Prove that
[tex]x {}^{2} - 2[/tex]
will never be divisible by 3.​

Answers

Answer 1

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!

:)


Related Questions

16. Does this shape show thirds?
Explain.

Answers

Answer:

No

Step-by-step explanation:

This shape does not show thirds. Although the shape is cut up into 3 shapes, the shapes are not equal. Imaging a cake... would you be happy if your friend got the rectangle, but you got the square. Cutting something into thirds is the same way. They all need to be equal.

Answer:

No, It shows 1/2

Step-by-step explanation:

The small squares would constitute to a total of 4, so it shows 2/4 which is 1/2

you don't have to answer number 15. but pls answer the rest!

BEST ANSWER GETS BRAINLESST AND FOLLOW ASP HURRY!!​

Answers

Answer:

Step-by-step explanation:

13. 2,300mg > 2g

14. 3kg = 3,000g

16. 4120mg = 4.12g

17. 75g < 800mg

Josh started reading at 8:18 AM. He finished reading at 8:57 AM. How many

minutes did he read?

>) 41 minutes

1) 21 minutes

) 49 minutes

1)) 39 minutes

Answers

。☆✼★ ━━━━━━━━━━━━━━  ☾  

Subtract the minutes values:

57 - 18 = 39

He read for 39 minutes

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

。☆✼★ ━━━━━━━━━━━━━━  ☾

Total time for reading is 39 minutes

Given that;

Josh started at 8:18 AM

Josh ended at 8:57 AM

Find:

Total time for reading

Computation:

Total time for reading = 8:57 - 8:18

Total time for reading = 39 minutes

Learn more:

https://brainly.com/question/8806520?referrer=searchResults

Saturn is 8.867 *10g miles away from the sun. How many times farther is Uranus

Answers

Answer:

957.63- 194.7= 763 miles if you need to do the decimals it will be 763.853

Please mark.

Thanks

Jake

Solve the following quadratic equation using the quadratic formula.
5x^2 - 8x + 5 = 0
Write the solutions in the following form, where r, s, and tare integers, and the fractions are in simplest form.

Answers

Graph each side of the equation. The solution is the x-value of the point of intersection.
x
=
0
,
8
5

Stephanie is 5 feet tall.
How tall is Stephanie in inches?
A 15
B
C
50
D
60
need help please​

Answers

Answer:

60inces

Step-by-step explanation:

Answer:

D.60 inches

Step-by-step explanation:

calculate the area of a circle with a diameter of 8 feet

Answers

Answer: 50.27

Step-by-step explanation:

Area = pi r^2

= pi x 16

Answer:

50.265 [tex]ft^{2}[/tex]

Step-by-step explanation:

The formula of the area of a circle is [tex]\pi r^{2}[/tex] and the diameter is double the amount as the radius, so the radius would be 4 feet. 4 squared is 16. Multiply that by pi to get your answer, 50.265[tex]ft^{2}[/tex].

Suppose you have one pyramid with a base that is 10 meters long and 10 meters wide with a slant that is 15 meters. Now, if the length of the base is

Answers

Answer:

The difference between area of pyramids is 125 sq.m.

Step-by-step explanation:

Length of base = 10m

Breadth of base = 10 m

Slant height = 15 m

Area of pyramid = Area of 5 bases

Area of pyramid = [tex]\frac{1}{2} \times 10 \times 15+\frac{1}{2} \times 10 \times 15+\frac{1}{2} \times 10 \times 15+\frac{1}{2} \times 10 \times 15+10 \times 10[/tex]

Area of pyramid = 400 sq.m.

Now the length of base is increased to 15

Length of base = 15m

Breadth of base = 10 m

Slant height = 15 m

Area of pyramid = Area of 5 bases

Area of pyramid =[tex]\frac{1}{2} \times 15 \times 15+\frac{1}{2} \times 15 \times 15+\frac{1}{2} \times 10 \times 15+\frac{1}{2} \times 10 \times 15+10 \times 10[/tex]

Area of new pyramid = 525 sq.m.

Difference between area of pyramids=525 sq.m. - 400 sq.,. = 125 sq.m.

Hence The difference between area of pyramids is 125 sq.m.

