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

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Related Questions

Question is in Screenshot/Attachment! Hurry pls.

Answers

Answer:

[tex] y = 6x + 2 [/tex]

Step-by-step explanation:

To write a linear function to represent the situation in the form of y = mx + b, we need to find,

m = slope of the graph

b = y-intercept or starting value

✔️Finding slope (m) using two points on the line, (0, 2) and (1, 8):

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 2}{1 - 0} = \frac{6}{1} = 6 [/tex]

y-intercept (b) = 2 (i.e the value of y when x = 0, which is the starting value oflr the point where the line intercepts the y-axis)

Substitute m = 6, and b = 2 in [tex] y = mx + b [/tex]

[tex] y = 6x + 2 [/tex]

Of the
44
people who started a math class meeting at
10
:
00
each morning, only
37
finished the class. What fraction of people finished the class?

Answers

Answer: .8409 or 37/44

Step-by-step explanation:

Solve the equation. Then check your solution.

- 2/5 + a = 1/5

a. 3/5
b. - 1/5
c. 3/10
d. - 3/5​

Answers

Answer:

3/5 is the correct answer of the question

Answer:

The answer is

[tex] \frac{3}{5} [/tex]

Step-by-step explanation:

Let's solve this equation!

[tex] - \frac{2}{5} + a = \frac{1}{5} \\ \frac{ + \frac{2}{5} \: \: \: \: \: \: = + \frac{2}{5} }{a = \frac{3}{5} } [/tex]

Bobby's dad is 41 and is 6 more than 5 times Bobby's age. Bobby's little sister Emma is one less than half his age. How old are Bobby and his little sister Emma?

Answers

Bobby is 7 and his sister is 3.

Explanation : his dads age : 41
since his dads age is six more than, you would subtract 6 from 41 to get 35.
and since 35 is 5 times bobby’s age you would divide 35 by 5 to get 7
So bobby is 7.

bobby’s sister :
bobby’s age : 7
bobby’s little sisters age is one less than half of his age you subtract 1 from 7 and you would get 6
Now that it’s one less you have to find half so divide 6 by 2 and you’ll get 3
So bobby’s sister is 3.



bobby’s age : 41 - 6 = 35
35 (divided by) 5 = 7
bobby’s sister : 7 - 1 = 6
6 (divided by) 2 = 3

Ron measured his garden to be 12‘ x 8 1/3‘. He plant vegetables in 3/4 of his garden. What is the area of his vegetable garden?

Answers

Answer:

4/4

Step-by-step explanation:

Hope this helped have an amazing day!

Find 83 1/3 % of 384
Also, side info the answer is not 319.872

Answers

Answer:

320

Step-by-step explanation:

First, convert the percent into a fraction.

250/3*100 = 250/300 = 5/6

5/6 of 384 is 5 * 64 = 320

Answer:

320

Step-by-step explanation:

(83 1/3)% of 384 = 320

simplifyyyyyyyyyyyyyyyyyy

Answers

Answer:

Step-by-step explanation:

x^2 - 11x + 30 = (x - 6)(x - 5)

x^2 - 4 = (x + 2)(x - 2)

x^2 + 3x - 40 = (x + 8)(x - 5)

x - 2 = x - 2

Invert and multiply the right fraction.

(x - 6)(x - 5)           (x - 2)

===========   x   =======

(x - 2)(x + 2)          (x + 8)(x - 5)

x - 5 on the top cancels with x - 5 on the bottom

x - 2 on the top  cancels with x - 2 on the bottom left

So what's left?

(x - 6)

===============

(x + 2)(x + 8)

This is likely the answer.

Answer:

[tex]\frac{x-6}{x^{2} +10x+16}[/tex]

Step-by-step explanation:

to much to explain


Help this is really confusing i don’t know how

Answers

I believe that it is D


Enter the rate of change of the table below

This is the table
X. Y

1 73

2 96

3 119

4 142



What is the rate of change



Answers

the rate of change is 23

Solve for x.
2(3x – 4) + x – 1= –16

Answers

Answer:

x=-1

Step-by-step explanation:

it easy fhfhfhrbf

Answer:

-1

Step-by-step explanation:

6x-8+x-1=-16

7x-9=-16

7x=-7

x=-1

Which value is equivalent to the expression 4^5

Answers

Answer:

20

Step-by-step explanation:

Need help ASAP! I'll mark brainlyist

Answers

Step-by-step explanation:

(2+5i) equation goes to -20

(4+I) equation goes to -1

(3+2i) equation goes to 10

and the last one goes to 16

Find the value of x that makes the equation true:

x + 3 = 4

Answers

Answer:

x = 1

Step-by-step explanation:

Subtract 3 from both sides

x+ 3 - 3 = 4 - 3

gives x=1

LAST ONE !!! Ok here

Answers

Answer:

Market economy

Step-by-step explanation:

Once again this is because they are changing their prices and items for sale because of the changes in market.

