1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lilavasa [31]
3 years ago
5

Prove that if x and y are rational then their product is also rational. First write a proof on your own and then put the followi

ng statements into order to obtain the proof. Put N next to the statements that should not be used in the proof. 1. Then, xy=acbd . 2. Suppose x and y are arbitrary rational numbers. 3. Since a, c are integers, e=ac is also an integer.
Mathematics
1 answer:
Ymorist [56]3 years ago
7 0

Answer:

Step-by-step explanation:

The aim of this question is to prove that the product of two rationals is rational.

<u>To proof:</u>

If \mathbf{x  \ and  \ y} are arbitrary rational numbers.

Thus, going by the definition of rational, there exist integers

a, b, ≠ 0, c, and d ≠ 0 ; x = \dfrac{a}{b} \ and \ y = \dfrac{c}{d}

Hence, xy = (\dfrac{a}{b})(\dfrac{c}{d}) = \dfrac{ac}{bd}

Since a and c are integers, then e = ac appears to be an integer as well.

Also, provided that b and d are non-zero integers;

f =bd appears to be a non-zero integer.

Therefore, xy = \dfrac{e}{f}, and going by the definition of rational, xy is rational.

Hence, from the complete question:

The order of the statement is:

7,6,3,5,2,4

The statements that should not be used in the proof are:

1 N

8 N

9 N

10 N

11 N

You might be interested in
Find the zeros of the function.<br> f(x) = 2x2 – 2x – 12
Amiraneli [1.4K]

Answer:

Step-by-step explanation:

2x^2-2x-12

This has solutions of x=3 and x= -2

3 0
3 years ago
Read 2 more answers
HELP ME PLEASE! I need to find the Interquartile range of : 0,0,0,1,1,3,3,3,4,4,4,6,6,7,7,7,8,8,9,10
Lana71 [14]

Answer:

The interquartile range is 5

4 0
2 years ago
Jake was in a bicycle race. his average speed was 22 miles per hour. at this rate, how many feet per hour did jake travel?
Harlamova29_29 [7]
<span>Since there are 5280 feet per mile:
22 miles/hr * 5280 feet/mile
= 116160 feet per hour
</span>
8 0
3 years ago
What is 5% of $30?<br>$150<br>$35<br>$1.50<br>$25​
fomenos

Answer:

$1.50

Step-by-step explanation:

5% of 30 is 1.5 AKA 1.50

All you have to do is remove then add the dollar sign again!

Hope this helps! :)

6 0
3 years ago
Read 2 more answers
please help i am failing math class she said if you dont turn in this Backpack artifact task am going to fail it is 6th grade ma
agasfer [191]

Answer:

I might be able to help as long as there's no algebra involved

6 0
3 years ago
Read 2 more answers
Other questions:
  • 63 decreased by twice Vidya's height
    12·1 answer
  • Help me please Idk what to do
    15·1 answer
  • Pls answer this with an explanation if you can
    5·2 answers
  • What is 149.6 billion in scientific notation?
    5·1 answer
  • What is -2(5) ? I need it really quick pls !
    13·2 answers
  • What is the product of 14,560 times 10 and explain the number of zeros
    6·2 answers
  • In wxy x=y, wx= 9x-11, xy= 4x-1, and wy= 7x-3, find x and the measure of each side
    11·1 answer
  • Fully simplify the fraction in the photo. <br> No links.
    5·1 answer
  • What is the value of x
    15·2 answers
  • Triangles A B C and D E F are shown on the coordinate grid with congruent corresponding parts.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!