chứng minh rằng S= 5+ 5^2 + 5^3 + ...+ 5^1991 + 5 ^1992 chia hết cho 6

Answers

Answer 1

Answer:

steps below

Step-by-step explanation:

5¹+5² = 30        30/6 = 5¹

5³+5⁴ = 125 + 625 = 750     750/6 = 125 = 5³

5⁵+5⁶ = 18750         18750/6 = 3125 = 5⁵

...........

(5¹⁹⁹¹+5¹⁹⁹²)/6 = 5¹⁹⁹¹

sum of every couple consecutive multiple of 5 are multiple of 6, the sum

S= 5+ 5^2 + 5^3 + ...+ 5^1991 + 5 ^1992 IS multiple of 6


Related Questions

The scale drawing at right shows the first slope of a house, the actual dimensions of the garage are 20 feet by 25 feet. All angels are right angels.

A. how many feet does each inch represent? That is, what is the scale?

B. What are the length and width of the living room on the scale and drawing( in inches)?

C. What are the actual length and width of the living room( in feet)?

D. if the family wants to lay carpet in the living room and carpeting cost $1.25 per square foot, how much will carpet cost

Answers

Answer:

See below

Step-by-step explanation:

A)

According to dimensions of the garage, the scale is:

1 in : 20 ft, as the width of the garage is 20 ft and on paper is 1 in

B)

Living room

Dimensions on paper:

2 in x 1 1/4 in

C)

Actual dimensions:

2*20 ft = 40 ft and1 1/4 * 20 ft = 25 ft

D)

The area of the living room:

A = lw = 25*40 = 1000 ft²

Cost of carpet:

1000*$1.25 = $1250

Length

20(2)=40ft

Width

1.25(20)25ft

Area

25(40)1000ft²

Total cost

1000(1.25)$1250

I’m don’t understand stand these that well, can someone please explain step by step to get marked.

Answers

Answer:

10

Step-by-step explanation:

press calculate

pls give brainliest

Answer: 10

Step-by-step explanation:

The sign √ means square root. Squaring is like multiplying a number by its own self again ( for example, x times x is equal to x squared). A square root is like dividing the square by its own self ( for example, √x^2 is equal to x ).

The square root of 100 is 10, since 10 squared is equal to 100.

oh god please help I have no idea what this is

Answers

Answer:

1. 10/7, 2/1, 1,5

2. 5/8 * 3/2

Step-by-step explanation:

(:

Answer:

Which part exactly.. Or which number exactly

The larger trapezoid is dilated form the
smaller trapezoid

Answers

Answer:

are there any equations for this possibly? and if not it is just a smaller scale version of the dilated trapezoid.

Caleb wants to rent a kayak. Kayak rentals cost $70.58  for a half hour. If Caleb rents a kayak for 5.0 hours, how much will it cost him?

Answers

Answer:[tex]{ \times 2 + \times - 20} \div { \times - 4[/tex]

Step-by-step explanation:

divide each of the following: using the two methods

Can you please Help me?

Answers

Answer:

D. 5i

Step-by-step explanation:

edge 2021

how many feet in 2/5 of a mile

Answers

1 mile is equal 5280 feet. So 2/5 of a mile is 2/5*5280=2112 feet.

The answer is 2112.

Find the greatest common factor of 50,75, and 150​

Answers

Answer: 25

Step-by-step explanation:

To find the greatest common factor of an number, you start by listing the factors of each number. The factor that appears the greatest amount of times is the greatest common factor.

175: 1,5,7,25,35,175.

75: 1,3,5,15,25,75.

25:1,5,25.

The number 25 in this case appears the most frequently, therefore the answer is 25.

The greatest common factor (GCF), of the given numbers 50, 75, and 150 is 25.

To find the GCF, we identify the common factors of the given numbers and then select the largest one. The common factors of 50, 75, and 150 are the numbers that divide each of them without leaving a remainder.

In this case, 25 is the largest number that divides all three numbers evenly.

50 = 2 × 5 × 5

75 = 3 × 5 × 5

150 = 2 × 3 × 5 × 5

Since 25 is present as a factor in all three numbers, it's the greatest common factor.

Therefore, The GCF of 50, 75, and 150 is 25.

