For which other positive integers a, less than 11, will the number (a^n) + (a^n+1) + (a^n+2) + (a^n+3) + (a^n+4) always be divisible?
Pls, Answer with the entire explanation.

Answers

Answer 1

If the number is supposed to be

[tex]a^n + a^{n+1} + a^{n+2} + a^{n+3} + a^{n+4}[/tex]

then it can be factorized as

[tex]a^n \left(1 + a + a^2 + a^3 + a^4\right)[/tex]

but there's not much to say about divisibility here without any more information about a.

If you meant

[tex]a^n + (a^n+1) + (a^n+2) + (a^n+3) + (a^n+4)[/tex]

simplifying gives

[tex]5a^n + 10 = 5 (a^n+2)[/tex]

which is clearly divisible by 5.


Related Questions

How much time has passed 8:15 to 2:30

Answers

Answer:

The time passed between 8:15 to 2:30 is 6 hours 15 minutes.

What is the median of the followng set of number 1,6,8 and 10

Answers

The answer is 2.5

Step-by-step explanation:

Formula = (N + 1 / 2th) term

So,

Total numbers (N) = 4

Now,

(N + 1 / 2th) term

= (4 + 1 / 2th) term

= (5 / 2th) term

= (2.5th) term

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What factors of -6 have the sum of -5

Answers

Answer:

-6 and 1

Step-by-step explanation:

-6*1=-6

-6+1=-5

Calculate the straight line distance between the points (-10, -7) and (-8,1).
G.2(B)

Answers

Answer:

2√(17) or about 8.2462 units.

Step-by-step explanation:

We want to determine the distance between the two points (-10, -7) and (-8, 1).

We can use the distance formula. Recall that:

[tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Substitute and evaluate:

[tex]\displaystyle \begin{aligned} d &= \sqrt{((-10)-(-8))^2 + ((-7) - (1))^2} \\ \\ &=\sqrt{(-2)^2+(-8)^2} \\ \\ &= \sqrt{(4) + (64)} \\ \\ &= \sqrt{68}\\ \\ &= 2\sqrt{17}\end{aligned}[/tex]

Hence, the distance between (-10, -7) and (-8, 1) is 2√(17) units or about 8.2462 units.

[tex] \qquad \qquad\large\rm{Together \: We \: Go \: Far!} \\ \qquad \qquad \sf \small{\red{♡}\:Swifties\:\red{♡}}[/tex]

Question :-

Calculate the straight line distance between the points (-10, -7) and (-8, 1).

Answer :-

The straght line distance between the two points is 8.2462 units.

[tex] \rule{200pt}{3pt}[/tex]

Solution :-

As per the provided information in the given question, we have been given that:

[tex](x_1, y_1) = (-10, -7)[/tex][tex](x_2, y_2) = (-8, 1)[/tex]

To calculate the distance between the two points, we will apply the formula below:

[tex] \bigstar \: \: \: \boxed{ \sf{ \: \: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \: \: }}[/tex]

Substitute the given values into the above formula and solve for d:

[tex]\sf:\implies{ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}[/tex]

[tex]\sf:\implies{d = \sqrt{[-8 - (-10)]^2 + [1 - (-7)]^2}}[/tex]

[tex]\sf:\implies{d = \sqrt{(2)^2 + (8)^2}}[/tex]

[tex]\sf:\implies{d = \sqrt{4 + 64}}[/tex]

[tex]\sf:\implies\bold{d = \sqrt{68} \approx 8.2462 \: units}[/tex]

Therefore :-

The straght line distance between the two points is 8.2462 units.

[tex]\\[/tex]

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12 4 + 2 X 3 Evaluate 2 O A) 11 OB) 13 OC) 20 OD) 27​

Answers

4 + 2 · 3² = 4 + 2 · 9 = 4 + 18 = 22

22 : 2 = 11

Answer → A)

If a distribution is skewed to the right with no outliers, which expression is correct?
mean < median
mean ≈ median
mean = median
mean > median
We can’t tell without examining the data.

Answers

Answer:

Mean>Median

Step-by-step explanation:

A right skewed distribution with no outliers will have it's mean value greater than the median ( mean > median)

A distribution is said to be right skewed if it's peak is to the left such that it has a long tail to the right.

Conversely, a distribution with it's peak to the right such that it has a long tail is said to be left skewed.

Using the analogy of a boxplot, a right skewed distribution will have it's box to the left and a longer whisker to the right. This means that the median point which is the vertical line in between the box will be lesser than the mean value.

