n is the middle integer of three consecutive positive integers.
The three integers are multiplied to give a product.
n is then added to the product.
Prove that the result is a cube number.
n must be used in your proof.
Your final line must consist of only,
= n^3

Answers

Answer 1

Answer :

[tex]\boxed{\textsf{ The final answer is \textbf{n}$^{\textbf{3}}$ .}}[/tex]

Step-by-step explanation:

Its given that n is the middle out of the three consecutive integers . So ,

The last integer will be :-

[tex]\sf\implies Last \ Integer \ = \ n - 1 [/tex]

The next Integer will be :-

[tex]\sf\implies Next \ Integer \ = \ n + 1 [/tex]

Now the Question says that the three integers are multipled to give a product . So that would be.

[tex]\sf\implies Product_{(three\ consecutive\ integers)}= (n-1)n(n+1) = (n^2-1)(n) = \pink{n^3-n}[/tex]

Now thirdly it's given that n is added to the given integer . That would be ,

[tex]\sf\implies Adding\ n = \ n^3 - n + n = \pink{n^3} [/tex]

Here - n and +n gets cancelled. So we are ultimately left out with .

Hence the final number is a cube of some number.

Answer 2

The result is n³.

What are consecutive number?

Numbers that appear in a particular order are known as consecutive numbers. Every pair of numbers has a difference of one. The mean and median of consecutive numbers are equal. In the event that n is a number, n, n+1, and n+2 would be consecutive numbers.

Given three consecutive positive integers,

and middle integer is n

the integer before n is (n - 1)

the integer after n is (n + 1)

product of three integer is

(n - 1) × n × (n + 1)

(n² - 1) × n

n³ - n

now add n in product

n³ - n + n

Therefore, the result is n³.

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Related Questions

can you help me please ​

Answers

Answer:

437.3 ft

Step-by-step explanation:

By sine rule:

[tex] \frac{x}{ \sin(90 - 29) \degree} = \frac{500}{ \sin \: 90 \degree} \\ \\ \frac{x}{ \sin 61 \degree} = \frac{500}{1} \\ \\ x = 500\sin 61 \degree \\ \\ x = 500 \times 0.8746197071 \\ \\ x = 437.309854 \\ \\ x = 437.3 \: ft[/tex]

Answer:

437.3 ft

Step-by-step explanation:

ΔA = 90° - 29°

= 61°

sin A = perpendicular ÷ hypotenuse

sin 61° = x ÷ 500 ft

0.8746 = x ÷ 500 ft

x = 500 × 0.8746

x = 437.3 ft

plz follow me

Solve for x, please!

Answers

Answer:

45

Step-by-step explanation:

Answer:

30 + 70 + 2x-10=180

90+2x=180

2x=180-90

x=90/2

x=45

X=45

Hope it helps

What is the measurement of angle A, side b, and side a

Answers

Answer:

a=26.039, b=58.021, c=42, A=24 degrees, B=115 degrees, C=41 degrees

Step-by-step explanation:

trig

Answer:

Step-by-step explanation:

It says to simplify it​

Answers

the answerrr is v11

Answer:

2v^9

I think this is the answer, I'm sorry if it's wrong :(

What is the measure of arc AC? Pls explain and I will mark brainliest!

Answers

Answer:

D. 146°

Step-by-step explanation:

Arcs in the circle sum to 360°

Arc AB = 2*∠C = 2*(48°) = 96°Arc BC = 138° - givenArc AC = 360° - (96° + 118°) = 146°

11=p-7-3p
Please help me

Answers

Answer:

p=-9

Step-by-step explanation:

11= p-7-3p

you can slove p-3p now which is -2p, then add -7 to both sides.

18=-2p

then divide by -2

p=-9

Robin can run 1.71 kilometers in 10 minutes. How far can she run in 1.5 hours?

Answers

Answer:

I think is 15.39 kilometers

Step-by-step explanation:

1 hour=60 minutes +.5 hours =90 minutes = 9 x 1.71 = 15.39

i need help now pleaseeee

Answers

Answer:

y=75° (opposite angle of parallelogramare equal)

x+8=16(opposite sides are equal)

x=16-8

x=8

Answer:

y=75

x=8

Step-by-step explanation:

Hope this helped!

Explain how you can use slope-intercept form to write an equation of a line given its slope and y-intercept
Substitute the slope for
and the y-intercept for
in the slope-intercept form

Answers

Answer:

Step-by-step explanation:

example

we are given: slope = 5, y-intercept = 9

y=mx+b

we just plug it in

y=5x+9

HELP!!!! IT'S DUE TONIGHT!!!!!!!!!!!!

Answers

Pretty sure it’s B
Down 8 units means you’re going down the y axis which I’m pretty sure means the -8 is supposed to be on the outside

A circle has a radius of 6 centimeters. If you copy the circle using a size factor of 75%, what will the radius be of the new circle

Answers

The new radius is 10.5.
75% of 6 is 4.5.