Jenna saves $2,500 per year in an account that earns 10% interest per year, compounded annually. Jenna will have saved in 30 years. Her account balance is a result of Jenna’s .

Answers

Answer:

$43,625

Step-by-step explanation:

Hello,

The question is a direct application of compound interest and we'll approach this question using the formula of compound interest.

A = P(1 + r/n)^nt

A = compound interest

P = principal

r = rate of the interest

n = number of times compounded

t = time interval for the money to be compounded.

Data;

A = ?

P = $2,500

r = 10% = 0.1

n = 1 (since it's compounded annually)

T = 30 years

A = 2,500 [1 + (0.1 / 1)]^(1 × 30)

A = 2,500 × [1 + 0.1]³⁰

A = 2,500 × 1.1³⁰

A = 2,500 × 17.45

A = $43,625

In 30 years, Jenna would've saved $43,625

Standard form of the equation that goes through (3, -1) with a slope of -1, please!

Answers

Answer:

x+y=2

Step-by-step explanation:

Standard Form: ax+by=c

For most convenience start with slope-intercept form: y=mx+b

1. -1 = -1(3)+b -  solve for b

b=2

y= -1x+2 (slope-intercept form)

2. Now convert to standard form

Add 1x to both sides:

1x+y=2

Which of the following is an odd function?
f(x) = 3x²+x
fx) = 4x^3 +7
fx) = 5x^2 + 9
f(x) = 6x^3 + 2

Answers

The third one seems like an odd function because I haven’t seen a function like that to be honest. Hope this little explanation helps, I tried my best

The number of sunrises that happen each year is measured in the __
A. hundreds
B. ones
C. tens
D. thousands

Answers

Mostly likely the hundreds

Use K to write an equation, y=kx, for the relationship.

Answers

Y= 1x because the slope is 1 because rise over run 1

Who Ever Answers Correct I'll Mark Brainliest. 1. Can the following situation be described by a positive integer or a negative integer? David deposited his weekly paycheck from his job in the amount of $287. Neither Positive Negative 2. List the following numbers from least to greatest: -4, |-6|, 3, -2, |5| |-6|, |5|, 3, -2, -4 -4, -2, 3, |5|, |-6| |-6|, 5, -4, 3, -2 |-6|, -4, -2, 3, |5| 3. Which rational number is the opposite of 1.9? Select all that apply. -1 9/10 1 9/10 -1.9 4. Find the sum of - and it's opposite. 7/8 2/3 0 14/16

Answers

Answer:

-1.9 is the one

Step-by-step explanation:

If Aniyah can run 6.5 miles per hour, and she runs for 15 minutes, how far did she go?

Answers

Step-by-step explanation:

PRIMERO CONVIERTES MINUTOS A HORAS

15 MIN = 0.25 h

LUEGO CON LA ECUACIÓN DE GALILEI:

x = 6.5 mi/0.25 h = 26 mi

5{ 10[6 + 2(17 - 8) + 12]}

Answers

Answer: 1,800

Step-by-step explanation:

=5(10(6+(2)(9)+12))

=5(10(618+12))

=5(10(24+12))

=5(10)(36)

=(5)(360)

=1800

Hope this helps :)

The right answer is 1800

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Someone wanna help on this one? The Chain Reaction bike shop is running a special that allows a family to rent all the bikes and equipment they need for an hourly rate and a nonrefundable $15 deposit. The Morales family can rent bikes for 2 hours for $57. The cost of the rental can be represented by a linear function where x represents the number of hours the bikes are rented and y represents the total cost of the rental. What is the equation here and what are the slope and y-intercept?

Answers

Someone pls answer I need this as well

Answer:

y=21x+15, where 21 is the hourly rate and the slope, 15 is the non-refundable deposit, and y is the total amount payed

Step-by-step explanation:

the slope is the hourly rate, the y int is the deposit of 15$

thus,

to find the slope, we can use the equation:

57=m*2+15

42=2m

m=42/2

m=21

thus, the whole equation is:

y=21x+15, where 21 is the hourly rate and the slope, 15 is the non-refundable deposit, and y is the total amount payed

How many solutions does the equation have 4p + 1 = 49 - 7

Answers

Answer:

so one solution

Step-by-step explanation:

4p+1=49 - 7

minus 1 to -7= -8

4p= 49-8

4p=41, divided by 4 and you'll get a decimal, 10.25

Answer:

1 solution if solving for p.

