Prove the sum of three consecutive is divisible by three, that the sum of 5 consecutive integers is divisible by 5, but the sum of four consecutive integers is not divisible by 4

Answers

Answer 1

Answer:

Proved

Step-by-step explanation:

Solving (a):

Let the numbers be: [tex]x, x + 1, x + 2.[/tex]

Their sum is:

[tex]Sum = x + x + 1 + x + 2[/tex]

Collect Like Terms

[tex]Sum = x + x + x + 1 + 2[/tex]

[tex]Sum = 3x + 3[/tex]

Divide sum by 3.

[tex]Result = \frac{Sum}{3}[/tex]

[tex]Result = \frac{3x+3}{3}[/tex]

[tex]Result = \frac{3(x+1)}{3}[/tex]

[tex]Result = x + 1[/tex]

Hence, this is true because there is no fractional part after the division

Solving (b):

Let the numbers be: [tex]x, x + 1, x + 2,x+3,x+4[/tex]

Their sum is:

[tex]Sum = x + x + 1 + x + 2+x + 3 + x + 4[/tex]

Collect Like Terms

[tex]Sum = x + x + x + x + x+1 + 2 + 3 + 4[/tex]

[tex]Sum = 5x+10[/tex]

Divide sum by 5.

[tex]Result = \frac{5x + 10}{5}[/tex]

[tex]Result = \frac{5(x + 2)}{5}[/tex]

[tex]Result = x + 2[/tex]

Hence, this is true because there is no fractional part after the division

Solving (c):

Let the numbers be: [tex]x, x + 1, x + 2,x+3[/tex]

Their sum is:

[tex]Sum = x + x + 1 + x + 2+x + 3[/tex]

Collect Like Terms

[tex]Sum = x + x + x + x + 1 + 2 + 3[/tex]

[tex]Sum = 4x+6[/tex]

Divide sum by 4.

[tex]Result = \frac{4x + 6}{4}[/tex]

Split

[tex]Result = \frac{4x}{4} + \frac{6}{4}[/tex]

[tex]Result = x + 1.5[/tex]

The 1.5 means that the sum can not be divisible by 4


Related Questions

mark takes a 40 question test for which he receives 2.5 for each correct answer and losses 1 point for each wrong answer. If mark answers all the questions and gets a grade of 65% of the test, what percent of the questions did he answer correctly?

Answers

Answer:

he answered 26% correctly

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

The radius of a circle is 12 centimeters. What is the circle's area?
r=12 cm
Use 3.14 for a
square centimeters

Answers

Answer:A=452.16

Step-by-step explanation:

A=π·r²

A=3.14·12²

A=3.14·144

A=452.16

Thanks to the rise of texting, emojis are becoming increasingly common. What does this suggest about graphics?

Question 2 options:

They are now a significant part of communication.


They are only used by young people in our society.


They will replace written language entirely one day.


They serve the exact same function as medieval illustrations.
PLEASE IM BEING TIMED

Answers

Answer:

A. They are now a significant part of communication

Step-by-step explanation:

take care

Find the value of w°

Answers

Answer:

w = 59

Step-by-step explanation:

90 + 31 +w = 180

121 +w = 180

w = 180 - 121

w = 59

2. Are the triangles shown below similar
not? How do you know? (Explain your reasoning)

Answers

Answer:

yes the both have all the same angles

Step-by-step explanation:

180-90=90

90-35=55

these triangles are not similar because although they are the same shape, they are not the same size.

How to write the question using the follow sentence#1


Will mark Brainliest

Answers

Answer:

7 times 4 = 28

28 + 6 = 34

Step-by-step explanation:

Find the missing side length

Answers

Option b 10.44 ...........

Please answer this I’ll give you brainliest!!!

Answers

Step-by-step explanation:

im not sure

how many subsset can be obtained from the set A={ m, a ,t ,h}​

Answers

Answer:

Step-by-step explanation:

{m}, {a} , {t} ,{h} ,{m,a}, {m,t} ,{m,h} ,{a,t} ,{a,h} ,{t,h} ,{m,a,t} ,{m,a,h} ,{m,t,h} ,{a,t,h} ,{ m,a,t,h} , {} are the subsets of the given question.

If you found my answer useful then please mark me brainliest.

JOE'S MOUNTAIN BIKE WEIGHS 7 POUNDS MORE THAN ANDY'S. IF THEIR BIKES WEIGH 45 POUNDS ALTOGETHER, HOW MUCH DOES JOE'S BIKE WEIGH?

Answers

Answer:

26

Step-by-step explanation:

45-7=38,

38/2= 19,

19+7=26

Please help me! Will actually mark Brainliest!!!!

Answers

The answer is I think option B

Answer:

B

Step-by-step explanation:

what is the answer? please​

Answers

hahaha so -2x² + 8x -1

can someone see and answer this

Answers

Answer:

D

Step-by-step explanation:

you can rule out answers A through C because the y values never match up to the ones on the table. D shows an increase in y by 4

Can someone help me on this

Answers

9514 1404 393

Answer:

  100°

Step-by-step explanation:

Angle AKC is a vertical angle with angle BKD, so has the same measure. Since K is the center of the circle, arc AC has the same measure as angle AKC: 100°.

