Prove: An odd number cubed is an odd number. (2n + 1)^3 = [ ? ]n^3 + [ ? ]n^2 + [ ? ]n [ ? ](4n3 + 6n2 + 3n) + [ ? ] = an odd​

Answers

Answer 1

An odd number cubed is an odd number.

To answer the question, we need to know what odd numbers are

What are odd numbers?

Odd numbers include 1,3, 5,7... and take the general for (2n + 1) where n = 0, 1, 2...

Now, we need to show that an odd number cubed is an odd number.

So, the odd number (2n + 1) cubed is

(2n + 1)³ = (2n + 1)(2n + 1)²

= (2n + 1)(4n² + 4n + 1)

= 8n³ + 8n² + 2n + 4n² + 4n + 1

= 8n³ + 12n² + 6n + 1

= 2(4n³ + 6n² + 3n) + 1

Since (4n³ + 6n² + 3n) is an integer say k, we have that

2(4n³ + 6n² + 3n) + 1 = 2k + 1

Since 2k + 1 is an odd number, 2n + 1 is an odd number and (2n + 1)³ = 2k + 1 which is an odd number.

So, an odd number cubed is an odd number.

Learn more about odd numbers here:

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Related Questions

8 + h = -2

Help plzzzzz

Answers

Answer:

h= -10

Step-by-step explanation:

Basically you’re finding out what h is equal to because h can’t be a real number i guess i would say. It is but it also isn’t if that makes sense. Basically just subtract 8 on both sides ands you get your answer. Hope this helped :)

The set of numbers 1, 7, 11 and 36 contains values for n. What value of n makes the equation below true? 4n + 8 = 36

A) 1
B) 7
C) 11
D) 36

Answers

The answer is B
4(7)+8=36
28+8=36
36=36

Plsss i need help with homework

Answers

Answer:

The Answer is YES

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Use Pythagorean theorem.

The longest side will be the hypotenuse

Hypotenuse² = 17² = 289

base² + altitude² = 15² + 8²

                           = 225 + 64

                          = 289 =Hypotenuse²

So, 8 m , 15 m , 17 m forms a right angled triangle

A man wants to determine the height of a light house. He measured
the angle at A and found that tan A = 3/4. What is the height of the
light house if A is 40 m from the base ?

Answers

Answer:

Step-by-step explanation:

height/A = tanA

height/40 = 3/4

height = 30 meters

How would you express the area of the rectangle using the Distributive Property?

Answers

Answer:

C

Step-by-step explanation:

Step 1: Find your legth and width

Length = x + 5

Width = 3

Step 2: Use area formula to find area

l x w = A

(x + 5) x 3 = A

A = 3(x+5)

Step 3: Therefore Statement

Thereforethe answer to the question is C. 3(x+5)

Answer:

C. 3(x + 5)

Step-by-step explanation:

area of rectangle = length * width = width * length

A = area of largest rectangle

a1 = area of left rectangle

a2 = area of right triangle

The largest rectangle is made up of the the two smaller rectangles.

A = a1 + a2

Left rectangle: a1 = WL = 3x

Right rectangle: a2 = WL = 3 * 5

Total area of the two small rectangles:

A = a1 + a2 = 3x + 3 * 5

Apply the distributive property in reverse to 3x + 3 * 5 by factoring out a 3:

A = 3x + 3 * 5 = 3(x + 5)

The area of the largest rectangle is 3(x + 5)

We can also find an expression for the area of the largest rectangle directly by looking at its length and width.

The length of the largest rectangle is x + 5.

The width of the largest rectangle is 3.

A = WL

Substitute 3 for W, the width.

Substitute x + 5 for L, the length.

A = 3(x + 5)

Answer: C. 3(x + 5)

The island has 600 bikes and 900 people. What is the bike to person ratio

Answers

Answer:

2:3 (2 bikes for every 3 people)

Step-by-step explanation:

hope this helps

How many TERMS are there in 8.4n - 3.2p?

