The square of an odd number is always odd

Try Examples with three odd numbers to check this conjecture And find where it’s false

Do you believe it’s true or false

Explain why it’s true or false

Answers

Answer 1

Answer:

True

Step-by-step explanation:

3² = 9  ⇒ odd

7² = 49 ⇒ odd

9² = 81 ⇒ odd

Therefore, the square of an odd number is always odd.

Proof

If n is an odd number, it can be written as n = 2k + 1, for some integer k.

Therefore, n² = (2k + 1)²

                      = 4k² + 4k + 1

                      = 2(2k² + 2k) + 1

As 2(2k² + 2k) + 1 is odd, this proves that the square of an odd number is always odd.


Related Questions

3.84761 to 3 decimal place

Answers

the answer is 3.848.

The number 3.84761 become 3.848 after round off to 3 decimal place or thousandths place.

What is rounding off number?

Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.

We have a number:

= 3.84761

It is required to round off to 3 decimal place.

= 3.848  (0.0076 = 0.008)

Rounded to the nearest 0.001 or the Thousandths Place.

Thus, the number 3.84761 become 3.848 after round off to 3 decimal place or thousandths place.

Learn more about the rounding off number here:

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What is an equation of the line that passes through the point (–2, 5) and is perpendicular to the line y=12x + 5 ?


What is an equation of the line that passes through the point (–2, 5) and is perpendicular to the line y=12x + 5 ?

Answers

y = 12x + 5

- 12x + y = 5

gradient 1 = -a/b

= -(-12) / 1

= 12/1

= 12

gradient 2 × 12 = -1

Gradient 2 = -1/12

y - y1 = m (x - x1)

y - 5 = -1/12 ( x - (-2))

multiply all, by 12

12y - 60 = - 1 (x + 2 )

12y - 60 = -x - 2

x + 12y = - 2 + 60

x + 12y = 58

The figure below hows three quadrilaterals on a coordinate grid:
Which of the following statements is true about the three quadnlaterals?
O A and B are similar but not congruent.
O A and C are similar but not congruent.
O A and B are similar and also congruent.
O B and C are similar and also congruent.

Answers

A and C are similar but not congruent

The table shows the side length and area of several different squares. Complete the table using
exact values.
side length (cm)
5
V63
49
98
102
area (cm

Answers

Answer:

from left to right: 25cm², 7cm, 63cm², 9.90cm (2dp), 10.10cm (2dp), 125cm²

The area of a 2D form is the amount of space within its perimeter. The table that shows the side length and area of several different squares as shown below.

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of a square is the square of the length of the side of the square. Therefore, the area of the square and the length of the side of the square can be written as,

Length of the side                Area

         side                              Side²

   5                                  25    7                                  49√63                                 63√98                                 98√102                               102√125                               125

Hence, the table that shows the side length and area of several different squares as shown above.

Learn more about Area here:

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true or false pls answer

Answers

it's false because two lines cannot be horizontally parallel

This is incorrect the given picture is not a function. If we draw a vertical line through the graph we see that it touched the graph twice, meaning this is not a function.

(brainliest?)

7) Solve the equation for the variable given.

Solve for x.

m=2x+b/3

Answers

Answer:

x= m/2 - b/6

(its a lot of work...)

Step-by-step explanation:

1. Subtract 2x from both sides

-2x=2x+b/3-2x

2. Simplify

-2x=b/3

3. Factor

x(m-2)=b/3

4. divide both sides by m-2; m≠2

x(m-2)/m-2=b/3/m-2 m≠2

5. Simplify again...

x=b/3(m-2); m≠2

Wangari plants trees at a constant rate of 12 trees every 3 hours.

Write an equation that relates p, the number of trees Wangari plants, and h, the time she spends planting them in hours.

Answers

Answer:

[tex]p = 4h[/tex]

Step-by-step explanation:

The equation of straight line is given by:

[tex]y = mx[/tex]

where, m is the slope or rate of the line.

As per the statement:

Wangari plants 12 trees every 3 hours.

By definition of unit rate:

Unit rate per hour [tex]= \frac{12}{3} = 4[/tex] trees

⇒[tex]m = 4[/tex]

We have to find an equation that relates the number of trees Wangari plants (p) and the time she spends planting them (h) in hours.

then;

[tex]p=4h[/tex]
where, p represents the plant trees and the time she spends planting them in h hours
Therefore, [tex]p=4h[/tex]   an equation that relates the number of trees Wangari plants (p) and the time she spends planting them (h) in hours.

