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.

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Related Questions

A cylindrical soup can has a radius of 8.4 cm and a height of 13.2 cm. What is the volume of the soup can to the nearest tenth of a cubic centimeter?
A= 110.9 cm3

B= 348.3 cm3

C= 673.8 cm3

D= 2926.1 cm3

Answers

Answer:

Option D: 2926.1 cm³

Step-by-step explanation:

Dimensions of the cylidrincal soup can are given as;

Radius; r = 8.4 cm

height; h = 13.2 cm

Formula for area of cylinder is;

A = πr²h

Plugging in the relevant values gives;

A = π × 8.4² × 13.2

A = 2926.05 cm³

Approximating to the nearest tenth gives;

A = 2926.1 cm³

Player pays a fee, then reaches into a large jar and picks out a ball. The jar contains one ball for each letter of the alphabet. If the players picks out a ball with a vowel on it, the player wins 200 dollars. If the player picks out a ball with a consonant on it, the player wins nothing. What fee should be charged to play this game in order for it to be considered a fair game?

Answers

Answer:

€4.20

Step-by-step explanation:

the have a 5 in 26 chance in winning so 26(letters in alphabet) - 5(vowels) =21

21÷5 =4.2

4,0000000000×10,00000000

Answers

Answer:

yes 40

Step-by-step explanation:

she got it correct

Solve for x.
Round to the nearest hundredth if necessary.

Answers

Answer:

4.24

Step-by-step explanation:

By geometric mean property

[tex] {x}^{2} = 6 \times 3 \\ \\ {x}^{2} = 18 \\ \\ x = \pm\sqrt{18} \\ \\ x = \pm 4.24264069 \\ \\ \because \: x \: can \: not \: be \: - ve \\ \\ \therefore \: x = 4.24 \: units \\ [/tex]

please help i will name brainiest

Answers

Answer:

Step-29 (86by-step explanation:

Simplify this expression

help fast please​

Answers

Answer:

C i think

Step-by-step explanation:

g(x) = x^2 + 55
What is the minimum value of the given function?​

Answers

Answer:

Step-by-step explanation:

55.

The solution is, the function doesn't have a minimum value.

What is derivative?

A derivative is described as either the rate of change of a function, or the slope of the tangent line at a particular point on a function.

here, we have,

given that,

the function is,

g(x) = x^2 + 55

now, we have to find the min. value of the function.

so, we have,

g(x) = x^2 + 55

the 1st order derivative is,

g'(x)= 2x

now, we have, critical point, at g'(x)= 0

i.e. at 2x = 0

or, x = 0

so, min. value is at x= 0 of g''(x),

i.e.  g''(x) = 2

so, it doesn't have any minimum value.

Hence, The solution is, the function doesn't have a minimum value.

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Find x in the equation?

Answers

Its 9cm do not mind the K.E (top answer).

What is 39/20 written as decimal ?

Answers

Answer:

1.95

Step-by-step explanation:

39/20 * 5/5 = 195/100
Move decimal over 2 places
Solution: 1.95

Lee is making scarfs for a shelter. He purchased 11 skeins of yarns. Each skein has 660 feet of yarn. He needs 200 yards of yarn to make one scarf.

Answers

Answer:

Give me sum

Step-by-step explanation:

Answer:

Most scarves will use one to two skeins of yarn. According to the chart above, you will probably need about 300–650 yards, depending on the weight of yarn, the colors, the stitches, style, and length amongst other factors.

Step-by-step explanation:

7.) Caleb ran 240 yards. Which answer choices are equivalent to the distance
he ran?
A. 20 inches
B. 2,880 inches
C. 8,640 inches
D 80 feet
E 720 feet

Answers

Answer:

720 feet

Step-by-step explanation:

If you convert 240 yards to feet you get 720 feet. You're welcome! :)

MARKING BRAINLIEST
Find the angle measure

Answers

Answer:

42x - 9 = 35x + 12

42x - 35x = 12 + 9

7x = 21

x = 3

Answer:

Each angle = 117

Step-by-step explanation:

Parallel lines cut by a transversal have only 2 possible answers for each angle. The two answers are supplementary to each other. These two angles are obtuse (both of them) so they are equal.

42x - 9 = 35x + 12         Add 9 to both sides

42x = 35x + 12 + 9        Combine

42x = 35x + 21              Subtract 35x from both sides

42x - 35x = 21               Combine

7x = 21                           Divide by 7

x = 21/7

x = 3

That's not the answer

42x - 9

42*3 - 9

126 - 9

117

a local libary has 2500 fiction books and 5000 nonfiction books what is the nonfiction to fiction ratio in the libary?

Answers

Answer:

Step-by-step explanation:

5000 nonfiction and 2500 fiction

ratio is 5000/2500=2

ratio is 2:1

The correct answer is that the ratio is 2:1. I hope this helps.

2x+5=13


Help me out please

Answers

Answer:

4

Step-by-step explanation: 2x+5=13

                                                  -5   -5

                                                   2x=8

                                                   /2     /2

                                                      x=4

Answer:

X = 4

Step-by-step explanation:

Subract 5 from 5 and 13

Simplify: 2x = 8

divide both sides of the equation by the same term 2x/2 8/2

which gets you x = 4

Find the slope of the line in the given graph.