__

A diagram may help.

please help me with this
:(((
will give 5 stars

Answers

the answer would be
3x² + 6

Answer:

3x^2+6x

Step-by-step explanation:

the 3rd one

Can y'all help meh please!

Answers

Answer:

__________________the answer is C _____________

Answer:

C.

Step-by-step explanation:

The y intercept is when x=0

so (0, -7) is the y-intercept

slope is found when you subtract y-y1/x-x1

-10- (-7) / 9-0

-3/9

simplified is -1/3

slope is -1/3 and y intercept is (0, -7)

the difference of a number t and 9

t-9 or 9-t

Answers

T-9 the Clue is in the Problem I hope this helps

solve each equation. 7(x+4)-6(x+3)=x+5

Answers

Answer:

7(x+4)-6(x+3)=x+5

or , 7x + 28 - ( 6x + 18 ) = x + 5

or , 7x + 28 - 6x - 18 = x + 5

or , x + 10 = x + 5  

The equation is incorrect !!

Answer:

7(x+4)-6(x+3)=x+5

We simplify the equation to the form, which is simple to understand
7(x+4)-6(x+3)=x+5

Reorder the terms in parentheses
+(+7x+28)-6*(x+3)=x+5

Remove unnecessary parentheses
+7x+28-6+*(+x+3+)=+x+5

Reorder the terms in parentheses
+7x+28+(-6x-18)=x+5

Remove unnecessary parentheses
+7x+28-6x-18=+x+5

We move all terms containing x to the left and all other terms to the right.
+7x-6x-1x=+5-28+18

We simplify left and right side of the equation.
0x=-5

0=-5

The left and right sides are not equal, therefore there is no solution. This equation is invalid.

(hope that helps you out :)

what is 5x – 8x + 2 + 5=

Answers

Answer: -3x+7

Step-by-step explanation: Good luck! :D

Answer:

-3x+7

Step-by-step explanation:

(5x-8x)+(2+5) Like terms together

(-3)x+7 Combine within each group

-3x+7 Simplify the signs in the product

-3x+7 Is your answer

Hope that helps :)

Rose has a rectangular patio that is 5 tiles long and 8 tiles wide. She is changing the dimensions to 10 tiles long by 10 tiles wide. Draw a picture to determine how many new tiles Rose will add to her patio.

A. 5
B. 50
C. 60
D. 100

Answers

Answer:

C. 60

Step-by-step explanation:

First we mjust know that area is length times width (this will be the key to help you)

To find the old area we must: 5*8=40

Then we must find the new area: 10*10 = 100

Now we must subtract the tiles to get the new from old: 100-40=60

Therefore, your answer is 60.

Please mark me brainliest.

The correct answer is c I hope this helpsssssss

How many quarters and dimes must Jada have to equal $2 and 17 coins?

Answers

quarters: 8

dime: 1

explanation: 8 quarters = 2$ and 1 dime = 10 cents

Find each function value f(-7) if f(x) = 3x + 6

Answers

Answer:

-15

Step-by-step explanation:

3*-7=-21+6=-15

Answer:

Step-by-step explanation:

first multiply -7 and 3 since -7 is the element of the function (x)

then you should get (-21)

now add 6 and you answer should be (-15)

pls help i will give brainliest

Answers

Answer:

( -4 , 13 )

Step-by-step explanation:

2 ( -4 ) + ( 13 ) = 5

5 = 5

3 ( 13 ) = 15 - 6 ( -4 )

39 = 39

( -4 , 13 )

i need help on questions 4, 5, and 6. please help!

Answers

Step-by-step explanation:

4) d = √(3-1)²+(7-(-1))²

=√2²+8² = √4+64 =√68

5) AD=29

AB =2x+4,BC=2x,CD=x

AD = 2x+4+2x+x

29=2x+4+2x+x

29=5x+4

29-4=5x

x=25/5

x=5

AB =2x+4

=2(5)+4 =14

BD = BC +CD

= 2x+x

=2(5)+5 =15

8x-5y=-118x−5y=−118, x, minus, 5, y, equals, minus, 11 xxx-intercept: \Big((left parenthesis ,,comma \Big))right parenthesis yyy-intercept: \Big((left parenthesis ,,comma \Big))

Answers

You need to put a picture on here instead of that.
Will you add a picture please we don’t know what you are talking about!


Find the rate of discount for a pair of pants that cost $65 and are on sale for $42.25.

Answers

Answer:

35%

Step-by-step explanation:

42.25÷65 = .65

1-.65 = .35

Your favorite shoes were on sale for 35% off. The shoes have a regular price of $160. Sales tax was 4%. What is the total price paid for the shoes including the discount and tax?

Answers

Answer:

108.16

Step-by-step explanation:

Pls help, SHOW WORKINGS/ explain

Answers

Answer:

C. corresponding angles

Step-by-step explanation:

I think this because 1 and 5 are on the same side and they're angles formed by the transversal line that cuts across

describe the horizontal and/or vertical shifts used to transform the equation y=|x| to the equation y=|x|+4

Answers

It will move 4 to the right horizontally

Someone please help me

Answers

Answer:

Hundreds is 8, tenths is 5, and thousandths is 1!

Answer:

Hundreds: 8

Tenths: 5

Thousandths: 1

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