Prove that: 6^7-6^6+6^5 is divisible by 31
15 points!!!

Answers

Answer 1

Step-by-step explanation:

[tex]6^7-6^6+6^5=6^{5+2}-6^{5+1}+6^5\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=6^5\cdot6^2-6^5\cdot6^1+6^5\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\=6^5\cdot(6^2-6^1+1)=6^5\cdot(36-6+1)=6^5\cdot31\\\\6^7-6^6+6^5=6^5\cdot31[/tex]

therefore it's divisible by 31

[tex](6^7-6^6+6^5):31=(6^5\cdot31):31=6^5[/tex]

Answer 2

[tex]6^7 - 6^6 + 6^5[/tex] is divisible by 31.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]6^7 - 6^6 + 6^5[/tex] s

Taking common factors.

[tex]6^5[/tex] (6² - 6 + 1)

[tex]6^5[/tex] (36 - 6 + 1)

[tex]6^5[/tex] x 31

This is divisible by 31.

Thus,

[tex]6^7 - 6^6 + 6^5[/tex] is divisible by 31.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2


Related Questions

HEYYYYYYYYYYYY ONCE AGAIN THIS IS ONLY 3 OF 30 PlS HELPPP

Answers

Answer:

the 3rd one im pretty sure

Step-by-step explanation:

Answer:

the 3rd one <3

Step-by-step explanation:

how do you find a slope

Answers

Answer:

rise/run

Step-by-step explanation:

rise meaning the y value, run meaning the x value

PLZ HELP ME WITH THIS!?!? I WILL MARK BRAINLIEST!!!

Answers

Answer: can it be a bit clearer pls?

Step-by-step explanation:

HELP DUE IN 2 MIN
The ratio of boys to girls in a classroom is 6 to 5. If
there are a total of 18 boys in the classroom, find
the number of girls in the classroom.

Answers

Answer:

15

Step-by-step explanation:

18/3=6

15/3=5

Answer:

15

Step-by-step explanation:

If the ratio is 6:5 and we know the boys are 18, we have 18:?

18/6=3, so we have to do 5*3. 5*3=15.

The ratio is 18:15, the number of girls in the classroom is 15

Felipe sold t-shirts and hats at a festival. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. If he made a total profit
$125, how many t-shirts did he sell?

Answers

Answer:

He sold 17 shirts at the festival.

The total number of t-shirts Felipe sold is 17 t-shirts.

Consider that the number of t-shirts Felipe sold be "x".

Since He made a profit of $5 for each t-shirt sold. Therefore, his profit from selling t-shirts is 5x. also made a profit of $40 from selling hats.

His total profit is given as $125.

So we can write the following equation:

5x + 40 = 125

Subtracting 40 from both sides;

5x = 85

Dividing both sides by 5, we get:

x = 17

Therefore, Felipe sold 17 t-shirts.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ2

Which of the following is equivalent to 75/100? A 2/3 B 10/15 C 25/50 D 15/20​

Answers

Answer:

D. 15/20

Step-by-step explanation: Because if it is 100 divide by 5 then it equals 20 and since 75% is 3/4 then 15/20 is your answer.

Answer:

D 15/20

Step-by-step explanation:

PLEASE I WILL GIVE BRAINlEST ANSWER
"I’m thinking of a number. When I divide my number by four and add seven I get thirteen."


What’s my number? Show your work and explain how you know your answer is correct.

Answers

Answer:

The number is 24

Step-by-step explanation:

This can be written algebraically as:  [tex]\frac{x}{4}+7=13[/tex]

Solve for x, in which the steps are shown below.

Thanks for the question! :)

what's the area of the quadillateral​

Answers

Answer:

The area of the quadillateral is 360 degree.

Step-by-step explanation:

Hope this helped!

