Help me please thanks

Prove that <img src="https://tex.z-dn.net/?f=x%20%7B%7D%5E%7B2%7D%20%20-%202" id="TexFormula1" title="x {}^{2} - 2" alt="x

Zielflug [23.3K]

Answer:

Any integer x can be represent in form of 3k, 3k+1, or 3k + 2 (k is integer).

Case 1: x = 3k => x^2 - 2 = 9k^2 - 2, which will not be divisible by 3

(notice that 2 is not divisibble by 3, but 9k^2)

Case 2: x = 3k + 1 => x^2 - 2 = 9k^2 + 6k + 1 - 2 = 9k^2 + 6k - 1, which will not be divisible by 3

(notice that 1 is not divisibble by 3, but 9k^2 + 6k)

Case 3: x = 3k + 2 => x^2 - 2 = 9k^2 + 12k + 4 - 2 = 9k^2 + 12k - 2, which will not be divisible by 3

(notice that 2 is not divisibble by 3, but 9k^2 + 12k)

=> x^2 - 2 will never be divisible by 3

Hope this helps!

:)

6 0

4 years ago

Couldn’t find correct answer if you know please help

Gnoma [55]

Answer:

the answer to your question is 3

8 0

4 years ago

What is the slope of the line that passes through (-2, 7) and (4, 9)?

ANEK [815]

Answer:

The slope of the line that passes through (-2, 7) and (4, 9) is 1/3.

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1)

Substituting the values

m = (9 - 7)/(4 + 2)

So we get,

m = 2/6

m = 1/3

5 0

2 years ago

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 o

xeze [42]

Answer:

a) 95% of the widget weights lie between 29 and 57 ounces.

b) What percentage of the widget weights lie between 12 and 57 ounces? about 97.5%

c) What percentage of the widget weights lie above 30? about 97.5%

Step-by-step explanation:

The empirical rule for a mean of 43 and a standard deviation of 7 is shown below.

a) 29 represents two standard deviations below the mean, and 57 represents two standard deviations above the mean, so, 95% of the widget weights lie between 29 and 57 ounces.

b) 22 represents three standard deviations below the mean, and the percentage of the widget weights below 22 is only 0.15%. We can say that the percentage of widget weights below 12 is about 0. Equivalently we can say that the percentage of widget weights between 12 an 43 is about 50% and the percentage of widget weights between 43 and 57 is 47.5%. Therefore, the percentage of the widget weights that lie between 12 and 57 ounces is about 97.5%

c) The percentage of widget weights that lie above 29 is 47.5% + 50% = 97.5%. We can consider that the percentage of the widget weights that lie above 30 is about 97.5%

3 0

3 years ago

At a telethon, a volunteer can take 48 calls over a 4-hour shift. At this rate, how many calls can 12 volunteers take in a 4-hou

stellarik [79]

1 volunteer - 4 h - 48 calls
12 volunteers - 4 h - x calls

The time is the same, so it's irrelevant.
1 volunteer - 48 calls
12 volunteers - x calls

x=12*48=576

So it's 576 hours.

5 0

4 years ago