answers

Answer:

please mark me brainliest

Step-by-step explanation:

thousandth

The place Value of 2 is Thousand (1000)

Hope it helped you

50 points!!!!
1. Name a point that is coplanar are with points D, A, and B.

2. Name a point that is coplanar with points C, G, and F.

Answers

Answer:

Coplanar points are the points on the same plane.

1.

Additional points on the same plane as D, A and B are:

C and I

2.

Additional points on the same plane as C, G and F are:

B and I

Using the graph, find the equation of the line in slope-intercept form.
What is the slope-intercept form of the equation of the line?
y =

Answers

Answer:

y = 2x + 2

BRAINLIEST, PLEASE!

Step-by-step explanation:

(-2, -2) (-1, 0)

y = mx + b (m = slope, b = y-intercept)

m = rise/run = change in y / change in x

change in y: +2

change in x: + 1

change in y/change in x = 2/1 = 2

m = 2, y = 2x + b

We can plug -1 in for x, and 0 in for y.

0 = 2(-1) + b

0 = -2 + b

b = 2

y = 2x + 2

Answer:

y = 2x + 2

Step-by-step explanation:

please help fassttttt​

Answers

Answer:

Step-by-step explanation:

h = 20 + 1.7 + 50 = 71.7 m

johanna starts the month with $54 in her savings account. at the end of each week, johanna adds $8 to the account. how much will johanna have in her account after 5 weeks?

Answers

Answer:

$94

Step-by-step explanation:

To find out how much she has after 5 weeks we need to use how much she has at 1 week. We know she starts the month with $54 and adds $8 at the end of a week. Knowing this we can multiply her amount for 1 week by 5 weeks (8x5), this gets us to $40, but since she started the week with 54 we need to add that to her 5 week's total (54+40), so we get a total of $94 after 5 weeks.

The total amount in Johanna's account after 5 weeks will be $94 if Johanna starts the month with $54 in her savings account at the end of each week, Johanna adds $8 to the account.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Johanna starts the month with $54 in her savings account.

At the end of each week, Johanna adds $8 to the account.

Let x be the total amount in Johanna's account after 5 weeks.

The linear equation in one variable can be framed as:

x = 54 + 8×5

x = 54 + 40

x = $94

Thus, the total amount in Johanna's account after 5 weeks will be $94 if Johanna starts the month with $54 in her savings account at the end of each week, Johanna adds $8 to the account.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

Does amyone know the answer ??​

Answers

The only visible points in the picture are (-2,0) and (2,0). These are points to be plotted on a grid. The first number is always the x axis (horizontal) . The second number is always the y axis (vertical).

2. Discounts - You go to the store the next day and the $28.62 shirt is on sale for 15%
off, how much is the shirt before tax?

Answers

Answer:

a = 15 /100  * 28.62 = 4293 /1000

= 4.293

Hope this helps! :)

Geometry homework very confusing

Answers

Answer:

Step-by-step explanation:

Help please and thank you (Alegbra 1)

Answers

Answer:

n = 3

Step-by-step explanation:

The entire equation needs to cancel out and for q to cancel out, n needs to be 3.

Please help me on this it’s due tomorrow.

Answers

Answer:

i don't know the answer becausr i am in class 8 sorry bro

which number has a 3 that is ten times greater than the 3 in 513

Answers

Answer:

5130

Step-by-step explanation:

You just multiply 513 by 10 to get 5130.

You can check this answer by just seeing if it fits the requirements, which it does. Making it the correct answer.

sin^2a + tan^2a sin^2a = tan^2a​

Answers

the answer is in picture

When dividing 592 by 9.25, how many zeros will be placed in the dividend?When dividing 592 by 9.25, how many zeros will be placed in the dividend?

Answers

Answer:

Step-by-step explanation:

[tex]9.25=\frac{925}{100} \\592 \div9.25=592 \div \frac{925}{100} =\frac{59200}{925}[/tex]

Answer:

the answer is two B btw brainly just has bots

Step-by-step explanation:

Where is the blue dot on the number line?

Answers

Answer:

–6.8

Method:

Counting backwards from –7 to –6.5

Answer:

-6.8

Step-by-step explanation:

it is 3 units from -6.5 so you can even add them

-6.5 + 3

= -6.8

Solve the following equation
a 4 (x + 3)=16
b 3 (p - 6)+ 15 =0

Answers

Answer:

x = 1, p = 1

BRAINLIEST, PLEASE!

Step-by-step explanation:

a. 4(x + 3) = 16

4x + 12 = 16

4x = 4

x = 1

b. 3(p - 6) + 15 = 0

3p - 18 + 15 = 0

3p - 3 = 0

3p = 3

p = 1

Which equation represents a line which is perpendicular to the line 2 – 2y = 2?
Oy= 2x + 1
y=-x-5
Submit Answer
Oy= *x+8
y = -2x + 5
Pls help ASAP

Answers

Answer:

[tex]y = \frac{1}{2} x - 1[/tex]

Step-by-step explanation:

Hope it is helpful....

Use the numbers 12 through 17. Place them in the connected circles so that the numbers along each line have a sum of 50. Do this in two different ways.

Someone please help me, my brain is stuck.
(Fun question every week to answer) - Yes this is really verixsans second account -_-

Answers

Answer:

[13, 15, 17, 16, 12]

[16, 12, 17, 13, 15]

[16, 15, 14, 13, 12]

[17, 13, 15, 12, 14]

Step-by-step explanation:

Writing a Python code, I got the answers given, reading from left to right to down. For example, for [13, 15, 17, 16, 12], 13 is the top left circle, 15 is the middle right, 17 is the far right, 16 is the bottom left, and 12 is the bottom right

For her phone, Halima pays a monthly fee of 18 AED and she pays an additional 5 fils per minute of use. The least she has been charged in a month is 71.90 AED. What is the minimum number of minutes she has used on her phone in a month?

Answers

Answer:

1078 minutes

Step-by-step explanation:

18 + 0.05x = 71.90

0.05x = 71.90 - 18

0.05x = 53.9

x = 53.9/0.05

x = 1078 minutes

The minimum number of minutes is 1078 minutes.

To find the minimum number of minutes she has used on her phone in a month.

What is arithmetic?

The branch of mathematics dealing with the properties and manipulation of numbers.

Given that :

Halima pays a monthly fee of 18 AED and she pays an additional 5 files per minute of use. The least she has been charged in a month is 71.90 AED.

so, that

18 + 0.05x = 71.90

0.05x = 71.90 - 18

0.05x = 53.9

x = 53.9/0.05

x = 1078 minutes

So, the minimum number of minutes is 1078 minutes.

Learn more about arithmetic here:

https://brainly.com/question/24394764

#SPJ2

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