Let S be the statement: The product of any irrational number and any nonzero rational number is irrational. (a) Write a negation for S. (b) Prove S by contradiction.

Answers

Answer 1

Answer:

Negation: The product of any irrational number and any nonzero rational number is not irrational.

Step-by-step explanation:

(a)

Given statement: The product of any irrational number and any nonzero rational number is irrational.

Negation: The product of any irrational number and any nonzero rational number is not irrational.

(b)

Let if possible the product of any irrational number and any nonzero rational number is not irrational that is rational.

Let [tex]x[/tex] be an irrational number and [tex]y\neq 0[/tex] be a rational number.

[tex]xy=z[/tex] where [tex]z[/tex] is rational.

So,

[tex]xy=z\\x=\frac{z}{y}[/tex]

As quotient of two rational numbers is also rational, [tex]x[/tex] must be rational which is a contradiction to the fact that [tex]x[/tex] is irrational.


Related Questions

over a two hours time period, a snail moved 108 inches . how far is this in yards?​

Answers

Answer:3 yards

Step-by-step explanation:

36 inches equals a yard so 36 Multiplied by 3 is 108 Therefore 3 yards

4 x 12 = 6 x n.

4
6
8
12

Answers

Answer:

The answer is 8

Step-by-step explanation:

Because 4x12 is 48 and so is 6x8

Answer:

C. 8

Step-by-step explanation:

4 ⋅ 12 = 6n (6 ⋅ n is the same as 6n)

Multiply 4 ⋅ 12.

48 = 6n

Divide both sides by 6

n = 8

Hope I helped :)

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Is this a function or not a function? (Picture)

Answers

Answer:

Not a Function

Step-by-step explanation:

Comparing Two Linear Functions Use the graph and table to answer the questions. Which vehicle loses the most value each year? Car: 20 000 (2. 16500) 15 000 (G, 10900) Which vehicle will lose all of its value first? Value ($) 10.000 5000 6 8 If the truck's rate of depreciation changes to a decrease of $1,650 each year, which vehicle will lose all of its value first? Years Truck: Years: x Value ($) y 21,000 3 17,700 6 14.400

Answers

Answer:

Use the graph and table to answer the questions.

Which vehicle loses the most value each year?

Car

Which vehicle will lose all of its value first?

Car

If the truck’s rate of depreciation changes to a decrease of $1,650 each year, which vehicle will lose all of its value first?

Truck

Step-by-step explanation:

Answer:

car car truck

Step-by-step explanation:

4(x + 1) = 4x + 4
The equation has infinite solutions.
A value of x that makes the equation true is
which when substituted into the
equation and simplified makes the equation turn into
Another value of a that makes the equation true is
which when substituted
into the equation and simplified makes the equation turn into

Answers

Answer:

the 4 can change to any nummber

Step-by-step explanation:

Question 1
What is the 11th multiple of 15?

Answers

Answer:

165

Step-by-step explanation:

15*11=165

Can someone help me answer these please?

Answers

G and c map to -3,-1

Answer: I think that the person above me is right so you should mark her/him brainliest.

The correct Standard Form of the equation y=−2/7x−11/7:

Answers

Answer:

y=-(2)/(7)x-5

Step-by-step explanation:

cual es el valor de la expression
7×3²+3×7+6​

Answers

Answer:

90

Step-by-step explanation:

7 x (3x3) + (3x7) +6

(7 x 9) + 21+6

63 + 21 + 6

        90

2.685
x 102
Expanded form

Answers

Answer:

2.685 + 2.685 + 2.685 + 2.685 + 2.685 + 2.685. . . . . 102 times.

Step-by-step explanation:

Think of this as 102 times of 2.685.

So you would add 2.685 together 102 times.

(I didn't want to type out 2.685 that many times)

Hope I helped :)

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The sum 51 + (-37) is equal to what? -14 88 88 14

Answers

Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

the answer is 14 and it's postive

Solve for x: 4/9 x + 36 = 1/3

Answers

Answer:

x = -321/4

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

what is 2848448 X 39494948​

Answers

Answer:

1.12499306E14

Step-by-step explanation:

i did the math

please help asap 14 points​

Answers

Answer:

can i friend you

Step-by-step explanation:

the polynomial p(x) has factors of x-5 and x-8. Which must be correct ?

Answers

Answer:

Find an answer to your question The polynomial p(x) has factors of x – 5 and x + 8. Which MUST be correct?

Step-by-step explanation:

If x – a is indeed a factor of p(x), then the remainder after division by x – a will be ... the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor ... completed division: 2 2 5 0 7 ... x + 4 is a factor of 5x4 + 16x3 – 15x2 + 8x + 16.

