proves that the sum of
5 consecutive natural numbers is divisible by 5 ​

Answers

Answer 1

Answer:

n = 5m + 10 = 5(m + 2), since m + 2 is an integer, then the n is divisible by 5.

Step-by-step explanation:

Answer 2

Answer:

Natural numbers are simply positive integers.  For now, refer to the middle number (the third number), as x.  Thus, the numbers are: x - 2, x - 1, x, x + 1, and x + 2.  Simply add all these numbers to get 5x, a number that is divisible by 5.  As such, you can conclude that any 5 consecutive numbers are divisible by 5, and the quotient would be the third, or middle number.

Hope it helps :) and let me know if you want me to elaborate.


Related Questions

The sum of two numbers is 88. The larger number is 16 more than the smaller number. What is the smaller number?

Answers

Answer: please mark me brainliest

28

Step-by-step explanation:

you half 88 you get to 44 and then you add 16 that is 60. 88 subtract 60 is 28

recipe☝️
Question: How many cups of sifted cake flour will you need for 2 cakes? Show your work.​

Answers

Answer:

5 cups of flour need to make two cakes

2.9. What is the equation of a line parallel to 3x + 4 = y and passing through
(4,-2)?
A. 3x + 10 = y
B. 3x – 14 = y
C. -*-=y
D. --*x+10=y

Answers

Hello! (:

3x+4=y

We want to convert it into slope-intercept form:

y=mx+b

Our equation looks like this:

y=3x+4

Now, parallel lines have the same slope. So if one line has a slope of 3, the line parallel to it has a slope of 3 as well.

Now, we have the slope and a point, so we write the equation in point-slope form:

y-y1=m(x-x1)

y-(-2)=3(x-4)

y+2=3x-12

y=3x-12-2

y=3x-14

Hence, that is the required equation, Hope it helps you!

If you have any question or query, feel free to ask! (:

~An excited gal

[tex]SparklingFlower (:[/tex]

The lengths of the sides of a triangle are square root 139, square root 73, and 6. Classify the trianglo as “acute", "right", or "obtuso".
Choose the correct type of triangle below.
O acute
obtuse
Oright

Answers

Answer:

It's obtuse.

Step-by-step explanation:

Mumble. Smells al-kashi laws of cosine to me.

[tex]a^2-b^2-c^2 = -2bc cos\alpha\\b^2-c^2-a^2=-2ca cos \beta\\c^2-a^2-b^2=-ab cos \gamma[/tex]

Now, we don't need to calculate the RHSs, and then:

If at least one of the three LHSs is greater than zero, the triangle is obtuse

If at least one is zero, it's a right triangle (pythagorean theorem anyone?)

if all three numbers are less than zero, the triangle is acute

Start crunching numbers.

[tex]139-73-36 = 30[/tex] First try was  the charm. finding 30 means that the product [tex][-2(\sqrt{73})(6) ]cos \alpha[/tex] is positive, and since the product in the large bracket is negative, the cosine has to be 0, thus the angle has to be greater than 90°, QED

Rachel has a $23,000 six year loan with APR of 7.25%

Answers

Answer:6,000 is the answer

Step-by-step explanation:

can someone please help me! :) ​

Answers

A all the other answers are too high or too low for the day on speaker

What is the stimated difference of 31,523 - 23,589

Answers

Answer:

8000 (Estimated) and the real difference would be 7934

Step-by-step explanation:

An estimated difference would be 8000, we get this number by subtracting 23,000 from 31,000 to make the subtraction much faster. The real answer to this would be 7934 which is pretty close to 8000 which is the estimation

Liam invests $3,670 in a savings account at his local bank which gives 1.9% simple annual interest. He also invests $2,040 in an online savings account which gives 5.5% simple annual interest. After five years, which one will have earned more interest, and how much more interest will it have earned, to the nearest dollar?

Answers

Step-by-step explanation:

Given:

Investment P₁ = $3670Investment P₂ = $2040Rate of interest r₁ = 1.9% SIRate of interest r₂ = 5.5% SITime t = 5 years

Find amount of interest in both investments:

I₁ = P₁r₁t = $3670*(1.9/100)*5 = $348.65I₂ = P₂r₂t = $2040*(5.5/100)*5 = $561.00

As we see the online savings account earns more interest and the difference is:

$561.00 - $348.65 = $212.35 ≈ $212

Which of the following expressions has the greatest​ value?

Answers

Answer:

[tex](0.1)^2[/tex]

Step-by-step explanation:

The top number known as an exponent tells you to multiply the number by its self that many times so the other number will get very small.

Hey there!

Option A.

0.01^4

= 0.01 * 0.01 * 0.01 * 0.01

= 0.0001 * 0.0001

= 0

Option B.

0.1^4

= 0.1 * 0.1 * 0.1 * 0.1

= 0.01 * 0.01

= 0.0001

Option C.