Answers

the are two terms in the expression

Ben is paid £9.60 per hour.
If he works for more than 7 hours in a day, he is paid overtime for the additional hours at a rate of 1.5 times his normal rate of pay.
Yesterday, Ben worked for 12 hours.
How much money did he earn

Answers

The answer is 85.20$

Answer:

u liar>>>>>>

Step-by-step explanation:

properties of isosceles triangle:)

i’ll give a brainiest

Answers

Answer:

2 sides re equal

and 2 base angles are equal

Mark it as the brainliest answer

please thanks

Suppose cos(x)=-1/3, where pi/2≤x≤ pi. What is the value of tan(2x)?

Answers

Answer:

4√2/7

Step-by-step explanation:

Suppose cos(x)=-1/3, where pi/2≤x≤ pi

tan(2x) = sin(2x)/cos(2x)

Since sin2x = 2sinx cosx

cos 2x = 2cos²x-1

Substitute

tan(2x) = 2sinx cosx/ 2cos²x-1

Given cosx = -1/3

adjacent = -1

hyp = 3

opp = √3²-(-1)²

opp = √9-1

opp = √8

sinx = opp/hyp

sinx = √8/3

tan(2x) = 2sinx cosx/ 2cos²x-1

tan(2x) = 2(√8/3)(-1/3)/ 2(-1/3)²-1

tan2x= (-2√8/9 )÷ (2/9 - 1)

tan2x = -4√2/9 * 9/-7

tan 2x = 4√2/7

Candace has $15 more than Amar. Their combined money totals $85.Which system of equations represents this situation? *
A. c + a = 85 ; a + c = 15
D. a - c = 85 ; c - a = 15
C. c - a = 85 ; c + a = 15
B. c + a = 85 ; c - a = 15

Answers

Answer: c - a = 85 ; c + a = 15

Hope it helps

MATH HELP! BRAINLIESTT!!

Answers

Answer:

14

Hope it helps

.......⋋✿ ⁰ o ⁰ ✿⋌

Answer:

n = 14

Step-by-step explanation:

ΔABC was dilated by a scale factor of 2.

two step equations that equal 23, 26, 28, and 29

Answers

Answer:23 - 3 = 20 + 3 = 23

Step-by-step explanation:

Will has a spinner with six equal sections numbered one through six. If Will spins the spinner 150 times, how many times can he expect to spin a number less than 5?

A)30
B)110
C)100
D) 25


pls hurry!!!

Answers

Answer:30

Step-by-step explanation:

30 times he can expect to spin a number less than 5.

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

A spinner with six section numbered from 1 to 6.

total number of times spins = 150

So, the number of times the number comes less than 5 is

= 150 x 1/5

= 150/5

= 30

Learn more about Probability here:

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PLZ HELP
Which is the best estimate for the amount of liquid a watering can holds?



5 ounces


5 cups


5 quarts


5 gallons

Answers

Answer:

5 quartz would make the most sense, hope this helps

Step-by-step explanation:

A cell phone provider offers a plan that costs $20 per month plus $0.20 per text message sent or received. A comparable plan costs
$30 per month but offers unlimited text messaging. Complete parts a. and b. below.
a. How many text messages would have to be sent or received in order for the plans to cost the same each month?
In order for the plans to cost the same.
text messages would have to be sent or received
b. If you send or receive an average of 200 text messages each month which plan would you choose and why?​

Answers

Answer:

Step-by-step explanation:

a)

30=20+0.2m

10=0.2m

50=m

So after sending 20 messages the plans would cost the same.

b)

Obviously from the first part that the unlimited plan is cheaper when sending 200 messages, but the costs numerically would be.

Unlimited plan costs $30 while the other plan costs

20+0.2(200)=$60

They would have sent 5

$9.27 for 48 oz of taco meat

Answers

Answer:

Need more info to answer your question!