Median < mean = mean > median

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Please help i will give extra points

Answers

Answer:

20

Step-by-step explanation:

solve expression like in the image attached

The answer to your question is 20

the radius of a circle is 3 in . find area to the nearest tenth

Answers

The radius r = 3 in

Area of circle = πr² = 3.14*3*3= 28.26 in²

(5.01 x 10^5) / (7.8 x 10^2)

Answers

Answer:

numerator; 5.01×(10^5)= 5.01×100000

denomenator ; 7.8×(10^2)= 7.8×100

therefore : 501000/780

= 642.3077 answer

Which product is negative?

Answers

Answer:

Second answer

Step-by-step explanation:

first answer: 4 negative numbers  multiplied = 2 postive numbers multipled = 1 positive number

second answer: 3 negative numbers multiplied = 1 positive number multiplied by 1 negative number = 1 negative number

third answer: Negative and positive numbers multiplied by zero = 0

fourth answer: 2 negative numbers multiplied by 2 positive numbers = 1 positive number multiplied by 1 positive number = positive number.

-6 * -6 + 7 * -6 + 8​

Answers

Answer:

0

Step-by-step explanation:

The * means multiplication where the ^ means exponents, so you multiply in this case.

-6 * -6 = 36

Two negatives equals a positive.

PEMDAS shows that multiplication and division occurs first so...

7 * -6 = -42

36 + -42 + 8

-8 + 8

= 0

You can search it up to see what PEMDAS is.

The process of translating phrases or sentences into algebraic expressions or equations is called

Answers

Answer:

Modeling with Linear Equations

In this section, you will use algebra to solve problems that occur in real-life situations. The process of translating phrases or sentences into algebraic expressions or equations is called

Answer:

Modeling with Linear Equations

In this section, you will use algebra to solve problems that occur in real-life situations. The process of translating phrases or sentences into algebraic expressions or equations is called

Step-by-step explanation:

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7th grade math find the volume of the solid

Answers

Answer:

252 Inches cube

Step-by-step explanation:

So for this question you need to find the area of cross section which is the H,

2 Times (3 Inches by 7 Inches) {The 2 same shape}

+

3 Inches by 7 Inches {The middle shape}

For the H Shape = 63 Inches Square

Then you'll time the lenght which is given 4 Inches

63 Inches square ×4 Inches

252 Inches Cube

The volume of this shape will be 252 Inches cube

Hope this helps dont hesitate to ask any question!!

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To evaluate the following expression, what step should you do first? 7 X (4 + 16) = 4 - 2​

Answers

Answer:

Remember BODMAS

Bracket first, then division, then multiplication, then addition, then substraction

Answer:

PEMDAS

Step-by-step explanation:

In order to evaluate the expression, use PEMDAS. It stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.7 × (4 + 16) ÷ 4 - 2 7 × 20 ÷ 4 - 2 = ?140 ÷ 4 - 2 = ?35 - 2 = ?32

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

4(x − 3) = 8
solve please

Answers

4x-12=8
4x=8+12
4x=20
x=5

Answer:

x = 5

Step-by-step explanation:

4(x - 3) = 8

=> x - 3 = 8/4

=> x - 3 = 2

=> x = 2 + 3

=> x = 5

3x(2 + 5y)?

What is the correct formula to get the correct answer ?

Answers

Answer:15xy+6x

Step-by-step explanation:

3x(5y+2)

15xy+6x

0.066 rounded to the nearest cent

Answers

It would be 0.07 cents

Write 2 1/4 miles in 3/4 hour as a unit rate.

Answers

6 3/4 per hour or in an hour

6 3/4 per hour or, in an hour

2 1/4 miles in 3/4 of an hour

2 1/4 miles = 9/4 miles in 1/3 of hour

9/4 miles divided by 1/3 hr

9/4 ÷ 1/3

Remember: Keep, Change Flip

9/4 x 3/1 = 27/4

Simplify:

27/4 = 6 3/4

So,

6 3/4 in one hour

I hope this helps!

A box has 59 cubic inches we need to find what is the length and width and also height explain how you got the answer and also solve the problem

Answers

Answer:

59÷4

you will find the answer

What is the difference between the mass of a solid and the mass of a liquid?

Answers

Answer:

A solid is a form of matter characterized by a particular shape that also has volume. A liquid, on the other hand, has volume but no exact shape, taking the shape of its container. The molecules in solid matter are compressed as its molecules are closely bound together and can only vibrate.

