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
Bingel [31]
3 years ago
5

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]3 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]3 years ago
4 0

Answer:

I believe the answer is B

Step-by-step explanation:

You might be interested in
May someone please help me with this Math problem, Thank you
Semmy [17]

Answer:

c. 10

Step-by-step explanation:

Eliminate parentheses using the distributive property.

3(b+4) -2(2b+3) = -4 . . . . given

3b +12 -4b -6 = -4 . . . . . parentheses eliminated

-b +6 = -4 . . . . . . . . . . . . collect terms

-b = -10 . . . . . . . . . . . . . . subtract 6

b = 10 . . . . . . . . . . . . . . . . multiply by -1

_____

The rules of equality require that any operation you perform on one side of the equal sign must also be done on the other side. So when we say "subtract 6", we assume you know that means "subtract 6 from both sides of the equation", for example.

8 0
3 years ago
3x/2x simplified into racio
Alik [6]

Answer:

Simplify the expression.

3x2/2

hope this makes sense lol

Step-by-step explanation:

5 0
2 years ago
pam deposited $6,900 in a savings account with simple interest. Four months later she had earned $23 in interest. What was the i
3241004551 [841]

Answer:

1%

Step-by-step explanation:

We use the simple interest equation of A=P(1+rt).

A-the total amount with interest earned

P-the initial amount or principal

r-rate

t-time in years

We substitute the values P=6900, A=6923, and t=0.33 since 4 months divided by 12 months is 0.333 years. We then solve for r.

6923=6900(1+r(0.33))\\6923=6900(1+0.33r)\\\frac{6923}{6900} =\frac{6900(1+0.33r)}{6900} \\1.0033=1+0.33r\\1.0033-1=1-1+0.33r\\0.0033=0.33r

Our final step is to divide both sides by 0.33.

\frac{0.0033}{0.33} =\frac{0.33r}{0.33} \\0.01=r

This is the decimal of the rate. We convert to a percentage by multiplying by 100. 0.01(100)=1%.


5 0
3 years ago
The sum of the first 150 negative integers is represented using the expression What is the sum of the first 150 negative integer
Kamila [148]

Answer:

C. -11,325

Step-by-step explanation:

  • To know the answer, is convenient to replace some values of "n" in the sum \sum_{(n=1)}^{150}[-1-(n-1)].
  • The result would appear after adding up every value of the expression \sum_{(n=1)}^{150}[-1-(n-1)] when n=1,2,3.....,150.
  • When n=1, the expression takes the value of (-1): [-1-(1-1)]= (-1)-0=-1.
  • When n=2, the expression takes the value of (-2): [-1-(2-1)]=-1-1=-2.
  • Following this way, for every n, we will obtain -n, then, the sum will be: -1-2-3-4-5-6-...-150. This sum can actually be expressed as \sum_{n=1}^{150}(-n), which is the result of solving the initial expression of the sum -1-(n-1)=-1-n+1=-n.
  • Finally, the sum of n=-1 to n=-150 equals -11,325.
7 0
4 years ago
Read 2 more answers
Help Please?<br> Solve for x. <br><br> x − 2.7 ≥ 10.3<br><br> Solve for x. <br><br> −0.84x ≤ 168
stiks02 [169]
For the first one, we add 2.7 to both sides to get x≥13. Next, we divide both sides by -0.84 to get x≥ 168/-0.84. SInce we multiplied or divided by a negative number, we switch the sign around and end up with x≥200
4 0
4 years ago
Other questions:
  • 12 POINTS<br>Simplify i38. <br> i <br> −1 <br> −i <br> 1
    7·2 answers
  • What is the value of x in the equation 1/5x-2/3y=30 when y=15
    7·2 answers
  • What is 129 divided by 12
    15·2 answers
  • Solve: 4x - 3 = x + 9
    15·2 answers
  • Whats the answer 5h-8=2h+19 equality
    15·1 answer
  • 1. If y + 1/y = 2 cos teta find y​
    14·2 answers
  • What is ( n^2+6n-4)(2n-4)
    12·1 answer
  • Pleaseeeeeeeeee help
    6·2 answers
  • Which of the following radical expressions simplifies to 6x^4y^3√2y?
    15·1 answer
  • Helpppp with this :&gt;
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!