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
wolverine [178]
2 years ago
8

Prove that the natural number x is prime if and only if x>1 and there is no positive integer greater than 1 and less than or

equal to \sqrt{x} that divides x.
Mathematics
1 answer:
UNO [17]2 years ago
3 0

There are several ways to prove a mathematical statement. These ways include: by contradiction, by induction, contraposition, etc

<h3>How to prove the statement by contradiction</h3>

To prove the statement, we make use of proof by contradiction

From the question:

x is a composite number such that: x > 1

This means that 1 < a < x is a factor of x

This can be represented as:

x = a * b

Where:

  • a  and b  are  positive  integers
  • 1 < a, b < x

Assume that b is less than or equal to a.

Also, let

b > \sqrt x​

This means that:

\sqrt x < b \ge a

The above becomes

\sqrt x < a

Rewrite as:

a > \sqrt x

So, we have:

x = a * b > \sqrt x * \sqrt x = x

The above means that:

x > x

The above inequality is a contradiction because, a number x cannot be greater than itself

This means that, the supposition is wrong.

Hence, the given statement has been proved by contradiction

Read more about proof by contradiction at:

brainly.com/question/8062770

You might be interested in
Please Answer This, the question is on the picture. it needs to be a fraction
SpyIntel [72]

Answer:

cos ∅ = 15/17

Step-by-step explanation:

hypotenuse² = 15² +8² = 225 + 64 = 289

hypotenuse = √289 = 17

cos ∅ = 15/17 =

3 0
3 years ago
Someone tell me where everyone is going right please !!
marysya [2.9K]
1,3and 5 are functions
5 0
3 years ago
Read 2 more answers
If −1 is a zero of the polynomial p(x)=ax^3−x^2+x+4, find the value of a.
vitfil [10]

Answer:

a = 2

Step-by-step explanation:

given x = - 1 is a zero then f(- 1) = 0 , that is

a(- 1)³ - (- 1)² - 1 + 4 = 0

- a - 1 - 1 + 4 = 0

- a + 2 = 0 ( subtract 2 from both sides )

- a = - 2 ( multiply both sides by - 1 )

a = 2

8 0
2 years ago
Plz help need to find both answers
saul85 [17]

Answer:

I hope it helped u.

Step-by-step explanation:

7 0
3 years ago
Please help me I need to solve for x.
Sav [38]
Answer: x=7

12x-4=0.5(22x+6)
12x-4=11x+3
-11x -11x
x=7

Explanation: use the tangent-chord angle theorem.
4 0
3 years ago
Other questions:
  • Solve for x. You must write your answer in fully simplified form.<br><br> -12x = 10
    11·1 answer
  • What is equal to 275%
    6·2 answers
  • What does x equal if the circumference of a circle equals 113.04
    7·1 answer
  • 20% of Desiree's math test problems consisted of word problems. 30% of Everett's math test problems consisted of word problems.
    14·2 answers
  • Check for Understanding
    12·1 answer
  • 24a²-30 at 9<br> Solve please
    11·1 answer
  • Please solve for x and show explanation
    12·2 answers
  • Write two expersions equivalent to -5/4x-3/4
    7·2 answers
  • Express the value of each tangent ratio to the nearest tenth or as a fraction
    11·1 answer
  • Pls help due soon!! (no scam answers or links) :)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!