Step-by-step explanation:

which system of equations graphed below has a solution of (2,1)​

Answers

Answer:

Sorry to say this... but neither of them have a solution of (2,1)

Step-by-step explanation:

The top one has a solution of (-2,-1). The one on the bottom has a solution of (-2,1). So... I'm not sure how this can help... but yeah...

A rectangle has an area of 22.64 inches squared. If the coordinates of one of its sides are (0, 0) and (4, 4), what are the dimensions of the rectangle?

(Please only answer if you know how to solve it and maybe know an app, don't answer just because you want the points.)

Answers

Answer:

width= 4

hieght- 5.65

Step-by-step explanation:

so first lets find the diestnce between 0,0 and 4,4

which is 4 root 2

which is approciamitlty 5.65 and this would be the hieght

the width would be 22.64/5.65= approxiamitly 4

 if you found my answer helpful please mark as brainliest.

If 8 men on a construction crew make up 40% percent of the entire crew, how many people are in the crew?

Could someone explain this question to me? I don't get it at all

Answers

Answer:

Step-by-step explanation:

Since 40% of the crew are men, which means n. 40=8 n=8/. 40 n=20 total number of crew 20 - 8=12 are women

x(0.4)=8
x=8/0.4
x=20
so there’s 20 people in the crew
hope this helps !

Someone please help and make sure the answer right :)

Answers

Answer:

It's 10

Step-by-step explanation:

It's 10 because 7x is congruent to 70 and 7 times 10 equals 70 :))

Answer:

It's 10

Step-by-step explanation:

It's 10 buddy lol

Factor the following using identities wherever necessary
1) x² + 8x
2) x2 - 4x
3) x² + x - 2
4) x2 - 9
5) x² + 22x + 121
6) x² - 8x + 16​

Answers

Answer:

1. x(x+8)

2. x(x−4)

3. (x−1)(x+2)

4.(x+3)(x−3)

5. (x+11)(x+11)

6. (x−4)(x−4)

Step-by-step explanation:

convert to logarithmic form pls!! :))

Answers

Answer:

16=(2/3)

Step-by-step explanation:

convert the exponential to a logarithmic equation using the loarithmic base (64) of the right side (16) equals the exponent (2/3)

1.) The length of a rectangle is 4 cm longer than the width. The
perimeter is 80 cm. Find the length and width. Write a system and
use substitution to solve.

Answers

Step-by-step explanation:

if a rectangle has 4 sides and there are two lengths and two widths

then we could split 80 by 2 and minus 4 from the length and then split that into two.

then your answer would be  and 36 and 44

and the total answer would be half of each so the L=22 and L=22

and the W=18 and W= 18

sorry if this is wrong it least i tried :9

Jenna uses 6.1 pints of white paint and blue paint to paint her bedroom walls. 4/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?

Answers

Answer:

2.44 pints of white

Step-by-step explanation:

please help me if you can please

Answers

Answer:

17. m=-1/2

18. m=-1

Step-by-step explanation:

A retailer paid $33.00 for a lamp. What price should she sell the lamp for if she wants to make a 35% profit?

Answers

Answer: $44.55

Step-by-step explanation:

She should sell if for $33.00 x 1.35 = $44.55.

Can someone please help
Evaluate the function.

Answers

Answer:

Hello I'm pretty sure the answer is 20

Hope This Helps :D

Please let me know if I am incorrect pretty sure its right tho

Answer:

f(1) = 32

Step-by-step explanation:

f(x) = 4x^2 + 3x + 13

4(1)^2 + 3(1) + 13

4^2 + 3 + 13

16 + 3 + 13 = 32

A drain empties a bathtub at a rate of 0.5 gallons per minute. A
30-gallon tub was full and the shower head was turned off,
how long would it take the tub to empty through the partly
unplugged drain?

Answers

I’m gonna say an hour

1/2(5x−8)=21 solve for x and brainliest

Answers

Answer:

x=10

Step-by-step explanation:

see picture for explanation

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