Describe a time when you use math outside of school ( pls I need help with this writing prompt)

Answers

Answer:

Counting my money

Step-by-step explanation:

Answer: You use it in gardening if you need to plant or sow new seeds or seedlings you need to make a row or count them out or even make holes. So even without thinking you are doing math. Measuring skills is always needed, and calculations of the essence when doing something new in the garden. You also use in it the kitchen Every ingredient has to be measured and sometimes you need to multiply or divide to get the exact amount you need.

help me, please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

Answers

Answer:

The first one is the answer

PLEASE HELP!! 20 POINTS!
- ✓ 81+ ✓–49 + ✓ 25+ ✓-1

Answers

Answer:

Step-by-step explanation:

=-9+7i+5+i

=-4+8i

Answer:

It's indeterminate; because a negative number can't have an rational root when goes under an even radical.

Identify the term that completes the equation.

XZ2=(WZ)(?)

Answers:
WZ
XW
XZ
YZ

Answers

Answer:

1: b. YZ, see "geometric mean theorem" in Wikipedia

2: a. sin Y = 7.4/10.9 ≈ 0.68,  sine = opposite/hypotenuse

3: c. tan P = 8.5/16 ≈ 0.53, tangent=opposite/adjacent

4: a. AC = 11.7, sine = opposite/hypotenuse, sin(43) = 8/AC

5. KM = 10.68 use Pythagorean Theorem

measure of angle M = 35 degrees, use definition of tangent

measure of angle K = 55 degrees,  M and K are complementary angle

Step-by-step explanation:

i hope this help

The term that completes the equation is YZ.

Option D is the correct answer.

We have,

From the figure,

∆WXY and ∆XYZ

∠WXY = ∠XZY = 90

∠ZYX = ∠XYW (common angle)

∆WXY ≅ ∆XYZ

And,

∆WXY and ∆WXZ

∠WXY = ∠WZX = 90

∠YWX = ∠XWZ (common angle)

∆WXY ≅ ∆WXZ

Now,

From (1) and (2),

∆XYZ ≅ ∆WXZ

This means,

The corresponding sides are proportional.

We can write as,

YZ/XZ = XZ/ZW

XZ² = WZ x YZ

Thus,

The term that completes the equation is YZ.

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Sebutkan nama sisi rusuk dan sudut dari bangun ruang di bawah ini​

Answers

Answer:

could u translate it to english?

Step-by-step explanation:

P(x)=-0.001x2+3x-1800

Answers

Answer:

P=−0.001x+3−1800/x

Step-by-step explanation:

Write the problem as a mathematical expression.

P(x)=−0.001x²+3x−1800/x

Divide each term in Px=−0.001x²+3x−1800 by x.

Px/x=−0.001x²/x + 3x/x + −1800/x

Cancel the common factor of x.

P=−0.001x²/x+3x/x + −1800/x

Simplify each term.

P=−0.001x+3−1800/x

The population of Central Arkansas is 734,622 and is decreasing by 8 per
year.

Answers

Answer:

734622-8x

Step-by-step explanation:

Help with some of my homework, please and thank you

Answers

Your answer is C

Area = length x width

Substitute in the values & expressions you know:

(12m + 18) = length x 6

Divide both sides of the equation by 6:

(12m + 18)/6 = length

2m + 3 = length

Answer:

C is right

Step-by-step explanation:

:))

All the sides of a quadrilateral measure 5 cm. What else must be true about this shape? Select all that apply. a.The diagonals are congruent. b.The diagonals are perpendicular. c.Consecutive angles are congruent. d. Opposite angles are congruent.

Answers

Answer:

a.The diagonals are congruent.

d. Opposite angles are congruent.

Step-by-step explanation:

From the above question, we are told that:

All the sides of a quadrilateral measure 5 cm.

This means this quadrilateral is a square.

The properties of a square states that:

1) Opposite sides of a square are equal each other or congruent.

2) Opposite angles are equal each other or congruent

3) Consecutive angles of a square are supplementary angles which means that they add up to 180.

4) A square has two diagonals and they are congruent or equal to one another.

Therefore, the correct options are options a and d

To become a member of an ice-skating rink, you have to pay a one-time $50 membership fee. The cost of admission to the rink is $6 per visit for members $10 per visit for nonmembers. After how many visits to the rink is it less expensive to be a member than a nonmember?

Answers

Answer:

10x=50+6x more than 10

Step-by-step explanation:

Pedro read
1/4
of a book in the morning, and he read some more at night. By the end of the day, he still had
1/3
of the book left to read. How much of the book did Pedro read at night? write you answer as a mixed number!! Your help means the world to me. ill mark brainly! 16 points!

