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

HELP ME, THE MIDPOINT OF AB IS M (-4,-7). If the coordinates of A are (-7,-6) what are the coordinates of B?

Answers

Answer:

(-1,-8)

Step-by-step explanation:

Multiply each value of midpoint by 2 and take away given points coordinates

The area of a rectangular wall of a barn is 33 square feet. Its length is 8 feet longer than the width. Find the length and width of the wall of the barn.

Answers

Answer:

Width=3ft

Length=11ft

Given that A = 60° and B = 30'. evaluate (sin
2 cos A) + cos B. leaving your answer in surd
form

Answers

Can you please upload a pic

Which equation shows the quadratie formula used correctly to solve 7x? = 9+X for x?

Answers

Exact form niya is ung pang c

last answer(4 )

x=7x^2-x-9

FAAASSSTTT II HAAVVEE 3 minutes

Answers

Answer:

A. 16 March

Step-by-step explanation:

1) f`(x)=-0.028x+0.448;

2) f`(x)=0, then -0.028x+0.448=0, then

3) x=16 is {max}.

4) answer March 16th.

A wire 18 cm long is cut into two pieces. The longer piece is 6 cm longer than the shorter piece.

Find the length of the shorter piece of wire

Answers

The long piece is 12” and the short one is 6”.

Guys please help out with this asap ! thanks

Answers

you’re gonna wanna round up both sides of your equation which will give u 224, then divide both by 16 which will leave u with 178

Show your solution follow the steps
need an answer, please need an answer, please.​

Answers

Answer:

after calculating I got this answer.

hope this answer helps you dear...take care

Charlie drove 495 miles in 9 hours. How long would it take to drive 715 miles?

Answers

Answer:

13 hours

Step-by-step explanation:

if he drives 495 miles in 9 hours, he drives 55 miles each hour. 55x13=715

Answer:

13 hours

Step-by-step explanation:

Charlie drove 495 miles in

= 9 hours

∴ Rate

= miles/hours

= 495/9

= 55 miles per hour

∴ No. of hours to travel 715 miles

= miles/miles per hour

= 715/55 hours

= 13 hours

Thus, 13 hours would it take to drive 715 miles.

Will mark as brainlist


The title of the poem, "Poetry and Prose, 'is an example of antonyms. Poetry and prose are "opposite' ways of writing.
Search the poem to find the other antonym pairs. Ust the words in the order that they appear in the poem. There are
seven more pairs. Separate each word with a comma. For example: poetry, prose.



If it isn't a poem. It's prose:
And friends cannot be foes.
A package not heavy is light.
And after the day comes night.
if it's ap. it can't be down:
The country is never a town.
When asleep we aren't awake:
To give is never to take

Answers

ah, yes, college mathematics. how riveting

poem, prose

friends, foes

heavy, light

day, night

up, down

country, town

asleep, awake

give, take

I truly commend you on your pursuit of such higher level mathematics studies.  Good luck!

c. The number of men in a community is 2,400. If the ratio of women to men in the community is 5:4,
find
i. The total number of people in the community.
ii. The number of women in the community.
iii. How many more women are there than men if 400 men joined the community.

Answers

Answer:

women : men

5. : 4

x. : 2400

x = 3000

i) 3000 + 2400= 5400

ii) 3000

iii) 3000 - ( 2400+400) = 200

the 4.1 m of concrete is made into the shape of a cylinder. The base has radios 0.5 metres. work out the height of the cylinder ( photo attached)

Answers

Answer:

5.2 metres

Step-by-step explanation:

v = pi. r^2 . h

4.1 = 3.1416 × 0.25 * h

h = 5.22 m

6 ÷ 0.5 plss answer

Marking Brainliest!!

Answers

Answer:

12

Step-by-step explanation:

0.5 = 1/2

6 ÷ 0.5 = 12

or

6 : 1/2 =

6 × 2 = 12

Steven drove 12,060 miles in the last 12 months. On average, how many miles did Steven drive each month?

Answers

The average distance traveled by Steven in 1 month is 1,005 miles.

What is the average?In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. Scoring an average of 85 on the test means may signify a value in the middle of two extremes or the simple average.

So, average miles traveled in 1 month:

Distance Steven drove is 12060 miles.Distance traveled in 12 months.

So, the average distance traveled in 1 month is:

12060/12 1005 miles

Therefore, the average distance traveled by Steven in 1 month is 1,005 miles.

Know more about averages here:

https://brainly.com/question/20118982

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Answer:

The average distance traveled by Steven in 1 month is 1,005 miles.

Step-by-step explanation:

What is the image point of (-5,-6) after the translation

Answers

Answer:

what's the translation?

Which best describes the value of 8 in 3.458?
Since 8 is in the thousandths place, the value of the digit is 0.008.
Since 8 is in the hundredths place, the value of the digit is 0.08.
O Since 8 is in the thousandths place, the value of the digit is 0.08.
Since 8 is in the hundredths place, the value of the digit is 0.008.

Answers

Answer:

Since 8 is in the thousandths place, the value of the digit is 0.008.

um I hope that's correct.


What is the distance between -33 and -18.5 on a number line

Answers

Step-by-step explanation:

The distance between two numbers in a number line is obtained by subtract the two numbers. The order of the subtraction starts with the number a bigger value followed by the number with the smaller value. For example,

x

and

y

are the two numbers and

x

y

, then the correct order should be

x

y

.

