Prove that the square of an odd number is always 1 more than a multiple of 4.
Input note: use 2n +1 as your odd number, and leave your answer in the form
4(...) +1
(4 marks)

Answers

Answer 1

Answer:

See explanation.

Step-by-step explanation:

If the odd number is 2n+1 note that n can be any number because any even number plus one will be odd. Let's start by squaring 2n+1 to get:

[tex]4n^2+4n+1[/tex]

Consider xy (x times y). xy is a multiple of both x and y because xy/x = y and xy/y = x. So it doesn't matter what n is it will be a multiple of 4. So now we know that 4n^2 and 4n are both multiples of 4. If we add them together, it will still be a multiple of 4. 2x + 4x = 6x and 6x is still divisible by x.

Now the plus 1 will always make it so it will be one more than a multiple of 4.


Related Questions

A population of amoebas is measured at 14,000 and grow at a rate of 11% per hour. How many amoebas are expected in one day?

Answers

Answer:

Calculating Growth Rates. The annual percentage growth rate is simply the percent growth divided by N, the number of years. ... The population of Lane County grew 12 percent between 1980 and 1990 or at an rate of 1.2 percent annually.

Step-by-step explanation:

3.7 x 10 to the power of 2​

Answers

Answer:

1369

Step-by-step explanation:

3.7 x 10 = 37 x 37 = 1369

What makes a mathematical statement an equation.

Answers

Answer:

Step-by-step explanation:

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=".

Can you people please help me with some more math that I can't understand?


Please see the following image below:

Answers

Answer:

He would collect 28 cans

Step-by-step explanation:

Ethan = 1/3

84 * 1/3 = 28

Answer:

28 cans were collected by Ethan

Step-by-step explanation:

It says that the total amount of cans collected was 84 cans. Of the 84 total cans, Ethan collected 1/3 of them. To find the number of cans Ethan collected, you would multiply 84 • 1/3. (You could also divide 84 by 3 in this case)

84 • 1/3 = 28

Dot the angles 133 degrees, 124 degrees, and 51 degrees make a triangle?

Answers

Answer:

No

Step-by-step explanation:

CHECK MY ANSWER PLSS

Answers

Answer:

The third and fifth option are correct too.

How many faces does a solid with 12 vertices and 18 edges have?
28, 18, 6, or 8?

Answers

Answer:

8 faces

Step-by-step explanation:

In geometry, the hexagonal prism is a prism with a hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices.

Hope this helps!

Help me please!!

I’ll give brainliest♡

SOLVE FOR THE LETTER!!

Answers

Step-by-step explanation:

p/8=13/2

p/8=52/8

p=52

3/13=v/3

9/39=13v/3

v=9/13

A student said that 3 raised to power 5 / 9raised to power 5 is the same as1/3. What mistake has the student made?Write the correct answer.

Answers

3^5/9^5=243/59049=0.0041152263

math please help <<--- aaaa

Answers

Answer:

Step-by-step explanation:

[tex]H(t) = 14000(0.8)^{t +3}\\\\ = 14000*(0.8)^{t}*(0.8)^{3}\\\\=14000*(0.8)^{t}*0.512\\\\=7168(0.8)^{t}[/tex]

Answer:

it is 7168(0.8)t

Step-by-step explanation:

hope this helped

Model With Mathematics A photographer is
placing photos in a mat for a gallery show.
Each mat she uses is x in, wide on each side.
The total area of each photo and mat is
shown

Answers

Answer:

a. The possible dimensions of the total area are;

The width of the total area is (2·x + 8) inches

The length of the total area is (2·x + 10) inches

b. The dimensions of the photos are as follows;

The length of the photos are 10 inches

The width of the photos are 8 inches

Step-by-step explanation:

a. Given that the area, A = 4·x² + 36·x + 80

We get;

A = 4 × (x² + 9·x + 20) = 4 × (x + 4) × (x + 5) = (2·x + 8)·(2·x + 10)

Therefore, the possible dimensions of the total area (photo + mat) are;

The width of the total area (photo + mat) = (2·x + 8) in.

The length of the total area (photo + mat) = (2·x + 10) in.

b. The dimensions of the photos alone are shorter than the dimensions of the photo and mat combined by 2·x each

Therefore, we have the dimensions of the photos are as follows;

The length of the photo = (2·x + 10) in. - 2·x in. = 10 in.

The width of the photos = (2·x + 8) in. - 2·x in. = 8 in.

What is the solution y=5(x/10-2)​

Answers

Answer:

you weren't clear if we have to solve for x or y so I did both of them. hope this helps!

Step-by-step explanation:

Which of the following values are zeros for the function below? Select all that apply.
g(x) = (x² + 4x - 12)(x - 3)
-6
03
-2
0 0
2
3
06

Answers

-2 because I just guess jk

ill brainlist u if u get this correct, someone who knows.

what's the number of terms in this expression: 9m⁴ + 7p - 17

Answers

Answer:

There are 3 terms

Step-by-step explanation:

Here, we want to get the number of terms in the given expression

Mathematically, each of the terms are separated by an operator

Thus, we have it that;

9m^4 is a term

7p is a term

and 17 is a term

That makes a total of 3 terms

is 1,250 More than or less than 1.25​

Answers

1,250 is more then 1.25 because it’s a greater number
1,250 is more than 1.25

Grace earns $7 for each car she washes. She always saves $21 of her weekly earnings. This week, she
wants to have at least $66 in spending money. How many cars must she wash?