Fatore a expressão algébrica a seguir:

20x³ y³ + 10x² y² + 2xy

Answers

Answer:

[tex]32 {x}^{6} {y}^{6} [/tex]

The length of a rectangle is four times its width. If the perimeter of the rectangle is 50 in, find its area

Answers

Answer:

The perimeter of a rectangle is the sum of all of it’s sides. Since a rectangle has 2 lengths of the same size and two widths of the same size, the perimeter is length + length + width + width, or 2(length) + 2(width), or, to make it shorter, 2l + 2w.

Since the length of the rectangle (l) in this scenario is really 4w, we can replace those, and get 2(4w) + 2w, and since we know the total is 50, we can say 2(4w) + 2w = 50.

Using the distributive property, we get 8w + 2w = 50, and 10w = 50, or w = 5. Since the length is 4w, the length is 4*5 = 20.

To find the area, you multiply length and width to get 5 * 20 = 100 sq meters.

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number 15. The digit in the hundred thousands place has 10 times the value it would have if it was in the (blank) place.

Answers

Answer:

ten thousands place

Step-by-step explanation:

10,000 × 10 = 100,000

Solve the equation
5(x + 8) = 4(x - 8) + x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution is
(Simplify your answer.)
OB. The solution is all real numbers.
O C. There is no solution.

Answers

9514 1404 393

Answer:

  A. the solution is x = -72

Step-by-step explanation:

Eliminating parentheses gives ...

  5x +40 = 4x -32

  x = -72 . . . . . . . . . . . subtract (4x+40)

There is one solution: x = -72.

Given are the slopes of several lines. Indicate whether each line is horizontal, vertical, rises from left to right, or falls from left to right.

Answers

Answer:

Rises from left to rightVertical LineHorizontal LineFalls from left to right

Step-by-step explanation:

Keep in mind we read graphs from left to right just like how we read and write.

A positive slope will be increase from left to right. A negative slope with decrease left to right. A vertical line will have a undefined slope.A horizontal line will have a slope of 0.

We can use those tips to solve the problem.

Option A:

4/5 is a positive slope so it will rise from left to right.

Option B:

No slope automatically means "undefined" so that falls in the definition of a vertical line.

Option C:

A slope of 0 is defined as a horizontal line.

Option D:

-4/5 is a negative slope so it will fall from left to right.

Best of Luck!

What is the approximate value of each radical expression to the nearest tenth?

Drag and drop the answer into the box to match each radical expression.​

Answers

Answer:

19−−√ 4.4

23−−√ 4.8

37−−√ 6.1

Step-by-step explanation:

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The value of the radical expressions is given below:-

√19 = 4.4

√23 = 4.8

√37 = 6.1

What is a radical expression?

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The radical expression is one in which all the numbers are represented in the form of the roots.

The given expressions are √19,√23, and √37. The value of the radical expressions are given below:-

√19 = 4.4

√23 = 4.8

√37 = 6.1

Therefore, the answers are given above.

To know more about radical expressions follow

https://brainly.com/question/738531

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Lol help What is 3.5 × 1.2 =

Answers

Answer:

4.2

Step-by-step explanation:

3.5 x 1.2 = 4.2

Answer:

3.5 x 1.2 = 4.2

Step-by-step explanation:

Write a addition equation or a subtraction your choice to section your diagram

Answers

Answer:

7 - 2 = 5

Step-by-step explanation:

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Fun Fact: The hagfish is the only animal that has a skull but no spine.

1 1/11 rewrite each number as a single fraction greater then one

Answers

Answer:

12/11

Step-by-step explanation:

11/11=1

1/11=1/11

11/11+1/11=12/11

[tex]1\frac{1}{11}[/tex]  rewritten as a single fraction is 12/11

[tex]1\frac{1}{11}[/tex] is a mixed fraction.

A fraction is a number that is made up of a numerator and a denominator.

A mixed fraction is made up of a whole number and a proper fraction. A proper fraction is a fraction that is made up of a numerator that is less than a denominator.

For example, [tex]\frac{1}{11}[/tex] is a proper fraction. The numerataor,1, is less than the denominator, 11.

We are to convert the mixed fraction to an improper fraction. An improper fraction is a fraction that its numerator is greater than the denominator.

In order to convert to an improper fraction, take these steps

multiply the whole number with the denominator ( 1x 11) = 11Add the numerator to the answer gotten in the previous step = 11 + 1 = 12 Divide the answer gotten in the previous step by the denominator : 12/11

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I really do need help solving this equation

Answers

Answer:

D

Step-by-step explanation:

3/5 = 0.6

75% = .75

0.8, 0.75, 0.6, 0.56

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