Have an amazing day!

if f = 3, g = -4 and h = -5
[3-h]+13

Answers

21 is the answer because -5 becomes a positive since it’s 3-(-5)
The answer is 21 for sure

2 L = _____ ml can someone help? :((

Answers

Answer:

2000

Step-by-step explanation:

Answer:

2000 ml

Step-by-step explanation:

Jake decides to mow lawns for the first two weeks in June to earn money to buy a new bicycle . If the bicycle cost $153.73 and jake chargers $10.25 to mow each lawn, how many lawns will he need to mow in two weeks to buy the bicycle?

Answers

Answer:

14

Step-by-step explanation:

(7+ 1 4) + 6 = 7 ( ■ + 1 6)

Answers

The answer for this is 4.

PLEASE HURRY) The graph indicates the running route for Tobias

Which best describes his run

A. From time 0 to 6, he went fast and then slowed down.
B. From time 6 to 10, he was at his slowest.
C. From time 12 to 14, he went very slow.
D. From time 14 to 18, he went toward the starting point.

Answers

Answer: B. From time 6 to 10, he was at his slowest.

Step-by-step explanation: I just took the same quiz so HURRY!!!

Answer:

b

Step-by-step explanation:

What is the sum of 4.3943 and 5.4157?
A.9.71
C. 9.81
B.9.72
D.9.82​

Answers

Answer:

9.81

Step-by-step explanation:

You have to add them up: 4.3943 +

                                            5.4157

                                            ----------

                                            9.8100

C - 9.81 hope this helps:)

6(x−2)=−18
x=?
Anybody know what X is equal to?
If you know a little bit about this question, thank you for your help.
(If the answer is right, this person will be the smartest.)

Answers

first distribute the 6

6x-12=-18

now we add the 12 to both sides

6x=-6

then we divide 6

x= -1

What is the answer to this radical functions equation ASAP

Answers

It’s d
Hope it help
Mark Brainly

In the diagram m<3 = x +30 and m<4= 2x - 80. What is the measure of angle 3?
A)50
B)80
C)110
D)140

Answers

Answer:

110,........................

Which expression is equivalent to 42 + 12? 7(6+5) 2(40+6) 6(7+2) 10(32+2)

Answers

Answer:

6(7+)

Step-by-step explanation:

1) Start by solving the original equation

42 + 12 = 54

2) Solve the other equations until you find a match

2a) Start with what's in the parenthesis

7(6+5) = 7(11) = 77

2b)

2(40+6) = 2(46) = 92

2c)

6(7+2) = 6(9) = 54

This is your answer

2d)

10(32+2) = 10(34) = 340

Answer: 6(7 +2)

Step-by-step explanation:

Calculate 42 + 12, which is 54.

Calculate 7(6 + 5), which is 7 * 11 = 77.

Calculate 2(40 + 6), which is 2 * 46 = 92.

Calculate 6(7 + 2), which is 6 * 9 = 54.

Calculate 10(32 + 2), which is 10 * 34 = 340.

And, we can conclude the expression 6(7 + 2) is equivalent to 42 + 12.

{(-3.7).(-5, -8), (-6, -1). (-9, -1), (0, -3) }
Domain:
Range
Function?
State if it is a function or not

Answers

Answer:

The domain is the set of all the values of x, so it would be -3, -5, -6, -9, 0. The range would be every set of y, so it would be 7, -8, -1, -3. Finally, this relation is indeed a function.

Domain: -3, -5, -6, -9, 0

Range: 7, -8, -1, -3

Is it a function? Yes

Use mental math to solve the equation.
5) C-(-15) = 38
7) Write a pairs of negative intogoro

Answers

23 I think is the answer

!!! time sensitive please answer !!!

consider the sequence below. 3, 1, 1/3, 1/9

select the explicit function which defines the sequence

A. f(n) = 1/3 • 2^(n-1)

B. f(n) = 2 • (1/3)^(n-1)

C. f(n) = 3 • (1/3)^(n-1)

D. f(n) = 1/3 • 3^(n-1)

Answers

D is the right answer

What is the vertex of the following: y=1/4x^2+2x+6

Answers

Answer:

Yea i definitly just lost brain cells

Step-by-step explanation:

28.2% of 92 this is for math

Answers

Hey there!

