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
Pani-rosa [81]
3 years ago
14

Which axiom is used to prove that the product of two rational numbers is rational

Mathematics
1 answer:
aliina [53]3 years ago
5 0

Answer:

First, a rational number is defined as the quotient between two integer numbers, such that:

N = a/b

where a and b are integers.

Now, the axiom that we need to use is:

"The integers are closed under the multiplication".

this says that if we have two integers, x and y, their product is also an integer:

if x, y ∈ Z ⇒ x*y ∈ Z

So, if now we have two rational numbers:

a/b and c/d

where a, b, c, and d ∈ Z

then the product of those two can be written as:

(a/b)*(c/d) = (a*c)/(b*d)

And by the previous axiom, we know that a*c is an integer and b*d is also an integer, then:

(a*c)/(b*d)

is the quotient between two integers, then this is a rational number.

You might be interested in
According to the data in the figure, find the value of x and y.
drek231 [11]

Answer:

This is a educated guess, but x is 80 and y is 100.

Step-by-step explanation:

My logic here is that the triangles are the same because of all the congruent lines and stuff. But from there, you know that both the right and the left side are 40 degrees. You know the total degree of a triangle is 180 so 180 - 40 - 40 is 100. So the final angle is 100. If you look at x, its on the outside, but on a line. If you can imagine a circle, its half, so its a 180 degrees total. Then its 180 = x + 100. So x is 80. And then by that same logic its y = 100.

6 0
2 years ago
What is the best price?
skad [1K]

Answer:

1 bag

Step-by-step explanation:

because the other ones are more expensive

3 0
3 years ago
Help!! Answer !!! about to run out of time in test!!
Gemiola [76]

\qquad \qquad\huge \underline{\boxed{\sf Answer}}

Here's the solution ~

Let's find the measure of hypotenuse first, by using Pythagoras theorem ;

\qquad \sf  \dashrightarrow \: h {}^{2}  =  {8}^{2}  +  {6}^{2}

\qquad \sf  \dashrightarrow \: h {}^{2}  =  {36}^{}  +  {64}^{}

\qquad \sf  \dashrightarrow \: h {}^{2}  = 100

\qquad \sf  \dashrightarrow \: h {}^{}  =  \sqrt{100}

\qquad \sf  \dashrightarrow \: h {}^{}  =  {10}

Now, let's find the asked values ~

\qquad \sf  \dashrightarrow \:  \sin(x) =  \dfrac{opposite \: side}{hypotenuse}

\qquad \sf  \dashrightarrow \:  \sin(x) =  \dfrac{6}{10}

\qquad \sf  \dashrightarrow \:  \sin(x) =  \dfrac{3}{5}   \: or \: 0.6 \: units

For Cos y :

\qquad \sf  \dashrightarrow \:  \cos(y) =  \dfrac{adjcant \: side}{hypotenuse}

\qquad \sf  \dashrightarrow \:  \cos(y)   = \dfrac{6}{10}

\qquad \sf  \dashrightarrow \:  \cos(y)   = \dfrac{3}{5}  \: or \: 0.6 \: units

As we can see that both sin x and Cos y have equal values, therefore The required relationships is equality.

I.e Sin x = Cos y

Hope it helps ~

3 0
2 years ago
Can you please help me out?
larisa86 [58]

Answer:

- 3.5229

Step-by-step explanation:

Using the rules of logarithms

logx + logy = log(xy)

log_{10} 10^{n} = n

Given

log_{10} 3 ≈ 0.4771, then

log_{10} 0.0003

= log_{10} (3 × 10^{-4} )

= log_{10} 3 + log_{10} 10^{-4}

≈ 0.4771 - 4

≈ - 3.5229 ( to 4 dec. places )

8 0
3 years ago
The absolute value of -5 is...
ipn [44]

Answer:

The absolute value of -5 is...5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • Which shows a difference of squares? 10 y squared minus 4 x squared 16 y squared minus x squared 8 x squared minus 40 x + 25 64
    8·2 answers
  • It takes 7 weeks to build 8.75 kilometers. At what rate did they build it?
    11·1 answer
  • Can someone help me with the answer to this?? I don't understand it at all.
    9·1 answer
  • Solve for x. Determinants
    12·1 answer
  • Can someone please help
    6·1 answer
  • The sum of three consecutive integers is 33. What are the numbers?
    14·1 answer
  • Melissa went for a drive in her new car. She took 9 hours to drive 562.5 miles. What was her speed? miles per hour​
    6·1 answer
  • What is the expression for "the difference of 3 and 5times a number"?
    5·1 answer
  • Find the equation of the linear function represented by the table below in slope-
    10·2 answers
  • Simplify 1/2x - 2/3 + 7/8x + 5/6
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!