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
Marianna [84]
3 years ago
10

Prove: If n is a positiveinteger and n2 is divisible by 3, then n is divisible by3.

Mathematics
1 answer:
notka56 [123]3 years ago
5 0

Answer:

If n^2 is divisible by 3, the n is also divisible by 3.

Step-by-step explanation:

We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then, n^2 is not divisible by 3.

Let n not be divisible by 3. Then \frac{n}{3} can be written in the form of fraction \frac{x}{y}, where x and y are co-prime to each other or in other words the fraction is in lowest form.

Now, squaring

\frac{n^2}{9} = \frac{x^2}{y^2}

Thus,

n^2 = \frac{9x^2}{y^2}

\frac{n^2}{3} = \frac{3x^2}{y^2}

It can be clearly seen that the fraction \frac{3x^2}{y^2} is in lowest form.

Hence, n^2 is not divisible by 3.

Thus, by contrapositivity if n^2 is divisible by 3, the n is also divisible by 3.

You might be interested in
Factor completely 3x2-36x+96
allsm [11]

Answer:

do the possible math functions first like 3 x 2 and 6 + 96

3 0
3 years ago
WHY IS BRAINLY THE BEST!?
goldenfox [79]
BC I WONT DONT HAVE TO DO MY WORK
8 0
3 years ago
Which measures are the sides lengths of a right triangle?
Pavlova-9 [17]

Answer:

b)

Step-by-step explanation:

a) 4+12>8

12+8>4

4+8=12

NO

b) 5+12>10

10+5>12

12+10>5

YES

c) 16+4>6

6+4<16

NO

d) 30+12>6

12+6<30

NO

5 0
3 years ago
Out of 431 applicants for a job, 142 have over 5 years of experience and 103 have over 5 years of experience and have a graduate
Savatey [412]

Answer:

  • 0.2390

Step-by-step explanation:

<u>Given</u>

  • Total applicants = 431
  • Applicants with graduate degree and over 5 years of experience = 103

Probability = favorable outcomes/total outcomes

<u>Required probability </u>

  • 103/431 = 0.2390 rounded to 4 decimal places
3 0
3 years ago
there are 158 4th grade students and 139 fifth grade students going on a field trip .there needs to be at least 1 adult chaperon
strojnjashka [21]

Answer:

  (D) is the best explanation

Step-by-step explanation:

The total number of students is 158 + 139 = 297. This number can be rewritten as ...

  297 = 37 × 8 + 1

That is, if there were 37 chaperones, 1 student would remain without a chaperone. That means the number of chaperones must be increased by 1 to 38. This is best explained by choice D.

3 0
3 years ago
Other questions:
  • Petra started with a number added 3 multiplied the result by 4 subtracted 6 and multiplied that result by 3 her final answer was
    10·1 answer
  • Find the root(s) of f(x) = (x + 5)2(x - 9)2(x + 1).
    15·1 answer
  • Match the numerical expressions related to the function f(g) = 4g + 6 with their correct definitions.
    13·2 answers
  • Find the lowest common multiple of 15 and 12
    14·1 answer
  • Can someone please help me complete the factoring of the polynomial
    5·1 answer
  • Below is a set of data about temperatures. The range of a set of data is the distance between the lowest and highest value in th
    9·1 answer
  • Please help me solve this !:) <br> Explain your answer <br><br> I will give braisnlt .
    6·1 answer
  • 8. You are given two of the side lengths of a triangle: 3.1 in and 1 ft. What is the solution range for the 3rd side length? (co
    8·2 answers
  • 2 1/6 divided by 3/4
    6·2 answers
  • PLEASE HELP!!!!!!!!!!!!!
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!