Step-by-step explanation:

If solving for p:

4p+1=49-7

4p+1=42

Subtract 1 from both sides

4p=41

Divide both sides by 4

p=10.25

There is only one solution, 10.25

But I've seen this question on a Quizizz and the answer was no solutions. I don't think that's correct but... might be because the question didn't ask to solve for p.

(SAT Prep) In the given figure, the reflex angle ∠DOB has measure of 3.5y while the measure of ∠AOD is y. Find the measure of the non-reflex ∠DOB in degrees.

Answers

Answer:

252°

Step-by-step explanation:

In the figure attached, the diagram is shown. There, we can see that

∠DOB = ∠AOD + ∠AOC + ∠COB

Replacing with the equivalences: ∠DOB has a measure of 3.5y, the measure of ∠AOD is y, and ∠AOC + ∠COB measure 180°, we get:

3.5y = y + 180°

3.5y - y = 180°

2.5y = 180°

y = 180°/2.5

y = 72°

Therefore, ∠DOB = 3.5*72° = 252°

Answer:

108 degrees

Step-by-step explanation:

m∠DOB=m∠AOD+m∠AOC+m∠COB And then we substitute, m∠DOB=3.5y, m∠AOD=y, m∠AOC+m∠COB=180 degrees. So the equation will then be 3.5y=y+180 degrees

y= 72

m∠DOB=3.5 x 72   m∠DOB=252 degrees, this is the reflex angle.

360-252=108 degrees, the non-reflex m∠DOB= 108 degrees

A random variable, X, is defined for the number of times a coin lands on heads when flipped 4 times. The probability distribution is below.

X 0 1 2 3 4
P(X) 1/16 4/16 6/16 4/16 1/16
What is the expected value for the number of heads you expect after 4 coin flips?

Answers

Answer:

1/16

Step-by-step explanation:

Mark me brainlest plz.

Question 8 *
2 points
8. In the diagram below of LEO and TAM, angles A and E are right angles, and
LEO - TAM.
If TM - 12 and MA = 6, what is the measure of angle L, to the nearest degree?
1. 27°
2. 30°
3. 60°
4. 63°

Answers

Answer:

27

Step-by-step explanation:

i did it

Select the correct answer.
Which of these statements explains the term price?
A.
the money spent by a seller to advertise a product
B.
the money spent by a manufacturer to make a product
C.
the money spent by a buyer to purchase a product

Answers

Answer:

the money spent by a buyer to purchase a product

It should be the money spent by a seller to advertise a product

revious
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Post Test: Investing
Submit Test
Reader Tools
1
Select the correct answer from each drop-down menu.
Identify the type of chart described and complete the sentence.
A
chart shows open and close prices and highs and lows, but over a long time period it can also show pricing
Reset
Next

Answers

Answer:

The chart type described is the OHLC chart.

Step-by-step explanation:

An OHLC chart is a kind of bar-chart that displays open, high, low, and closing prices for each period. OHLC charts are beneficial since they demonstrates the four major data values over a period, with the closing price being reflected as the most significant by traders.

The chart type is valuable since it can represent increasing or decreasing movement. When the open and close are far-apart it represents strong movement, and when the open and close are close together it represents wavering or weak movement. The high and low displays the full price range of the period, useful in evaluating instability.  

Thus, the chart type described is the OHLC chart.

Answer:

Candlestick & Trends.

Step-by-step explanation:

Correct on edmentum.

Which is true about the line whose equation is y + 2 = 0?

Answers

Answer:

The y-intercept is -2

Step-by-step explanation:

Based on the equation y + 2 = 0 (y = -2), you can eliminate all answers except for the second one. This is because, the y is the horizontal line, while the x is the vertical line. The value of x does not always equal the value of y, only sometimes. Finally, the slope of y = -2 is 0, not undefined. However, the slope of x = -2 is undefined.

