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

Mangoes cost $4 each and nectarines cost $2 each. Dominic buys m mangoes and n nectarines for $32.
Fill in the missing values to write an equation for the information given.

Answers

Answer: 6m+4n=32

Step-by-step explanation:

m=4

n=2

From this, we can deduce that m+n=32.

6*4=24 and 4*2=8. 24+8=32

So, 6m+4n=32. Hope this was what you were looking for!

How many decimal places does
0.005011
have please? :)

Answers

Answer:

6

Step-by-step explanation:

6 decimal places

0.005011 has six decimal places.

What is a decimal place?

'The place value of a decimal number is recognized according to the position of the dot or decimal point. The first digit to the right of the decimal point indicates the number of tenths and the second digit to the right indicates the number of hundreths.'

According to the given problem,

For the number 0.005011, after the decimal there are numbers up to the sixth place which is that there are six numbers.

For counting decimal places, we need to count the number of digits present to the right of decimal point.

Hence, we can conclude that 0.005011 has 6 decimal places.

Learn more about decimal places here:

https://brainly.com/question/26568840

#SPJ2

10.
What is the volume of the rectangular prism?
3.in.
4 in.
52 in.

Answers

Answer

(3.5 times 5.25) times 4

Step-by-step explanation:

then convert the decimal to a fraction.

A rock climber is descending down a 500-foot tall cliff. After 8 minutes, the rock climber
has descended to a height of 280 feet. Find the height as a linear function of time

Answers

We have that The height as a linear function of time is

[tex]x=-27.5T+500[/tex]

From the Question we are told that

Time t=8 minutes

Height h=500

Descended height h_d= 280 feet.

Generally the equation for the linear function  is mathematically given as

Let

Height as a linear function =x

[tex]x=\frac{h_d-h}{t}*T+h[/tex]

[tex]x=\frac{280-500}{8}*T+500[/tex]

[tex]x=-27.5T+500[/tex]

In conclusion

The height as a linear function of time is

[tex]x=-27.5T+500[/tex]

For more information on this visit

https://brainly.com/question/12304809

pls answer my question ​

Answers

Answer:

a=1,2,4,5,6,7

b=1,7

c=2,5

d=4,6

HCF of 32,48,64 is 16

Which expression has a value of 48?


A . (16−8)×(2+4)

B . 16−(8×2+4)

C . 16−8×(2+4)

D . (16−8)×2+4

Answers

Step-by-step explanation:

(16-8)x(2+4)

= 8x(6)

= 8x6

= 48

Write a proof. Given x - 2 = 3(x - 4) Prove x = 5

Answers

x=5

Step-by-step explanation:

x-2=3(x-4)

x-2=3x-12

12-2=3x-x

10=2x

x=10/2

x=5

Answer:

x = 5

Step-by-step explanation:

x - 2 = 3(x - 4)

x - 2 = 3x - 12

-2x - 2 = -12

-2x = -10

x = 5

Which expression has the same value as 2 + (-3)?
23
O 2 - (3)
Submit Answer
0-2+(-3)
-3 - 2
o

Answers

Answer:

2-3 is same as 2+(-3)

.

.

.

Hope it helps

2+(-3) is actually mean 2-3 bcz if you see plus and minus together it bcomes negative. I hope you understand this<3

10. The translation (x, y) = (x + 10, y-6) is applied to ABC to create a new image A'B'C'. Graph
A'B'C' on the coordinate plane.

Answers

Answer:

here you go mate.

These are the solutions

contesteneme doy coronita y 25 puntos tambien 5 estrellas​

Answers

Answer:

4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80

1. Emma Lee needs a new road bike. The sale price is 10% lower than the original price. The sale price is $450. Write and evaluate an expression for the original price. Uses for sale price and p for original price.​

Answers

SP=450Discount=10%CP=?

100-10=90%=SP

[tex]\\ \sf\longmapsto 90\%\times x=450[/tex]

[tex]\\ \sf\longmapsto \dfrac{90}{100}x=450[/tex]

[tex]\\ \sf\longmapsto x=450\times \dfrac{100}{90}[/tex]

[tex]\\ \sf\longmapsto x=5(100)[/tex]

[tex]\\ \sf\longmapsto CP=500[/tex]

) A club on campus is selling Entertainment coupon books for $30 each. It costs the team $10 to
buy each book. The club has 500 books. The team's profit P(n) is given by the following
function where n represents the number of books sold.
p(n) = 30n - 5000
a. What does the 30n represent?
b. What does the 5000 represent?
c. How much profit would they make if they sold 400 books?

