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
Usimov [2.4K]
3 years ago
8

Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope

rty 1: Every integer is a rational number. Property 2: The sum of any two rational numbers is rational. Property 3: The product of any two rational numbers is rational. Note: Property 1 is Theorem 4.3.1, Property 2 is Theorem 4.3.2, and Property 3 is Exercise 15 in Section 4.3. Using these properties, choose explanations for each step in the given proof.
Mathematics
1 answer:
ziro4ka [17]3 years ago
6 0

Given:

Expression is

3r^2-2r+4

To prove:

If r is any rational number, then 3r^2-2r+4 is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.  

Let r be any rational number.

We have,

3r^2-2r+4

It can be written as

3(r\times r)-2r+4

Now,

3, -2 and 4 are rational numbers by property 1.

r^2=r\times r is rational by Property 3.

3r^2\text{ and }-2r are rational by Property 3.

3r^2+(-2r)+4 is rational by property 2.

So, 3r^2-2r+4 is rational.

Hence proved.

You might be interested in
Help please!! it’s due today and this is the one answer i still need!! (view picture)
matrenka [14]

Answer: q=0.3p-2

Well everytime P goes up by one then Q goes up by positive 0.3

7 0
3 years ago
Read 2 more answers
Someone help me with this ASAP!!!
Dafna1 [17]

Answer:

33.09

Step-by-step explanation:

You just subtract 26.91 from 60

4 0
3 years ago
Read 2 more answers
I need to know if it is less than greater than or equal two
Genrish500 [490]

Answer:

Greater than because 4,100 grams is 100 greater than 4 kilograms because 4 kilograms is equal to 4,000 grams

Step-by-step explanation:

A kilogram is 1,000 times larger than one gram

3 0
3 years ago
Are their always the same number of prime numbers between 2 consecutive multiples of 10
Harlamova29_29 [7]

Yes there are. Its just the way they work out!

3 0
3 years ago
How do you order two numbers written in scientific notation?
tresset_1 [31]
The correct answer is C
4 0
3 years ago
Read 2 more answers
Other questions:
  • if the side length of a square can be represented by 4x + 4 and its area is 1024 square units, find the value of x
    8·2 answers
  • Reduce 36/45 to lowest terms and write the numerator in the blank.
    12·2 answers
  • Which of the following trangles are right triangles
    14·2 answers
  • Point P(−3, −4) is rotated 90° counterclockwise about the origin. What are the coordinates of its image after this transformatio
    14·2 answers
  • In order to make 6 dozen cookies, you must use 3 eggs in the batter. How many eggs would be required to make 48 dozen cookies? U
    5·2 answers
  • What is 1.2÷33.6 is the answer 28?
    7·1 answer
  • Can you help ASAP......
    12·2 answers
  • Find the product and simplify.<br> (k+ 4)(-4k – 5)
    11·1 answer
  • 13. A counterexample
    15·2 answers
  • I need help with this its confusing me too much
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!