Answer and Explanation:

Become a Study.com member to unlock this answer! Create your account

Given the numbers

7

and

11

on the number line, find the distance between the two numbers.

Solution:

Since

7

is...

13.5

absolute value ig

Please answer this question!!!

Answers

Answer:

C: 3x (x-3)=0

Step-by-step explanation:

3x=0 or x-3=0

x=0 or x=3

the differentiation of x^4 + y^4=0 is..?​

Answers

Answer:

I am doinnnnnmngggg gggg

What is the ratio of vowels to consonants?

MATHEMATICS​

Answers

Answer:

3 to 10

Step-by-step explanation:

Vowels are a, e, i, o, u,  sometimes y

Vowels + consonant = Total letters

6 + consonant  =  26

vowels to consonants = 6 to 20 = 3 to 10

Find the value of x so that L||M

Answers

9514 1404 393

Answer:

  x = 19

Step-by-step explanation:

The marked (consecutive interior) angles will be supplementary when the lines are parallel.

  (3x +10)° +(5x +18)° = 180°

  8x = 152 . . . . . . . . . . . . . . . divide by °, subtract 28

  x = 19 . . . . . . . . . . . divide by 8

Convert the unit measure

Answers

41lbs is equal to 656oz

To find the quotient of 3 1/6 multiply 3 by? A.1/6 B.3/6 C.3 or D.6?????!!!!! Hellpppppp meeeeeeeeee

Answers

Step-by-step explanation:

first, you multiply 3 by 6 and then add 1 to the answer the quotient will be 19/6

What phrase in the problem indicates that estimated product is being asked for?


Pa HELP POOOOOOOO​

Answers

Answer:

571 x 32 = 18,272

Step-by-step explanation:

Okay, multiplication was always a favorite.

Think of this, 571 thirty-two times.

4/8 x 4/8

i want some friends
answer if you like and comment if you want to be my friend​

Answers

Answer:

i will be ur friend........ with pleasure

Answer:

1/8

Step-by-step explanation:

Have a good

bye bye

Sidney originally had c cups of Greek yogurt. He used 1.75 cups to make a salad dressing and now he has 5.5 cups left over. Which equation can be used to determine the value of c?
A.1.75c=5.5
B. c/1.75=5.5
C.c-1.75=5.5
D. 1.75+c-5.5

Answers

c. c-1.75=5.5 !:!:!!

he heights of one hundred trees in a certain forest are measured. It’s found that the mean height of the trees is 48 feet. Use this information to answer the following:
Would it be possible to have a standard deviation of 7.5 feet? If so, what would this tell us about the tree heights in the forest?
Would it be possible to have a standard deviation of 1? If so, what would this tell us about the tree heights in the forest?
Would it be possible to have a standard deviation of 0? If so, what would this tell us about the tree heights in the forest?
Would it be possible to have a standard deviation of -2.5? Why or why not?

Answers

Using the concept of standard deviation, it is found that:

It would be possible to have standard deviations of 7.5 feet and 1 feet, which would mean that the distribution of tree heights are normal.It would be possible to have a standard deviation of 0 feet, which would mean that all trees have the same height.It would not be possible to have a standard deviation of -2.5 feet, as it is always a positive value.

The standard deviation of a data-set is given by the square root of the sum of the differences squared of each observation and the mean, divided by the one less than the number of values. It is always a positive value, thus, a standard deviation of -2.5 feet, for example, is not possible.If a data-set has a standard deviation of 0, it means that all values in the data-set are the same.

In a normal distribution, 99.7% of the measures are within 3 standard deviations of the mean.

[tex]48 \pm 3(7)[/tex] and [tex]48 \pm 3(1)[/tex] are both reasonable distributions for the tree heights, thus, it is possible to have standard deviations of 7.5 and 1 feet.

A similar problem is given at https://brainly.com/question/24754716

Henry draws triangle FGH. Then, he translates that triangle to create triangle F'G'H'. The distance from F to F' is 4 centimeters. What is the length of sides GG'? a. 2 cm b. 3 cm c. 4 cm d. 6 cm​

Answers

The length of sides GG' when the distance from FF' is 4 cm is also 4 cm.

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

When you perform translations, you slide a figure left or right, up or down. This means that, in the coordinate plane, the coordinates for the vertices of the figure will change.

It is given that Henry translates the ΔFGH to create ΔF'G'H'.

FF' = 4cm.

Translation is a rigid transformation. In translation, every point of the object must be moved by same distance and in the same direction.

In other words the distance between corresponding points are same.

GG' =?

Since G and G' are corresponding points, so

GG' = FF'

GG' = 4 cm

The length of GG' is 4 centimeters.

Hence, When the distance from FF' is 4 cm, the length of sides GG' is similarly 4 cm. so option C is the correct answer.

To learn more about Translation

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While at School Brian had a math quiz every 6 days and a science quiz every four days. On February 15 he had both tests. Assuming no school days off when will he have both tests on the same day again.

Answers

March 3rd, assuming that it’s not a leap year and there are no school holidays.
Days x # of tests = days until both
6x2=12
4x3=12

pls help me with question 3

Answers

No. I can’t. Just wanting to get some points man, 5 would be nice.
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