Answers

Answer: hola

Step-by-step explanationno

Which of the following sets could be the sides of a right triangle?

{2, 3, √10 }
{3, 5,√34 }
{5, 8, 12}

Answers

I believe that it’s the last one because it makes the most sence but then again i could be wrong

Find (h•g)(x)
h(x)= 3x-3 and g(x)=x^2+3

Answers:
A: 3x^3 - 3x^2 + 9x

B: 3x^3 - 3x^2 + 9x - 9

C: 3x^3 + 3x^2 + 9x - 9

D: 3x^3 - 9

Answers

Answer:

the answer is b!!!!!!!!!!!!

(3x-3)(x²+3)

=x²(3x-3)+3(3x-3)

=3x³-3x²+9x-9

A rectangle has an area of 21 square centimeters. Which of the following could be the rectangle's length and width? Area = length x width Choose all answers that apply

Answers

Width=1cm and length=21cm or width=3cm and length=7cm.

The line graph shows the cost of inflation in some country. What cost $10,000 in 1975 would cost the amount shown by the graph in subsequent years. Below are two mathematical models for the
lata shown in the graph. In each formula, C represents the cost x years after 1980 of what cost $10,000 in 1975.
Model 1 C = 840x +15,538
Model 2 C= -222 +900x + 14,204

Answers

Answer:

não sei nam mano foi mal ai

vei kskksksksk

Step-by-step explanation:

if (x+30°) and (180°-2x) are vertically opposite angles . Find the value of x .​

Answers

Answer:

50

Step-by-step explanation:

x + 30 = 180 - 2x   [vertically opposite angles]

x = 180 - 30 - 2x

x = 150 - 2x

x + 2x = 150

3x = 150

x = 150/3

x = 50

In which quadrant would the point
(9.-10) be located?
a) Quadrant 1
b) Quadrant 2
c) Quadrant 3
d) Quadrant 4

Answers

Answer:

D

Step-by-step explanation:

Start with the 9. It goes to your right. It is on the plus x axis.

You are either in quad 1 or quad 4

We need the - 10 to decide which.

+ 10 would go up and that would mean quad 1

- 10 mean going down so you are in Quad 4


What is the answer ?

Answers

Answer:

70 seconds

Step-by-step explanation:

first we'll divide seconds by shirts 28/2 to find out how long it takes to do one shirt. it takes Jonah 14 seconds to do 1 shirt so we can then multiply that by 5 shirts to get 70 seconds

help please I need help
[tex]40x = 60x(x - 1) \\ \\ 7 \times \frac{7x}{2} - 29x = - 9 [/tex]

Answers

Answer:

[tex]40x = 60(x - 1) \\ \\ 2x = 3x - 3 \\ \\ x = 3 \\ \\ \\ 7 \times \frac{7x}{2} - 29x = - 9 \\ \\ 49x - 58x = - 18 \\ \\ - 9x = - 18 \\ \\ x = 2[/tex]

Answer:

#140x = 60x(x - 1)40x = 60x² - 60x60x² - 100x = 03x² - 5x = 0x(3x - 5) = 0x = 0 or3x = 5 ⇒ x = 5/3#27×7x/2 - 29x = - 949x/2 - 29x = - 949x - 58x  = - 18-9x = -18x = -18/-9x = 2

dentify the error in finding the distance between A(6,2) and B(1,−4).