Credit Answers to: OrethaWilkison

Someone who likes to work alone on individualized projects has a _____. A. Bodily/kinesthetic learning style b. Intrapersonal learning style c. Rhythmic/musical learning style d. Logical/mathematical learning style Please select the best answer from the choices provided A B C D.

Answers

Someone who likes to work alone on individualized projects has a Intrapersonal learning style.

What does intrapersonal learner do?

Intrapersonal learners are those who prefer working alone.

Bodily learning style refers to practical or physical activities based learning, rather than lectures and theory.

Whereas musical learning is learning based on like memorizing by instrumental tones or learning with music in background etc.

Logical and mathematical learning is logic based learning.

And therefore, other options given doesn't fit the blank space, as we're asked the name of the person who likes working alone on individualized projects.

Thus, Someone who likes to work alone on individualized projects has a Intrapersonal learning style. (option B: Intrapersonal learning style)

Learn more about intrapersonal learning style here:

https://brainly.com/question/1235988

Answer:

Step-by-step explanation:Intrapersonal learners are those who prefer working alone.

Bodily learning style refers to practical or physical activities based learning, rather than lectures and theory.

Whereas musical learning is learning based on like memorizing by instrumental tones or learning with music in background etc.

Logical and mathematical learning is logic based learning.

And therefore, other options given doesn't fit the blank space, as we're asked the name of the person who likes working alone on individualized projects.

Thus, Someone who likes to work alone on individualized projects has a Intrapersonal learning style. (option B: Intrapersonal learning style)

Learn more about intrapersonal learning style here:

brainly.com/question/1235988

If a car is going at 30 km per hour and i need to drive 500 metres how long would it take

Answers

Answer:

So in 60 minutes it would travel 30 km.

Step-by-step explanation:

Distance travelled by the car=500 km. Total time taken=2 hrs.

Find the next 3 terms and how’s the numbers changing

Answers

-49, -63,-78

explanation:
-3 - 10
-13 -11
-24 -12
-36 - 13
-49 - 14
-63 - 15
=-78

Can anyone help me with this?

Answers

100 divided by 10
9/10

Answer:

See below.

Step-by-step explanation:

Whatever you divide/multiply the numerator by is what you have to divide/multiply the denominator by.

90/10=9

100/10=10

-hope it helps

There is a bag filled with 3 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 that are different in colour?

Answers

Answer:

15/28

Step-by-step explanation:

There are 3 blue, 5 red and the total of 8 marbles.

Two different colored marbles are:

blue, then red or red, then blue

Find the probability of each case:

P(b, r) = 3/8*5/7 = 15/56P(r, b) = 5/8*3/7 = 15/56

Required probability is:

P(different color) = 15/56*2 = 15/28

Answer:

15/28 is the probability of getting 2 that are different in colour.

Step-by-step explanation:

3 blue and 5 red marbles

He is going to pick any marble, in second try, it must be a different colour marble.

total marble: 3 + 5 = 8 marbles

For blue marble:

In first try for blue marble: 3/8

total marble will decrease by 1, 7 marbles.

second try for red marble: 5/7

probability then: 5/7 *  3/8 = 15/56 is the probability for blue marble.

For red marble:

In first try for red marble: 5/8

total marble will decrease by 1, 7 marbles.

second try for blue marble: 3/7

probability then: 5/8 * 3/7 = 15/56

**

total probability of getting different in colour:

15/56 + 15/56

15/28  **

An airplane climbs at an angle of 12° with the ground. Find the horizontal distance it has traveled once it has reached an altitude of 500 feet. using cos

Answers

Answer:

2352.32

Step-by-step explanation:

Sin 12 = 500/H

H = 2404.86717

Cos(12) = A/2404.86717

A = 2352.32

The horizontal distance it has traveled once it has reached an altitude of 500 feet is approximately 2352 feet.

The situation forms a right angle triangle

What is a right angle triangle?

A right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.

The altitude of the plane is the opposite side.

The horizontal distance it travelled is the adjacent side of the triangle formed.

Therefore,

tan 12 = opposite / adjacent

tan 12 = 500 / a

a = 500 / tan 12

a = 500 / 0.2125565616

a = 2352.31573723

a = 2352 feet

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Noah bought a new car costing $25,350 He took out a 5 year loan at a simple interest rate of 6 5% How much interest did Noah pay on his car?​

Answers

Answer:

1,647.75

Step-by-step explanation:

Well 25,340 times the interest rate .065 which equals 1647.75

PLEASE HELP LAST QUESTION IT NEEDS TO BE CORRECT (WILL GIVE 20 POINTS!)