0.01^3

= 0.01 * 0.01 * 0.01

= 0.001 * 0.01

= 0.00001

Option D.

0.1^2

= 0.1 * 0.1

= 0.01

“ 0.01 > 0.0001 > 0.00001 > 0”

Therefore, your answer should be: 0.1^2 (option D)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

HELP ASAP FOR BRAINLIST CROWN
Which function has the greater y-intercept? What is that value?

-10


4


10


3


16


Function A; 1.5


Function B; 30


Function B; 23


Function B; 3


8


2


Function A; 1


Function B; 1


Function A; 9

Answers

Answer:

function A;1

function B:30

Help pls I don’t understand this shi

Answers

Answer:

It's kind-of blurry, can you copy-paste the questions?

Step-by-step explanation:

Pls answer the questions, I would really appreciate it, thx, :)

Answers

Answer:

7V

The average amount of minutes exercised on each day

Step-by-step explanation:

We are given that every day "V" amount of vegetables are eaten everyday.

If there are 7 days in a week then the amount of vegetables eaten in 1 week would be 7V

E = ( M + W + F ) / 3

M = # of minutes exercised on Monday

W = # of minutes exercised on Wednesday

F = # of minutes exercised on Friday.

Note that to find the average of something you find the sum of the values and divide that by the number of values.

The equation "E" is adding up the # of minutes exercised on Monday, Wednesday and Friday and dividing the sum of that by 3, which happens to be the number of values being added( those values being the # of minutes exercised on Monday, Wednesday and Friday) . So we can conclude that the equation E represents an average, more specifically the average # of minutes exercised on each day.

1.
What is the sum of
4 |
22 (1 point)
+
+
3
011
o

IN IN NII am |
0
0 0

Answers

Answer:

B. One whole number one over two. 1½

Wjejjejjsnsbbnxkskakksnsnsnznsmsnndndd

Answers

Answer:

whats

Step-by-step explanation:

[tex]\orange{\rule{40pt}{555555pt}} \green{\rule{40pt}{555555pt}} \blue{\rule{40pt}{555555pt}} \red{\rule{40pt}{555555pt}}\pink{\rule{40pt}{555555pt}}\yellow{\rule{40pt}{555555pt}}[/tex]

omg please help idek ​

Answers

I believe The exact form is 2/45, while the decimal form would be 0.4 continuous

Elena sold ice cream at the fair. One day she sold one-third of the gallons of vanilla ice cream that she had, and then gave away 3 more gallons of vanilla ice cream. At the end of the day, she had one gallon of vanilla ice cream left. Write an equation to find how many gallons of vanilla ice cream Elena had at the beginning of the day.

Answers

Answer:

Nn seem xjjxjjxncjicucdjxklzkjcjfnfklcocjcnndjcicjcnmdjdjxjxjcjcjckckckkckcmcjdjcjceujesjkxmcmckkckckckckckck

Step-by-step explanation:

Fand the most part in 2? the best. I think you are awesome. edit! edit on your post? edit! I cut off a bit of payer

Can some one help quickly. Please show work

Answers

Answer:    the answer is  2

Step-by-step explanation:

Solve the equations.
[tex]\sqrt{x^{2} } =14[/tex]
[tex]\sqrt{x^{2} } =17[/tex]
[tex]\sqrt{y^{2} } =5[/tex]

Answers

Answer:

[tex]x=\pm14\\x=\pm17\\y=\pm5[/tex]

Step-by-step explanation:

Generally, equations in the form [tex]\sqrt{x^2}=c[/tex] where [tex]c[/tex] is some constant, would have [tex]x=\pm c[/tex] as its solution.

This is because the square of a number is always positive regardless of the sign of [tex]x[/tex].

what type of triangle is ABC,give reasons ​

Answers

Answer:

ABC in the given figure is an equilateral triangle, its all sides are equal. AB = BC = CA. (i) A triangle in which all the three angles are acute is called an acute angled triangle

there is a bag filled with 6 blue and 5 red marbles.
a marble is taken at random from the bag the colour is noted and then it is replaced. another marble is taken at random. what is the probability of getting 2 reds​

Answers

Answer:

Step-by-step explanation:

The probability of obtaining a red marble in one sample is 5/11. Since you are sampling twice the probability of picking a red marble both times is 5/11 x 5/11 = 25/121. That is slightly less than one time in five.

Rewrite the equation below so that it does not have fractions.

3/4x-5=3/8

Do not use decimals in your answer.

Answers

Answer:

x=  

6

43

 

Step-by-step explanation:

pasos  

4

3

x−5=  

8

3

Agrega 5 a ambos lados.

4

3

x=  

8

3

+5

Convertir 5 a la fracción  

8

40

.

4

3

x=  

8

3

+  

8

40

 

Como  

8

3

 y  

8

40

 tienen el mismo denominador, sume sus numeradores para sumarlos.