Answers

The answer I think is A

Find the mode, median, and mean of each data set ( ASAP pls can someone help me )

Answers

Answer:

mean = 10.818181...

median = 10

mode = 5

Step-by-step explanation:

first put the numbers in order, smallest to largest

5 5 6 8 9 10 11 13 15 18 19

mean = 5+5+6+8+9+10+11+13+15+18+19 = 119 119÷11= 10.818181818... (round it)

median = 10

mode = 5

divide rs. 560/-among A,B and C in such a way that A and B are in 2:3 while B and C are in 4:5
plz help me with this answer

Answers

Answer:

128 : 192 : 240

Step-by-step explanation:

Given that

A : B = 2 : 3

That is B = 1.5A

Then in fractional form

[tex]\frac{B}{C}[/tex] = [tex]\frac{4}{5}[/tex] , so

[tex]\frac{1.5A}{C}[/tex] = [tex]\frac{4}{5}[/tex] ( cross- multiply )

4C = 7.5A ( divide both sides by 4 )

C = 1.875A = 1.875 × 2 = 3.75

The ratios of A : B : C = 2 : 3 : 3.75

Sum the parts of the ratio , 2 + 3 + 3.75 = 8.75

Divide the quantity by 8.75 to find the value of one part of the ratio

560 ÷ 8.75 = 64 , then

2 parts = 2 × 64 = 128

3 parts = 3 × 64 = 192

3.75 parts = 3.75 × 64 = 240

Then A : B : C = 128 : 192 : 240

Order from least to greatest
3.5,-2.1,√9,-7/2,√5

Answers

Answer:

-7/2,-2.1,✓5,✓9,3.5

Step-by-step explanation:

✓5=2.23

✓9=3

-7/2=-3.5

Robert wants to buy a digital piano at a yard sale. He makes a scale drawing of his living room. He uses a scale of 1cm in the drawing to 6 inches in the actual room. The width of the digital piano is 54 inches will it fit along the wal. Next to the bookshelf ?

Answers

Answer:

It’s 48 just do 8*6=48 I don’t know how I got that answer but Ik it’s right lol

Find the perimeter, in units, of the polygon with the given vertices. Plot the points.
Round to the nearest tenth.
5. A(8,0), B(-3, 2), C(10, 2)
6. A(4, -3), B(7, 10), C(-8, 2)
7. A(-5,5), B(5, -5), C(-5, -5)
8. A(4, -3), B(7,10), C(-8, 2), D(-1, -5)
9. A(-4, -8), B(4, -8), C(4, 0), D(0, 3), E(-4, 0)

Answers

Answer: 9

Step-by-step explanation:

Plot the points

Find the distance of each side

add the three numbers

9

Answer:

5. 27

6. 43

7. 47

Step-by-step explanation:

PLS HELP ASAP GIVE ANSWER RQ
Add 5 to x, double what you have, then subtract 3 from the result and simplify the expression.
a.2x + 10
b.2x + 7
c.x + 7
d.2x – 7

Answers

ANSWER:
b. 2x+7

work shown

Find the coordinates of the image of M (−3, −4) after the translation (x, y) → (x + 4, y).

A. (−3, 0)
B. (−1, −4)
C. (1, −8)
D. (1, −4)

Answers

Answer:

d

Step-by-step explanation:

its d

cause x becomes x+4 to get 1
and y remains y.

Show that the statement is true. If JK has endpoints J(−2, 1) and K(4, 3), and LN has endpoints L(0, 3) and N(2, 1) then JK and LN have the same midpoint.

Answers

Answer:

yes they both have the same midpoint of (1,2)

Step-by-step explanation:

For the midpoint of JK

[tex](\frac{-2+4}{2}, \frac{1+3}{2} )[/tex]

[tex](\frac{2}{2}, \frac{4}{2} )[/tex]

(1,2)

then for LN

[tex](\frac{0+2}{2}, \frac{3+1}{2} )[/tex]

[tex](\frac{2}{2}, \frac{4}{2} )[/tex]

(1,2)

Point C is on line segment BD
. Given BD=5x,BC=4x, and CD=4, determine the numerical length of BD.

Answers

Answer:

BD measures 20 units.

Step-by-step explanation:

We are given that Point C is on the line segment BD, where:

[tex]BD = 5x, BC = 4x \text{ and } CD = 4[/tex]

And we want to determine the numerical length of BD.

Since C is somewhere on BD, BD is the sum of BC and CD:

[tex]\displaystyle BD = BC + CD[/tex]

Substitute:

[tex](5x) = (4x) + (4)[/tex]

Solve for x. Subtract:

[tex]x = 4[/tex]

Hence, the value of x is 4.

BD is given by 5x. Therefore:

[tex]BD = 5(4) = 20\text{ units}[/tex]

In conclusion, BD measures 20 units.

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