Learn more about Greatest Common Factor here

https://brainly.com/question/33843471

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Which statements include two quantities in the real world that are additive inverses?

Select each correct answer.


A. Mia walked 5 mi north and then walked 5 mi west.

B. A scuba diver descends 40 m from sea level and then descends another 10 m.

C. Gabriella charges $300 on her credit card and then pays the $300 credit card bill.

D. A helium atom has 2 positively charged protons and 2 negatively charged electrons.

Answers

Answer:

C and D

Step-by-step explanation:

Additive inverse is when two numbers add up to zero.

A. Mia walked 5 mi north and then walked 5 mi west.

False. It would be true if the directions are opposite.

B. A scuba diver descends 40 m from sea level and then descends another 10 m.

False. It is - 40 - 10 = -50 m, not zero

C. Gabriella charges $300 on her credit card and then pays the $300 credit card bill.

True. - $300 + $300 = 0

D. A helium atom has 2 positively charged protons and 2 negatively charged electrons.

True. The atom has neutral charge as + 2 + (-2) = 0

Answer:

It is given

4x+3y=24

We can also write it as

3y=24−4x

 y=324−4x

Substituting x=0 in the given equation

 y=324−4(0)

 So we get 

 y=324

 By division 

 y=8 

 Substituting x=3 in the given equation 

 y=324−4(3)

 So we get

 y=312

 BY division 

 y=4

whats 10x2= n nnn nnnnnnn

Answers

Answer:

20

Step-by-step explanation:

10 x 1 = 10. 10 x 2 = 20.

Answer:

20

Step-by-step explanation:

10 x 1 = 10

Then, 10 x 2 = 20

please help me with this sum​

Answers

Answer:

1. 384

2. 180

3. 324

4. 648

5. 476

6. 528

7. 294

8. 384

9. 414

10. 80

11. 72

12. 301

13. 222

14. 146

15. 156

16. 270

17. 283

18. 300

19. 292

20. 58

21. 64

22. 138

23. 296

24. 170

Hope it helps you

please help...... fast​

Answers

Answer:

SAS

Step-by-step explanation:

HELP MEEEEEEE (−4)÷(14)(−2)

Answers

(-4)/(14)(-2)
=-4/-7
=4/7

Hope this help

IF YOU ARE REALLY GOOD A MATH THEN PLEASE ANSWER THIS !!!
Your help will be much appreciated because i am losing my sanity doing this math

Answers

c-9

to find the amount of parents in the room we'd have take away the amoutn if children in the room from the total amount of people

25-9

thus, your expression to represent the amount of parents would be

c-9

Hope this helped you- have a good day bro cya)

–12+33a −46a

SIMPLIFY

Answers

Answer:

-12-13a

Step-by-step explanation:

Which of the following equations has both -6−6minus, 6 and 666 as possible values of ccc?
Choose all answers that apply:
(Choice A)
c^2 = 36c
2
=36c, squared, equals, 36

(Choice B)
c^3 = 216c
3
=216c, cubed, equals, 216

(Choice C)
None of the above

Answers

Answer:

It's the Choice A c² = 36

Find the product (answer )

-3/10 x 7/10

A) 21/100
B) 4/10
C) -21/100
D) -2/5

Answers

Answer:

[tex]C) -21/100=-0.21[/tex]

Step-by-step explanation:

[tex]→\frac{- 3}{10} \times \frac{7}{10} [/tex]

[tex]→ \frac{ - 3 \times 7}{10 \times 10} [/tex]

[tex] →\frac{ - 21}{100} [/tex]

Answer:

[tex]c) \frac{ - 21}{100} [/tex]

Step by step Explanation:

[tex] \frac{ - 3}{10} \times \frac{7}{10} = \frac{ - 21}{100} \: \: \\ option \: c \: is \: correct[/tex]

3 with an exponent -5

Answers

Answer:The answer would be 1/243

———————————————

In decimal form is would be: 0.00411522 . . .

Answer: 1/243

Step-by-step explanation:

3^-5=  1/(3^5) = 1/ (3*3*3*3*3) = 1/243

Use the IQR to determine if any of the data in the data set are outliers.

{23,80,43,23,0,20,23,23,20,28}

Answers

Using the IQR, the only outlier in the data set is: 0.