Usually when you come across the word “of” in mathematical problems , it simply means that you’re multiplying

So we can simply multiply 28.2% from 92

28.2% = 28.2/100 = 0.282

New equation

0.282 * 92 = the answer

0.282 * 92 = 25.944

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Car X travels 186 miles and 3 hours right the equation of the line that describes the relationship between distance and time

Answers

Answer:

Y=62x

Step-by-step explanation:

The equation of the line that describes the relationship between distance and time is (y = 62x) and this can be determined by using the definition of speed.

Given :

Car X travels 186 miles and 3 hours.

The following steps can be used to determine the equation of the line that describes the relationship between distance and time:

Step 1 - Let the total distance covered by car X be 'y' and the total time taken by car to cover that distance be 'x'.

Step 2 - The speed is given by the ratio of distance to time.

[tex]\rm Speed = \dfrac{Distance }{Time}[/tex]

Step 3 - Now, put the value of distance and time in the above equation.

[tex]\rm Speed = \dfrac{y}{x}[/tex]   ---- (1)

Step 4 - According to the given data the speed is given by:

[tex]\rm Speed = \dfrac{186}{3} = 62\; miles/hour[/tex]

Step 5 - Now, put the value of speed in equation (1).

[tex]\dfrac{y}{x}= 62[/tex]

y = 62x

The equation of the line that describes the relationship between distance and time is (y = 62x).

For more information, refer to the line given below:

https://brainly.com/question/23774048

1. Luis wants to buy Jordans for 75.23. He saves 10.27 per month. Write an equation to solve how many months he'll need to save. Use x for the variable and do not have any spaces.
2. Jovie earns $8.25 for the hours that she is at work. This week she earned $288.75. Write an equation to solve how many hours she worked. Use x for the variable and do not have any spaces. Pls help :(

Answers

Answer:

Chicken nugget

Step-by-step explanation:

Iooooooooooooookkn ooooo

Answers

ooooo nkkooooooooooooooI

Answer:

ok

Step-by-step explanation:

ok  

John made 3 out of 12 attempted baskets in the game. What percentage of the shots did he make?

Answers

Answer:25 percent

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

3/12 as a present is 25%

Representative: “I am planning to attend a company-paid conference. My charges will include $412.00 for airfare, $378.00 for conference registration, and $210.00 for food.” Supervisor: “Please submit an expense form for a total of __________ when you return.”

Answers

The answer is 1,000 dollars. :)

When he returns, the total will be "$1,000".

Given charges are:

For airfare,

= $412.00

For conference registration,

= $378.00

For food,

= $210.00

The total charges will be:

= [tex]Airfare+Conference \ registration+Food[/tex]

= [tex]412+378+210[/tex]

= [tex]1,000[/tex] ($)

Thus $1,000 is the right answer.

Learn more:

https://brainly.com/question/18057159

if i give Mr_MunchlyYumYum 800 bobux and gave him an extra 372 bobux and then cool nbayoungboy182 saw the bobux and took 1000 bobux and then bigwetslimyfart took 341 bobux from nbayoungboy182. nbayoungboy182 gives Mr_MunchlyYumYum 532 bobux. how much bobux does Mr_MunchlyYumYum have? (answer question for 46586373687634587476523498567823686857643872 bobux)

Answers

the answer is spammed key board

Answer:

EZ! 362 bobux

GO TO FLIMFLAM.SHOP

Do any of you guys know the answers to these! Need help

Answers

Answer:

(16) 0    (17) 36

Step-by-step explanation:

8-3 = 5

5x5 = 25

25 / 25 = 1

1 - 1 = 0

and 81 / 9 x 4 = 9 x 4 = 36

Answer:

0 and 36

Step-by-step explanation:

16

25 ÷ (8 - 3)² - 1 ← evaluate parenthesis

= 25 ÷ 5² - 1 ← evaluate exponent

= 25 ÷ 25 - 1 ← evaluate division

= 1 - 1

= 0

17

[tex]\frac{4}{9}[/tex] × 81 = 4 × 9 = 36

Other Questions
add up the total in each row of the tape diagram to determine how many quarts of blue and yellow pains the calry family needs. Question 181 ptsIf JKLM is an isosceles trapezoid, solve for x.(8x 23)(6x + 11)MLHELPPP Convert 6.1x10^4 into standard form ASAP! HELP PLZZ Which statement is true? Select 3 options. A. A function must have a return value. B. A function can use variables as parameters. C. The definition of a function must come before where the function is used. D. The definition of a function can come before or after it is used. E. A function can have more than one parameter. Tariffs are put in place to help do what?A. help the government save moneyB. help the government spend moneyC. earn the government more money How did Voltaires ideas influence the French Revolution? He supported freedom within the rule of law. He saw science as the best way to gain knowledge. He thought that monarchies are more effective than democracies. He believed that knowledge comes through questioning accepted ideas. Which statement BEST describes how the purpose of the Freedmen's Bureau differed from the purpose of the Klu Klux Klan?A It was designed to assist slaves after the Civil War.B It was designed to assist slaves and poor white people after the Civil War.C It was designed to provide land and voting rights to all freed slaves.D It was designed to protect slaves from the violence of Ku Klux Klan members. Rewrite as a simplified fraction 2.67 repeating Need help with these ASAP please Displacement can be added to get the totala) velocityb) distancec) speedd) acceleration HEYYYYYYYYYYYY ONCE AGAIN THIS IS ONLY 3 OF 30 PlS HELPPP The following directions are found at the beginning of a cookbook:1. Always use Pillsbury's Best Flour.2. Sift flour twice before adding to cakes or breakfast cakes.3. Make all measurements level by using edge of knife to lightly scrape off from top of cup or spoon until material is even with the edges.4. Use same sized cups or spoons in measuring for the same recipe.5. Before starting to make recipe, read through carefully, then put on table all the materials and tools needed in making that particular recipe.Based on the passage, the word LEVEL used in #3 most likely means a.to make sure all measurements are the same size. b.to get rid of any excess ingredients. c.to scrape spilled ingredients off the counter. d.to fill the measuring cups to the edge. A video game markup Games galore super store buys the latest video game at a wholesale price of $30.00. The markup rate at games galore is 40%. you use your allowance to purchase the game at the store. How much will you pay,not including tax?a. write an equation to find the price of the game at games galore super store. Explain your equation need help fast!!!!!!!! :(Compound interest is usually better than simple interest because it paysA: interest on the principal and the interest earned in each period. B: interest on the entire principal rather than the interest in each period.C: more, as it is matched by an employers 401k contribution. D: more often throughout the year rather than once a year. Car X travels 186 miles and 3 hours right the equation of the line that describes the relationship between distance and time The unit states that any animal that can be domesticated probably already has been. Explain the logic behind the statement and whether or not you find it convincing. A circular wire loop lies inside a region of space containing a magnetic field. The direction of the magnetic field is out of the screen and parallel to the central axis of the loop. The magnitude of the magnetic field increases as a function of time. A circular loop oriented parallel to the plane of the screen lies inside a region containing magnetic field B. The field is directed out of the screen and is increasing. What is the direction of the induced current in the loop fill in the blank please amino acids as _____ are to words Why..................................................... PLZ HELP!!!!!!!!!!! Part C Colony collapse disorder is a natural phenomenon in which the majority of worker honeybees-bees that collect food for the hive-die at the same time. If several hives in a region experience this phenomenon, how could it affect the life cycle of flowering plants in the region?