Simplify. Help:(
-7i•(-8i)

Answers

Answer:

I got - 56, I could be wrong though

Answer:

-56

Step-by-step explanation: multiply -7i (-8i)

Multiply -8 by -7 56ii

raise i to the power of 1

56(1 ii)

Use the power rule aman  m+n to combine exponents

56i  1+1

Add 1and 1   2

56i^2

rewrite i^2 as -1

56;-1

multiply 56 by -1

-56

List 5 significant advances in architecture Eastern Indians made

Answers

Answer:

Primarily, the Indian temple architecture has been classified into three broad types, namely; Nagara or the northern style, Vesara or mixed style, and the Dravida which is the southern style. All these styles carry their unique regional influences and lineages.

Step-by-step explanation:

Which complex number is equivalent to the given expression (2+I)(8-3i)-(23+34i)

Answers

Answer: -4 - 32i                  

i just took this test

The complex number is equivalent to the given expression (2+I)(8-3i)-(23+34i) is -32i-12.

The given expression is (2+i)(8-3i)-(23+34i).

What is a complex number?

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.

Now, apply the distributive property and multiply each term of the first complex number with each term of the second complex number.

That is, (2+i)(8-3i)=8+8i-6i-3i²=8+2i+3 (∵i²=-1)

Now, 2i+11-23-34i=-32i-12

Therefore, the complex number is equivalent to the given expression (2+I)(8-3i)-(23+34i) is -32i-12.

To learn more about the complex numbers visit:

https://brainly.com/question/28007020.

#SPJ2

What is the reciprocal of 4/12?​

Answers

Answer: 12/4 or 3

Step-by-step explanation: Switch the numerator and denominator. This should leave you with the answer above.

Answer:

12/4 = 3/1 = 3

Step-by-step explanation:

To find the reciprocal of a fraction, flip it.

The reciprocal of 4/12 is 12/4 which reduces to 3.

Plz answer fast! Thank you to whoever answers❤️

Answers

sunday she ran the fastest
Answer: Sunday that’s the answer I believe

i’ll mark brainlest! pls help :(

Answers

Answer:

square root: [tex]\sqrt{61}[/tex]

decimal: 7.81

Step-by-step explanation:

Help with this one please

Answers

Answer:

(3x - 14) (2x - 7)

I hope this helps!

A square is removed from the right hand corner

Answers

Answer:

C im pretty sure

Step-by-step explanation:

Because the square taken out has a 4x4 area which is 16 and the area of the whole square used to be 14x14 which is 196 and if u subtract 16 from that you get 180

|x |-8= -5
what's the answer​

Answers

Answer:

|x |-7 = -5     ( x = -3 )

Step-by-step explanation:

3 :::::::::::::::::::

evaluate. express your answer in simplest form. 7/9 - 2/8 x 4/9
A 20/9
B 5/9
C 2/3
D 48/72

Answers

Answer:

2/3

Step-by-step explanation:

[tex] \frac{7}{9} - \frac{2}{8} \times \frac{4}{9} \\after \: simlifying \\ \frac{7}{9} - \frac{1}{9} = \frac{6}{9} = \frac{2}{3} [/tex]

Help!!!!!!! solve the inequality

Answers

Answer:

25≥ w

i dont have the inquality sign

Step-by-step explanation:

multiply both sides by 5/4

What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete
your choice.
O A. The slope of the line is
(Type an integer or a simplified fraction.)
O B. The slope of the line is undefined.

Answers

[tex]\tt Step-by-step~explanation:[/tex]

Slope = rise/run

[tex]\tt Steps:[/tex]

Rise: The line travels 5 units vertically (up) from the first point to the second.

Run: The line goes 6 units horizontally (left) from the first point to the second.

Slope = rise/run; Slope = 5/6

[tex]\Large\boxed{\tt The~slope~of~the~line~is:~\frac{5}{6}~units }[/tex]

Answer:

Slope = rise/run

Step-by-step explanation:

Will give brainliest if correct what is the discriminant of the quadratic equation: (multiple choice)

Answers

Answer:
The discriminant is 60

Please help me............

Answers

Answer:

85°

Step-by-step explanation:

180° - (67°+28°) =p

180°- 95° = p

P = 85°

Kerry takes up a delivery consignment. He delivers a few packages and one-fourth of
the packages remains in the truck. This excludes 5 packages that were returned. If
the truck contains 65 packages now, how many packages were there in Kerry's
original consignment?

Answers

Answer:

multiply 65 by 5 and divide by 1 fourth

Step-by-step explanation:

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