Answers

9514 1404 393

Answer:

  5/12

Step-by-step explanation:

Since Pedro had 1/3 of the book remaining at the end of the day, he had read a total of 2/3 of the book. If n represents the amount read at night, you have ...

  1/4 + n = 2/3

  3 +12n = 8 . . . . . multiply by 12

  12n = 5 . . . . . . . .subtract 3

  n = 5/12 . . . . . .  divide by 12

Pedro read 5/12 of the book at night.

_____

Since Pedro reads only a fraction of the book, it is not a "mixed number."

__

The solution is equivalent to finding the difference ...

  2/3 - 1/4

  = 8/12 - 3/12 = 5/12

Sara buys a sweater at a department store. The sweater costs $3030. The store is having a 2525% off sale on everything in the store.

​Enter the amount of money, in dollars, Sara saves from the sale. Do not consider the sales tax.

Answers

Answer:

25% of 3030 is 757.5, so basically she is saving 757.5 dollars

The movie club is having a new member sale, so Mindy signs up. The equation -0.4x + 0.05y - 1.25 = 0 relates y, the total cost, and x, the number of months. What is the y-intercept of the line represented by the equation?

Answers

Answer:

Y intercept : ( 0 , 25 )

Step-by-step explanation:

Answer:

         (0, 25)

Step-by-step explanation:

We need to convert function to slope-intrcept form y=mx+b, where:

-0.4x + 0.05y - 1.25 = 0         {multiply both sides by 20}

-8x + y - 25 = 0                    {add (8x+25) to both sides}

y = 8x + 25     ⇒   b = 25

Therefore y-intercept of the line is (0, 25)

Y=x(4)/2+3x(3)-2x-12

Answers

Answer:

[tex]\displaystyle y' = -2x^3 + 9x^2 - 2[/tex]

General Formulas and Concepts:    

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/Coefficients

Calculus  

Derivatives    

Derivative Notation    

Derivative of a constant is 0    

Basic Power Rule:    

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle y = -\frac{x^4}{2} + 3x^3 - 2x - 12[/tex]

Step 2: Differentiate

Basic Power Rule:                                                                                           [tex]\displaystyle y' = -\frac{4x^{4 - 1}}{2} + 3 \cdot 3x^{3 - 1} - 1 \cdot 2x^{1 - 1}[/tex]Simplify Exponents:                                                                                        [tex]\displaystyle y' = -\frac{4x^3}{2} + 3 \cdot 3x^2 - 1 \cdot 2[/tex]Divide:                                                                                                             [tex]\displaystyle y' = -2x^3 + 3 \cdot 3x^2 - 1 \cdot 2[/tex]Multiply:                                                                                                           [tex]\displaystyle y' = -2x^3 + 9x^2 - 2[/tex]

y+8=x/2 linear or nonlinear

Answers

answer : linear
source: trust me bro

answer : linear

source: trust me people


A window washer on a ladder looks at a nearby building 102 ft away, noting that
the angle of elevation to the top of the building is 13.7° and the angle of
depression to the bottom of the building is 4.4°. How tall is the nearby building?
ok
The building nearby is blank feet tall.
(Round the final answer to the nearest foot as needed.

Answers

Answer:

about 32.71 feet

Step-by-step explanation:

see attached picture

The height of the building is 32.7 ft.

Given that, a window washer on a ladder looks at a nearby building 102 ft away, noting that the angle of elevation to the top of the building is 13.7° and the angle of depression to the bottom of the building is 4.4°.

We need to find the height of the building.

How do you find height and distance?

So if we know the height of the object and the linear distance, we can easily find out the angle by trigonometric formula. It is given by tan = Height / distance.

Now, tan 4.4°=x/102

⇒x=7.84 ft

tan 13.7°=y/102

⇒y=24.86 ft

Height of the building=x+y=7.84+24.86=32.7 ft

Therefore, the height of the building is 32.7 ft.

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Lines De and AB are parallel.
D
C
E
B
А
Which angles represent alternate interior angles?
angles A and C
angles B and D
angles C, D, and E
angles B and C

Answers

Answer:

option 2

angles B and D are the alternate interior angles

lines DE and AB being parallel lines and and line BC being the transversal

Answer:

The answer is B and D

Step-by-step explanation:

Confirmed

What is the range of the data set? {43.2, 46.8, 44.5, 46.8, 44.2, 41.9, 45.8, 46.9, 41.2, 46.8, 44.1}

Answers

Answer:

the range of this answer is 5.6

The population of a city decreases by 1.6% per year. If this year's population is 320,000, what will next year's population be, to the nearest individual?​

Answers

Answer:

314,880

Step-by-step explanation:

If the population decreases by 1.6% per year, this means the population is 98.4% of the population of the previous year. What this means is we can multiply the current population, 320,000, by 98.4/100, as 98.4/100 is equivalent to 98.4%. This gets us 314,880.

Answer:

314880

Step-by-step explanation:

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