Answers

Answer:

option A, 3/4

Step-by-step explanation:

slope / gradient formula:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

use the 2 coordinates from the graph

i) (-2,3)

x1 = -2

y1 = 3

ii) (2,6)

x2 = 2

y2 = 6

[tex] \frac{y 2 - y1}{x2 - x1} [/tex]

[tex] \frac{6 - 3}{2 - ( - 2)} [/tex]

[tex] \frac{3}{2 + 2} [/tex]

[tex] \frac{3}{4} [/tex]

Which expression is equal to 1-12|- |-3|?
О-15
9
o 9
o 15​

Answers

Answer:

15 i think 15 or 9 is the answer

Find the product: Negative StartFraction 4 over 9 EndFraction and Negative StartFraction 3 over 8 EndFraction
Negative StartFraction 1 over 9 EndFraction
Negative one-sixth
StartFraction 7 over 17 EndFraction

Answers

Answer:

c 1/6

Step-by-step explanation:

been there done that

Answer:

c

Step-by-step explanation:

i just did the test and got it right, hope this helps ^^

Annie's ant population doubles every week.
After 3 weeks of doubling, how many ants will she have if her colony
started with 50?

Answers

Answer:

400.

Step-by-step explanation:

50 doubles to 100 for the 1st week. 100 becomes 200 the 2nd and 400 for the 3rd week.

Answer:

400

Step-by-step explanation:

just did the work

I need 1 more credit to pass my class!

Answers

Answer:

the answer is 3

Step-by-step explanation:

you piece of garbage im tryna help why u report me

need this done fast pls.

Answers

Answer:

45°

Step-by-step explanation:

85 + 50 + ? = 180

? = 180 - 85 - 50

? = 45

failed my elementary statistics college class, 1st semester, can i retake the same class? or no

Answers

Answer:

I think you can

Step-by-step explanation:

Answer:

I think you can take it in the next semester

Step-by-step explanation:

plEASE HELP ME PEOPLE HUMPTH OK ILL SAY IT PEOPLE WANT MONEY TO ANSWER PROBLEMS HERE If the mean of six nu m b e rs is 48, does one
of the nu m b e rs have to be 48? Explain
why or why not. Give an example with six
nu m b e rs to show your answe

Answers

Answer:

No, none of the number need to be 48 for the mean to be 48. To get a mean, you add up all the number and divide it by the amount of numbers.

Example:

the mean of 10, 79, 42, 88, 19, and 50 is 48, but the actual number 48 was not part of the set.

10 + 79 + 42 + 88 + 19 + 50 = 288

288 ÷ 6 = 48

Geoff earns $9.25 per hour before taxes, and he works 40 hours per week. Geoff's employer withholds (takes out) 10.65% of geoff's income for taxes. What are geoff's total weekly earnings after taxes are withheld?
A) $ 39.41
B) $59.90
C) $ 330.60
D) $ 370.00

Answers

Answer:

a

Step-by-step explanation:

Solve for the variable in the proportion below. Type the number only. Your answer should be a whole number.

2/4 =5/x

x =

Answers

2/4 = 5/x <=>

2x = 5*4 <=>

2x = 20 <=>

x = 20/2 <=>

x = 10

Help me pleaseeeeeeeeeeeeeeeeee

Answers

The answer is 0.06 meters
0.06 meters is the answer

Find the number of subset and number of proper subset from A=(5,6,7,8)

Answers

Step-by-step explanation:

The number of subsets=2ⁿ where n=4 members

2ⁿ=2⁴=16

Number of proper subsets=2ⁿ-1

16-1=15

If a+b/a-b=5/3, what are the following ratios? 2a-4b/a-2b

Answers

Answer:

Hope this may helps you

The value of ratios (2a - 4b) / (a - 2b) is,

⇒ 2

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

The value is,

⇒ (a + b )/ (a-b) = 5/3

Now, We get;

⇒ a + b = 5

⇒ a - b = 3

Hence, By solving above equation,

a = 4

b = 1

Thus, The value of ratios (2a - 4b) / (a - 2b) is,

⇒ (2a - 4b) / (a - 2b)

⇒ (2 × 4 - 4 × 1) / (4 - 2 × 1)

⇒ (8 - 4) / (4 - 2)

⇒ 4 / 2

⇒ 2

Thus, The value of ratios (2a - 4b) / (a - 2b) is,

⇒ 2

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which transformation is happening in the image below​

Answers

Answer:

a

Step-by-step explanation:


PLEASE HELP





John runs 8/10 mile everyday. How many miles does he run in 30 days?

Answers

Answer:

24 miles

Step-by-step explanation:

(8/10)30=24

(8x30)/10

240/10

24

Answer:

24

Step-by-step explanation:

8/10 = 4/5

(4/5) times 30

= 4 times 6

= 24

Which Theorem do you use to solve for D?

Answers

Answer:

D + 50 - 20 = 70

D = 70

Step-by-step explanation:

Angle sum property
d + d +50 + d - 20 = 180
3d = 180 - 50 +20
3d = 150
d = 150/3
d = 50
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