How long is a guy wire reaching from the top of a 21ft. Pole to a point on the ground 15ft. From the pole

Answers

Answer:

26ft

Step-by-step explanation:

This would form a triangle so you would use Pythagorean theorem to find the hypotenuse ( the longest side )

Harley bought a one year $1000 treasury bond. He paid $950 for the treasury bond. What is his rate of return? Round to one decimal, such as: 6.7%.
0.053%
53%
5.3%
5%

Answers

Answer: 5.3%

Step-by-step explanation:

The formula to compute rate of return is given by :-

Rate of return = [tex]\dfrac{\text{Selling price - investing price }}{\text{ investing price}}\times100[/tex]

[tex]=\dfrac{1000-950}{950}\times100\%\\\\=\dfrac{50}{950}\times100\%\\\\=\dfrac{100}{19}\%\\= 5.3\%[/tex]

Hence,  his rate of return = 5.3%

Find the reference angle for a rotation of 220°.

Answers

Answer:

ans is 40 degree

i hope this is correct

I think it’s 140. 360-220=140

Solve #13 & #14 please ASAP!!!

Answers

Answer:

4th test is a great

Step-by-step explanation:

ok is the for this year as a family

24 = 3y Solve for y and show work

Answers

Y=8 Is The Answer I hope this helps

Answer:

y=8

Step-by-step explanation:

because 3×8 is 24

and 8 would be the missing number

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

Yes, one of the numbers has to be 48 because the mean of numbers is all the numbers added together, and then divided by how many numbers you added. In this case, we have the mean of 6 number is 48. Now if you think about it,
48*6 = 288
And if you divide 288 by 6, you get:
288/6 = 48.
To make it easier for you to understand, let’s do the original way of finding the mean of this, so :
48 + 48 + 48 + 48 + 48 + 48 = 288
There are six 48’s right? So we divide :

48+48+48+48+48+48
——————————— = 48.
6

Which graph below represents the solution to the inequality 6 x − 12 − x ≤ 3

Answers

Answer:

The solution is:

[tex]6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}[/tex]

The graph of the solution is attached below.

Both the number line and graph is attached below.

Step-by-step explanation:

Note: you missed to add the graph options. Therefore, I am solving the inequality and adding the corresponding graph which would anyways clear your concept.

Given the inequality expression

[tex]6\:x\:-\:12\:-\:x\:\le \:3[/tex]

Group like terms

[tex]6x-x-12\le \:3[/tex]

Add similar elements: 6x-x=5x

[tex]5x-12\le \:3[/tex]

Add 12 to both sides

[tex]5x-12+12\le \:3+12[/tex]

simplify

[tex]5x\le \:15[/tex]

Divide both sides by 5

[tex]\frac{5x}{5}\le \frac{15}{5}[/tex]

simplify

[tex]x\le \:3[/tex]

Therefore, the solution is:

[tex]6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}[/tex]

The graph of the solution is attached below.

Both the number line and graph is attached below.

COLOR THEME
Q ZOOM
ADD NOTE
QUESTION GUIDES
3. An architect built a scale model of an office building using a scale in which
2.5 inches represents 20 feet. The height of the building is 240 feet.
12 in
What is the height of the scale model in inches?
30 in.
Ο Ο Ο Ο
80 in.
25 in.
CLEAR ALL
REVIEWS
NEXT >
10
Os
INTL 3.59
(PREVIOUS
its

Answers

Answer:

30 inches

Step-by-step explanation:

240/20=12

12x2.5=30

Answer:

30 inches jrjdbdbrbejjr

Please need help on this one

Answers

If it’s asking for the degrees then the answer is 30, I done that before so..
30 annanamsmsnskksksksksksk

Anyone can answer?? if u can thank u soooo much it means the world to me

Answers

Answer:

Tulips• 7, 14, 21, 28 and 35.

Carnations• 3, 6, 9, 12 and 15.

Other:

Find above the whole number ratio for the tulips and carnations graph. Brainliest? Thanks!

Round 48.47 to the ones place

Answers

Answer:

48.7 I think

Step-by-step explanation:

hears the sender buddy

Answer:

48.5 the 7 is close to 10 so it rounds the 4 to 5

can someone show me how to do ones like this two

Answers

Just muiltply them I think by

how to graph y+9= -3x and find x-intercept

Answers

y+9=-3x can be turned into y=-3x-9 by subtracting 9 on both sides of the equation.
When you graph y=-3x-9 you find that the x-intercept is -9


WILL MAKE BRAINLIST


The booster club needs to raise at least $5000 for new football uniforms. So far they have raised 1,280 enter an inequality to find the a average amounts each of the 97 members can raise to meet the club's objectives

Answers

Answer:

Step-by-step explanation:

5000[tex]\geq[/tex]1280+97x

Translate this sentence into an equation. The sum of 18 and Mabel's savings is 49. Use the variable m to represent Mabel's saving

Answers

Answer:

18 + m = 49 or 49 = 18 + m

Step-by-step explanation:

P.S Can I have brainliest?

In 2007, Linda purchased a house for $120,000. In 2017, the house was worth $245,000. Find the average annual rate of change in dollars per year in the value of the house. Round your answer to the nearest dollar. (Let x = 0 represent 2000)

Answers

Answer:

12500 dollars/year

Step-by-step explanation:

A linear equation i in the form y = mx + b, where y is a dependent variable, x is an independent variable, m is the rate of change and b is the initial value of y (i.e. x = 0).

Let x represent the year and y represent the cost of the house. Given that x = 0 represent 2000, hence we can represent the problem in the form (x, y) as:

(7, 120000) and (17, 245000). The annual rate of change is gotten using:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{245000-120000}{17-7} \\\\m=12500\\\\m=125000\ dollars\ per \ year[/tex]

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