Answers

Answer:

it's 20 IT NEEDS TO BE CORRECT

PLEASE ANSWER FAST SORRY IM IN A RUSH
72t^2+225

Answers

Answer:

9(8t^2+25)

Step-by-step explanation:

Jacob has $50 to spend he is going to buy a game for $15 and he wants to buy a gift for seven of his friends how much can he spend on each friend?

Answers

Answer:

$5

Step-by-step explanation:

Start by finding how much money Jacob has after buying a game for himself:

$50-$15=$35

Now, we have to divide $35 by 7 since he has 7 friends...

$35/7=$5

He can spend $5 on each friend

15$ for the game and 5$ to spend for each of Jacobs friends

50-15=35 35/5=5 or I'm wrong?

Which of the following are exterior angles? Check all that apply.

Answers

Answer:

2, 3, 5, 6

Step-by-step explanation:

because the angles are outside

Yusra's dog is overweight. The vet says the dog needs to lose 7 pounds to get down to the desirable weight of 45 pounds. How much does Yusra's dog weigh? Define a variable and write an equation for this situation. Then solve the equation and check the solution.

Answers

Answer:

the dog weighs 52lb

Which equation is the inverse of y = 16x2 + 1?

Answers

D would be the best answer

Answer :

± [tex]\frac{\sqrt{x-1} }{4}[/tex]

plese guys I need help.

Answers

Answer:

1. 5 child tickets

Step-by-step explanation:

So 2 adult tickets would be 24$

So we do 64-24=40. So each child tickets cost 8$

So we do 40/8=5

So for number 1 they can buy 5 child tickets.

If 1 inch represents 68 miles on a map, then how many inches will represent 8600 miles

Answers

Answer:

126.470588235

Step-by-step explanation:

I like to set these up like how I set up my radian conversions so what I do is I have one unit on top of a fraction and another on the bottom so it would look like this 1/68 = x/8600 this equation will let us solve for x which would be our inches to get 8600 so we just times 1/68 by 8600 and get 126.470588235 and just to check 126.470588235 * 68 = 8600

what is the formula of circle​

Answers

I believe it is A=πr2

3x - 13 = 3(x - 6)

a
one solution

b
no solution

c
infinite many solutions

Answers

Answer:

B) No solution

Step-by-step explanation:

3x - 13 = 3(x-6)

3x - 13 = 3x - 18

-13 = -18

Since both sides are never equal to each other, there are no solutions

B: No solution is the answer

The length of a
rectangle is represented by
4a + 3b, and its width is
represented by 7a – 2b. Write
a polynomial for the perimeter
of the rectangle.

Answers

Solution:

Given:

Length of rectangle = 4a + 3bWidth of rectangle = 7a - 2bPerimeter of rectangle = 2W + 2L

Let's simplify the perimeter of the rectangle by using the expression for the perimeter.

=> 2W + 2L=> 2(7a - 2b) + 2(4a + 3b)=> 14a - 4b + 8a + 6b=> 22a + 2b

Hence, the polynomial that represents the perimeter of the rectangle is 22a + 2b.

please help I will give brainliest.

Answers

Answer:

Loan is increasing

Rate = 8% per year

Step-by-step explanation:

[tex]h(x) = 5000.(1.08) ^{x} \\ \\ \implies \: h(x) = 5000.(1 + 0.08) ^{x} \\ \\ \implies \: h(x) = 5000.(1 + 8 \%) ^{x} [/tex]

Since, rate of interest is positive, so loan in increasing.

Rate = 8 percent per year

can someone please help me solve the following?​

Answers

Answer try caculator soup it has so many diff calulators

Step-by-step explanation:

PLEASE HELP NO LINKS PLEASE

Answers

Answer:

x < -2

Step-by-step explanation:

its less than x, open circle

Answer:

x < -2

Step-by-step explanation:

Okay, so the dot is at -2 and is facing left. Left means less than, so, we know x is less than -2.

But we don't know if it's equal to or less than or just less than.

The dot is hollow, which in graphing means that it is not equal to or less than.

Therefore, the answer is x < -2

Brainliest please?  

yoooooooooooooooo I need help

Answers

Answer:

13/5 which is 2.6 so A.

Step-by-step explanation: Reduce the expression, if possible, by cancelling the common factors.

The answer is A the other person is right

Solve for x : Y=3x- 8
Y=-4x+6

Answers

3X-8=-4X+6 7X-8=6 7X=14 X=14\7=2
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