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telo118 [61]
3 years ago
14

If n and k are positive integers, is n divisible by 6 ? (1) n = k(k + 1)(k – 1) (2) k – 1 is a multiple of 3.

Mathematics
1 answer:
xz_007 [3.2K]3 years ago
4 0

Answer: yes, it is

Step-by-step explanation:

A number is divisible by 6 if it is divisible by 2 and 3 simultaniously.

n = k(k+1)(k-1)

If k-1 is a multiple of 3, n is divisible by 3, so one of the requirements is ok.

Now, if k-1 is a multiple of 3, it can be even or odd.

if k-1 is even, then it is divisible by 2 and as it is divisible by 3 as well, n is divisible by 6

if k-1 is odd, then k and k+1 is even, hence, divisible by 2.

As n = k(k+1)(k-1), n is also divisible by 6.

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Factorise 24e^2-28e-12
Helga [31]

Answer:

4(2e - 3)(3e + 1)

Step-by-step explanation:

Given

24e² - 28e - 12 ← factor out 4 from each term

= 4(6e² - 7e - 3) ← factor the quadratic

Consider the factors of the product of the e² term and the constant term which sum to give the coefficient of the e- term.

product = 6 × - 3 = - 18 and sum = - 7

The factors are - 9 and + 2

Use these factors to split the e- term

6e² - 9e + 2e - 3 ( factor the first/second and third/fourth terms )

= 3e(2e - 3) + 1 (2e - 3) ← factor out (2e - 3) from each term

= (2e - 3)(3e + 1)

Then

24e² - 28e - 12 = 4(2e - 3)(3e + 1) ← in factored form

8 0
3 years ago
15. What is the graph of the function rule? <br> y = |3x| - 1
VladimirAG [237]
<h3>Answer:</h3>

D

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The graph of |x| opens upward. Your graph is vertically stretched by a factor of 3 and translated downward 1 unit.

Graphs B and D open upward, but only graph D is translated downward (not upward, as in B).

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The range is 8
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