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
dezoksy [38]
3 years ago
14

Daniel says that when the irrational number 7√3 is multiplied by any rational number, the product is always an irrational number

. What value for the rational number disproves Daniel's claim?
Mathematics
1 answer:
jeka943 years ago
7 0

Answer: 0

============================================

Explanation:

When we multiply 0 by any number, we get 0 as a result

x*0 = 0

0*x = 0

for any number x.

The number 0 is rational since we can write it as a fraction of two integers

0 = 0/1

If Daniel were to correct his statement to say "multiply by any <u>nonzero</u> rational number", then his statement would be correct that the result is irrational.

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

Extra info:

Here's a proof showing why Daniel's claim is correct if we consider nonzero rational numbers

Let p be a nonzero rational number, so p = a/b for integers a,b where neither a or b are zero

Let q be an irrational number. We cannot write q as a ratio of two integers

The claim is that p*q is irrational. For now let's assume the opposite. So assume p*q is rational. This means p*q = r/s for integers r,s

This would be the same as (a/b)*q = r/s which solves to q = (r/s)*(b/a) = (rb)/(sa) making q rational, but that contradicts the fact we made q irrational earlier.

Therefore, the assumption p*q is rational cannot be the case, and p*q must be irrational.

You might be interested in
WILL MARK YOU BRAINLIEST
Anna007 [38]

rhoumbus that is what I use and got right!!

Step-by-step explanation:

5 0
3 years ago
I NEED THE ANSWER FAST PLZ!!<br> What is the slope of this line?
Elina [12.6K]

Answer:

the slope of this line is 0

hope it helps

Step-by-step explanation:

Is the horizontal line edging upward; that is, is it an increasing line? No, so its slope can't be positive. Is the horizontal line edging downward; that is, is it a decreasing line? No, so its slope can't be negative. What number is neither positive nor negative?

5 0
3 years ago
Find the output, b, when the input, a, is 6.<br> b = -1-7a<br> b=
natka813 [3]
The answer is -43
B=-1-7(6)
B=-1-42
B=-43
7 0
3 years ago
Help please !!!
dybincka [34]
The equation for this line would be y=2x-4
4 0
3 years ago
Which expression is equivalent to -3 (2m - 1) - n?
Semenov [28]

Answer:

−6−m+3

Explanation

-3 (2m - 1) - n?

Distribute

−3(2−1)−

−6+3−

Rearange

−6+3−

−6−m+3

7 0
3 years ago
Other questions:
  • What is the slope of a line with these coordinate points&gt;<br><br> (-5,-4) (5,1)
    6·2 answers
  • Birr 6500 were divided equally among a certain number of persons.Had there been 15 more persons,each would have got Birr 30 less
    12·1 answer
  • What is the unit rate for 692.08 ft in 21.1 s? Round to the nearest tenth if necessary. Enter your answer in the box.
    7·2 answers
  • Choose the correct simplification of the expression (6x2y)2(y2)3.
    5·2 answers
  • What is -34 + (-47)?
    7·1 answer
  • how much would 600 invested at 8% interest compounded continuously be worth after 3 years? round your answer to the nearest cent
    6·1 answer
  • The table shows the distance 4 people swam. Who swam a greater distance than Milo​
    9·1 answer
  • The Reyes want grilled chicken and tilapia for dinner. Mrs.
    6·1 answer
  • Matt makes the same amount of money each week working at his parents' store. The graph shows the amount of money Matt has spent
    15·1 answer
  • A circle with a circumference of 6 has an arc with 20 central angle
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!