4

3

x=  

8

3+40

 

Suma 3 y 40 para obtener 43.

4

3

x=  

8

43

 

Multiplica los dos lados por  

3

4

, el recíproco de  

4

3

.

x=  

8

43

×(  

3

4

)

Multiplica  

8

43

 por  

3

4

 (para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).

x=  

8×3

43×4

 

Realiza las multiplicaciones en la fracción  

8×3

43×4

.

x=  

24

172

 

Reduzca la fracción  

24

172

 a su mínima expresión extrayendo y anulando 4.

x=  

6

43

 

6x=43 should be the answer

how did you get m in the equation

Answers

to get m in an equation u find it in y=mx+b

Please solve these.
You will get all of my points if you get all of them correct

Answers

Answer:

Step-by-step explanation:

1) Area of triangle= 1/2 x b x h

b = 7.6cm h= 3.4cm

Area= 1/2 x 7.6 x3.4 = 12.92cm²

2)Divide the shape into a triangle and a rectangle

Area of rectangle : l x b

L= 20cm, b= 7cm

= 20 x 7 = 140 cm²

Area of triangle =1/2 x b xh

B = 20cm, h= 16 - 7 = 9cm

1/2 x 20x 9= 90cm²

Total area = 140 + 90 = 230cm²

3) area of triangle = 1/2 x b x h

B = 12cm, h= 5cm

= 1/2 x 12 x 5 = 30cm²

4) area of triangle = 1/2 x b x h

B = 15cm, h= 8cm

= 1/2 x 15 x 8 = 60cm²

5) divide the shape into two rectangles; the lower and the upper

Area of rectangle= l x b

Upper rectangle, l= 10cm, b= 27 - 9 = 18cm

Area= 10 x 18= 180cm²

Lower rectangle, l= 24cm, b= 9cm

Area = 24 x 9= 216cm²

180 + 216 = 396cm²

What is the range of the graphed function?
O [x1-2 O [yI-2 O {x | x is a real number}
O [vl y is a real number}

Answers

Answer:

first one my sister tried it

Step-by-step explanation:

graph the line y=3(x+3)+4

Answers

Answer:

Check out the image below the explanation.

Step-by-step explanation:

1. First, let's simplify the equation.

[tex]y = 3(x) + 3(3) + 4[/tex] [tex]y = 3x + 9 + 4[/tex] [tex]y = 3x + 13[/tex]

2. Since the equation is y = 3x + 13:

The y-intercept is 13.For every 1 unit we go to the right, we go 3 units up.

Now, here's the graph!

Wendy was riding her bike along a trail and travelled 63 miles in 6 hours. When Iman was riding on the same trail she travelled 10.1 miles per hour. What was Wendy's unit rate for her bike ride? (Miles per Hour) Who was riding faster?

Answers

Wendy was going faster at 10.5 mph.

To find mph, you divide the distance by the time. 63 divided by 6 is 10.5, which is faster than 10.1

The dimensions of a right triangle are shown in the diagram.

What is the length of the missing side, to the nearest tenth of a centimeter?

Answers

Answer:

18.4 cm

Step-by-step explanation:

For this problem, you would use Pythagorean Theorem or a^2+b^2=c^2. Don't forget that the c in the formula is always your hypotenuse or the longest side of the triangle. The a and the b are always the legs of the triangle. (It doesn't matter which leg is which letter) The hypotenuse is also always across from the 90 degree angle. Picture the 90 degree angle as an arrow pointing to the hypotenuse.  In this case, the hypotenuse (or c) is 20.7 cm. Now all you have to do is plug and chug! I hope this helps you and thanks for asking your question!!

If the nth term of a number sequence is 5n – 2n, find the first 3 terms and the 10th term.​

Answers

Answer:

0,3,6, and 30

Step-by-step explanation:

What is the best estimate for the volume of a jug of milk?

Answers

Answer:

3.785 litres

Step-by-step explanation:

The 5th term of an arithmetic sequence is 30, while the 13th term is 70

Answers

Answer:

a = 10

d = 5

Step-by-step explanation:

[tex]a_{n}=a + (n-1)d\\\\a_{5}=30\\\\a + (5-1)*d=30\\\\[/tex]

a + 4d = 30 ------------------(I)

[tex]a_{13}=70\\\\a + (13-1)d=70[/tex]

a + 12d =70 -------------(II)

Multiply equation (II) by (-1) and then add.So, 'a' will be eliminated and you can find the value of d

(I)         a +   4d = 30

(II)*(-1)   -a - 12d = -70   {Now add}

               - 8d   =  - 40

Divide both sides by (-8)

d = -40/-8

d = 5

Plugin d = 5 in equation (I)

a + 4*5 = 30

a + 20 = 30

a = 30 - 20

a = 10

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