All categories

4 years ago

Below is a proof showing that the sum of a rational number and an irrational number is an irrational number.

Mathematics

2 answers:

ankoles [38]4 years ago

4 0

Answer:

Step-by-step explanation:

To prove: The sum of a rational number and an irrational number is an irrational number.

Proof: Assume that a + b = x and that x is rational.

Then b = x – a = x + (–a).

Now, x + (–a) is rational because addition of two rational numbers is rational (Additivity property).

However, it was stated that b is an irrational number. This is a contradiction.

Therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number.

Hence, the sum of a rational number and an irrational number is irrational.

Goryan [66]4 years ago

4 0

Answer:

I believe the answer is B

Step-by-step explanation:

You might be interested in

On the graph of f(x) = sin x and the interval (-2pi,0), for what value of x does f(x) achieve a minimum? Choose all

V125BC [204]

Answer:

x = -pi/2

Step-by-step explanation:

hello :

f(x)=sin x x⋲(-2pi,0)

the derivate for f is : f'(x) = cosx

f(x) achieve a minimum when : f'(x) =0

cosx = 0 genral solution is :

x = pi/2 +kpi .. k in Z

but : x⋲(-2pi,0) so : x = -pi/2.....(k = -1)

7 0

4 years ago

What is the value of ??????

VashaNatasha [74]

Hey! the question mark equals 135°

6 0

3 years ago

0.05 is 10 times as much as?

alisha [4.7K]

0.5 / 10 = 0.05
0.5 is ten times as much as 0.05

You have to divide 0.5 by 10 to get a number that is 10 times less.

8 0

3 years ago

Read 2 more answers

У = 4х – 1<br> у = 2х – 5<br> How do you solve this, by using substitution?!

solmaris [256]

Answer:

x = -2, y = -9

Step-by-step explanation:

You can substitute the value of y into y. The first equation shows that y is equal to 4x -1, so we can switch this with the y in the second equation.

y = 2x -5 will become

4x - 1 = 2x - 5

Add 5 to both sides

4x + 4 = 2x

Subtract 4x from both sides

4 = -2x

Divide both sides by -2

-2 = x

Now we plug this number into an equation to find y.

y = 4x - 1 becomes

y = 4(-2) - 1

Simplifying it, we have:

y = -8 - 1

y = -9

7 0

3 years ago

Which graph shows the asymptotes of the function f(x)=4x-8/2x+3

Ksju [112]

Answer:

Graph C

Step-by-step explanation:

Assuming you mean $\displaystyle f(x)=\frac{4x-8}{2x+3}$ :

Our vertical asymptote will be the line equal to the solution of $2x+3=0$ , which is $x=-\frac{3}{2}$
Our horizontal asymptote will be equal to the ratio of the leading coefficients since they have the same degree, so $y=2$

Thus, the correct graph is C.

8 0

3 years ago