A _____________ is the information sent to a function in python

Answers

Answer:

Formal Parameters

Step-by-step explanation:

The arguments in the function definition bind the arguments passed at function invocation (i.e. when the function is called), which are called actual parameters, to the names given when the function is defined, which are called formal parameters.

PLEASE HELP WILL MARK BRAINIEST

Answers

Answer:

Because all consecutive angles in a parallelogram are supplementary, m∠SVU = 180 - 57 = 123°.

Answer:

Step-by-step explanation:

In a parallelogram, sum of adjacent angles is 180

∠TSV + ∠SVU = 180

57 + ∠SVU = 180

∠SVU = 180 - 57

∠SVU = 123°

Solve by taking the square root of both sides 3(x-1)^2-162=0
a. x = -1 - 3 sqrt 6 or -1 + 3 sqrt 6
b. x = 1 - 3 sqrt 6 or -1 + 3 sqrt 6
c. x = -1 - 3 sqrt 6 or 1 + 3 sqrt 6
d. x = 1 - 6 sqrt 6 or 1 + 6 sqrt 6

Answers

Answer:

see explanation

Step-by-step explanation:

Given

3(x - 1)² - 162 = 0 ( add 162 to both sides )

3(x - 1)² = 162 ( divide both sides by 3 )

(x - 1)² = 54 ( take the square root of both sides )

x - 1 = ± [tex]\sqrt{54}[/tex] = ± 3[tex]\sqrt{6}[/tex] ( add 1 to both sides )

x = 1 ± 3[tex]\sqrt{6}[/tex]

x = 1 - 3[tex]\sqrt{6}[/tex] or x = 1 + 3[tex]\sqrt{6}[/tex]

Converse, inverse, contrapositive or syllogism

Thanks

Answers

Answer:

7. Contrapositive

8. Converse

9. Inverse

Step-by-step explanation:

Contrapositive is the flipping of the pos/neg and the clauses.

- EX: If it rains today, the ground will be wet -> If the ground is not wet, it did not rain today

Converse is the switching of the clauses

- EX: If I just ate mac and cheese, I am happy -> If I am happy, I just ate mac and cheese

Inverse is swapping the positive/negative (not)

- EX: If I am hungry, I want food -> If I am not hungry, I do not want food

Hope this helps!

130% of what number is 36

Answers

Answer:

27.7

Step-by-step explanation:

130%=1.3

1.3x=36

x=27.7

27.6923077
Or
27.7
...........

please help me on this question.

Answers

answer=

72

hope this helps

:)
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What environmental process is this? A polynomial function has a root of 7 with multiplicity 2, a root of 1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true? The process in this simulation showed an energy transformation that occured as is absorbed and molecules are broken apart and then rearranged to form new molecules during the chemical reaction in the plant cell. A water molecule consists of an oxygen atom and two hydrogen atoms covalently bonded in a bent shape. Oxygen however, attracts the shared electrons more strongly than the hydrogen atoms. This structure leads to which important property of water?a. Water is non-polar, which means it has an uneven distribution of charge making it a good solvent of other non-polar molecules.b. 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A broadexpanse of the river was turned to blood; in the middjedistance the red hue brightened into gold, through wich asolitary log came floating, black and conspicuous; in one place along, slanting mark lay sparkling upon the water; in another thesurface was broken by boiling tumbling rings that were asmany-tinted as an opal; where the ruddy flush was falntest wasa smooth spot that was covered with graceful circles andradiating lines, ever so delicately traced; the shore on our leftwas densely wooded, and the somber shadow that fell fromthis forest was broken in one place by a long, ruffled trail thatshone like silver, and high above the forest wall a clean-stemmed dead tree waved a single leafy bough that glowed likea flame in the unobstructed splendor that was flowing from thesun. There were graceful curves, reflected Images, woodyheights, soft distances, and over the whole scene, far and near,the dissolving lights drifted steadily, enriching it every passingmoment with new marvels of coloring.I stood like one bewitched. I drank it in, in a speechless rapture.The world was new to me and I had never seen anything likethis at home. But as I have said, a day came when I began tocease from noting the glories and the charms which the moon What represents the value of the second-best alternative that a person gives up when making a choice?A marginal spendingB. marginal benefit.opportunity costDmarginal cost