Answers

Answer: 13

Step-by-step explanation:

[tex]66\geq 7x-21[/tex]

add 21 both sides

[tex]87\geq 7x[/tex]

divide both sides by 7

[tex]12.4\geq x[/tex]

So more than 13 cars

ILL GIVE BRAINLEIST

Options:

1. 40
2. 50
3. 80
4. 100

Answers

Answer: I would probably say c 80

Step-by-step explanation:

Since 2005​, the amount of money spent at restaurants in a certain country has increased at a rate of 5​% each year. In 2005​, about ​$290 billion was spent at restaurants. If the trend​ continues, about how much will be spent at restaurants in 2020​? PLEASE HELP ME

Answers

Answer:

About $603

Step-by-step explanation:

Given data

The time interval 2005-2020= 15 years

The principal amount spent= ​$290 billion

The rate= 5%

Let us apply the compound interest formula

A=P(1+r)^t

substitute

A=290(1+0.05)^15

A= 290(1.05)^15

A= 290*2.0789

A= $602.881

Hence about $603 will be spent in 2020

Landon, Wes, and Tim attempted 25 basketball shots each.HELP ASAP

• Landon made 36/100 of his shots.

• Wes made 2/5 of his shots.

• Tim made 32% of his shots.


Which statement it true

Wes made the most shots.

Landon made more shots than Wes.

Tim made more shots than Landon.

Landon, Wes, and Tim made the same number of shots.

Answers

Wes made the most shots.
Explanation.
Landon made 9 shots
Wes made 10 shots
Tim made 8 shots.
HAVE A GUD DAY

Answer: Wes made more shots

Step-by-step explanation:

In Sam’s pet corner, there are puppies and parrots. They have the total of 15 heads and 50 feet. How many parrots and how many puppies are there?

Answers

Answer:

10 puppies, 5 parrots.

Step-by-step explanation:

Puppies have twice the ammount feet, so it will be double the amount of parrots. 10 twice the amount of 5, so their would be 10 puppies, 5 parrots

ABC is dilated using a scale factor of 2.5. Which property does not change?
A. side lengths
B.angle measures
C.area
D.perimeter

Answers

C..................................................

classify as a acute, right, obtuse or not a triangle : 9in, 40in, 44in

Answers

Answer:

Acute.

Step-by-step explanation:

your welcome:)))))))

A triangle has side lengths 25 in 33 in and 41 in is a front of a cute obtuse or right

Answers

Answer

The triangle is an obtuse.

Step-by-step explanation:

25 + 33 + 41 = 99

90 Is a right angel.

But the triangle is 99 which makes it an obtuse.

The sum of squares of the two smaller sides is greater, the triangle is acute.

Acute triangle :

To determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side.

Given sides of triangle are, [tex]25,33[/tex] and [tex]41[/tex].

Squares of the two smaller sides is,

                            [tex]=25^{2} +33^{2} \\\\=625+1089=1714[/tex]

Square of third side [tex]=41^{2} =1681[/tex]

Since the sum of squares of the two smaller sides is greater, the triangle is acute.

Learn more about the triangles here:

https://brainly.com/question/17335144

I really need help!!!​

Answers

Answer:

which no. buddy??.........

Answer:

(1)...C-1

2-A...(2)

3-B...(3)

(4)....7x-6=0

(5)...7+4x

(6)...5x-10

(7)...5x= -5

x= -1

(8)....-3x= -9

x=3

(9)....x=2

(10...559100t+6423000=11000000

t=4577000/559100=8.18

Please help

A 297 and 323
B245and 323
C 297 and 369
D 323 and 369

Answers

C is the answer which is 297 and 369 not sure though

Answer: c

Step-by-step explanation:

The Graph of y = f(x) is shown below. Find the value of f(-1)​

Answers

Answer:

f(-1) = -4

Step-by-step explanation:

f(-1) means that x = -1, so find the y-coordinate that reaches at x = -1.

As you move down on x = -1, you find that -4 is where it meets.

The value of the function at x = -1 will be -4.

What is a function?

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The function of the given graph is as follows:-

F(x) = - ( x - 2 )² + 5

For calculating the value of the function f(-1) put the value of x in the function.

F(-1) = - ( - 1 - 2 ) ² + 5

F(-1) = - ( -3 )² + 5

F(-1) = -9 + 5 = -4

Therefore, value of the function at x = -1 will be -4.

To know more about function follow

https://brainly.com/question/25638609

#SPJ2

anyone English here???

Answers

Yes I’m English hahahah lol

Guys , pls help me with this.....pls pls , if u did i'll add u as brainliest and give u the highest rate so pls anyone help me this questions pls pls

Answers

47. 116-(-79)=195

48. 25×100/20=125

49. 14

50. r= 176/2π=28

51. 12x²+4xy-4y²

52 9×25=225

Step-by-step explanation:

1.166-79

2. 20÷100×25

3.2-1÷7

4.176÷2

What is the surface area?

Answers

The formula for the surface area of a rectangular prism is

A= 2(wl+hl+hw)

We are given the height =2cm, width= 5cm, and length= 10cm. All you have to do is plug this info in!

A= 2(wl+hl+hw)
= 2[(5)(10)+(2)(10)+(2)(5)]
= 2(50+20+10)
= 2(80)
=160 cm squared

Hope this helps!! :)

solve (8.5) . (-3) =a

Answers

Answer:

The answer is a = -25.5

Step-by-step explanation:

(8.5) . (-3) =a

-25.5 = a

a = -25.5 is your answer

Answer:

a = -25.5

Step-by-step explanation:

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