What is the IQR of a Data Set?

IQR = upper quartile (Q3) - lower quartile (Q1).

Given the data set, 23,80,43,23,0,20,23,23,20,28:

Quartile (Q1): 20

Quartile (Q3): 31.75

IQR = 31.75 - 20 = 11.75

The outliers are data values that lie below:

Q1  - (1.5 × IQR) = 20 - (1.5 × 11.75) = 2.375

And data values that are above:

Q3 + (1.5 × IQR) = 31.75 + (1.5 × 11.75) = 49.375

Therefore, the only outlier is: 0.

Learn more about the IQR on:

https://brainly.com/question/4102829

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Angle ABC has vertices A(-3,2) B(0,1) and C(-2,-3).
1. Graph angle ABC and its reflection across the line x=-2?
2. What are the coordinates of angle A'B'C' if angle ABC is reflected across the x-axis?
3. What are the coordinates of angle A'B'C' if angle ABC is reflected across the y-axis?
4. What are the coordinates of angle A'B'C' if angle ABC is reflected across the line y=x?
--- Sorry.

Answers

where’s the graph i will try to help

Please answer this question

Answers

Answer:

See explanation below:

see attached file below

–27y • (–z) what is the answer

Answers

Step-by-step explanation:

27yz

that is the answer

brainiest please

Hello!

The answer is 27yz.

Why?

Because if we multiply a negative times a negative, we always get a positive number.

Hope this helps you!

~Just a joyful teen

[tex]SilentNature\\(GraceRosalia)[/tex]

What is this answer

Answers

Answer:

2^3 + 5^2 = 34

7^2 - 3^3 = 22

8^2 + (square root) 100 = 74

Step-by-step explanation:

Hope this helps! Lol I couldn't find the square root symbol.

Find the length of x of the side of the larger triangle. (Assume that the two triangles are similar, and use the fact that corresponding sides of similar triangles are proportional)
X=

Answers

Similar triangles may or may not be congruent

The value of x that makes both triangles similar is 4.5

The equivalent ratio of both triangles is:

[tex]\mathbf{2 : 1 = 9 : x}[/tex]

Express the above equivalent ratio as a fraction

[tex]\mathbf{\frac 12= \frac x9 }[/tex]

Multiply both sides of the fraction by 9

[tex]\mathbf{\frac 12\times 9 = \frac x9 \times 9 }[/tex]

Cancel out common factors

[tex]\mathbf{\frac 12\times 9 = x}[/tex]

Divide 12 by 9

[tex]\mathbf{4.5 = x}[/tex]

Rewrite the above expression as:

[tex]\mathbf{x = 4.5 }[/tex]

Hence, the value of x is 4.5

Read more about similar triangles at:

https://brainly.com/question/14926756

place the boxes in the correct location this Math problem 15 points

Answers

Answer:

but where is the question please type your full questions

Do you have a picture

y-3(2y-7)=76 quick and with steps

Answers

Answer:

y = -11.

Step-by-step explanation:

Y-3(2y-7)=76

Y-6y+21=76

-5y+21=76

-5y=55

y=-11.

Answer:

Step-by-step explanation:

⇔y-6y+21=76⇔-5y+21=76⇔-5y = 76 -21⇔-5y=55 ⇔y= 55:(-5) ⇔y= -11

is a/b +b/c rational number

Answers

Answer:

Yes.

Step-by-step explanation:

Yes.

Assuming a, b and c are integers (not = 0)

a/b + b/c

= (ac + b^2) / bc   which is a rational number.

Hi i need help with this !

Answers

Answer:

4y+8x

Step-by-step explanation:

well, because that was the only one that did not have a line on desmos.

I have more question then this

Answers

reflection over y axis...........

2
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The numbers 7. 11, 12, 13, 14, 18, 21, 23, 27 and 29 are written on separate cards, and the cards are placed on a table with the numbers facing
down.
The probability of picking a card with an even number is?

Answers

Answer:

Answer=3/10

Step-by-step explanation:

even numbers=3

total cards=10

P=number of possible outcomes/total outcomes

=3/10

Answer:

you have a 3/10 probability of geting a even number bc

Step-by-step explanation:

there are ten numbers shown in the question and there are three even numbers out of ten so that is how you get you anewer

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