Prove the statement below directly from the definitions of the terms.

For all integers n, n2 + n +1 is odd.

Answers

Answer 1

Answer:

We know that:

If A is an even integer number, then A + 1 is an odd number

If B is an odd number, then B + 1 is an even number.

We also know that the product of two odd numbers is odd, and the product of two even numbers is even.

We want to prove that:

For all integers n, n^2 + n + 1 is odd.

We have two cases.

If n is even, then:

n^2  is the product of two even numbers, so is even.

n^2 + n is the sum of two even numbers, then it is even.

And:

(n^2 + n) + 1  is an even number plus one, so it is odd.

Now let's assume that n is odd.

n^2 is the product of two odd numbers, then n^2 is odd.

n^2 + n is the sum of two odd numbers, then it is even.

And similar as the previous case:

(n^2 + n) + 1 is an even number plus one, so it is odd.


Related Questions

Carlos buys a vintage automobile for $7300. He estimates that the value will increase by 3% every year. Estimate the value of the automobile in ten years.

Answers

Answer:

$9810.59

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Simple Interest Rate Formula: [tex]\displaystyle A = P(1 + r)^t[/tex]

P is principle amountr is ratet is time (in years)

Step-by-step explanation:

Step 1: Define

Identify variables

P = 7300

r = 3% = 0.03

t = 10

Step 2: Solve for A

Substitute in variables [Simple Interest Rate Formula]:                                 [tex]\displaystyle A = 7300(1 + 0.03)^{10}[/tex](Parenthesis) Add:                                                                                            [tex]\displaystyle A = 7300(1.03)^{10}[/tex]Evaluate exponents:                                                                                         [tex]\displaystyle A = 7300(1.34392)[/tex]Multiply:                                                                                                              [tex]\displaystyle A = 9810.59[/tex]

(2
(4+4)
X2
Answer
No step by step explanation just the answer

Answers

Answer:

1

Step-by-step explanation:

I had brainliest but some kid reported me soooooo

what is the volume of a sphere if the radius is 9?


ANSWER IN TERMS OF PI !!!

Answers

Volume of sphere =4/3 pi r^3
V(volume)=(3/4) pi r
Pi =3.14 or 22/7
R(r)= radius (9) in

In a nutshell :

The volume of a sphere is equal to 43 times Pi π times the radius cubed. Substitute the value of the radius r=9 into the formula to find the volume of the sphere. Pi π is approximately equal to 3.14 .

Find the area of the circle use 3.14 for pie d=6ft

Answers

Answer:

28.26 ft.²

Step-by-step explanation:

Mathematics: Explain/formula.

To find the area of a circle, multiply the radius by itself twice, then multiply the product by pi.

[tex]\pi r^2(3.14*radius*radius)[/tex]

[tex]\pi =pi[/tex]

Mathematics: Solve.

Here, the diameter is 6 ft.

To find the radius, divide the diameter by 2.

[tex]6/2=3[/tex]

[tex]radius=3[/tex]

Now, we can plug the numbers into the formula.

[tex]\pi 3^2(3.14*3*3)=28.26[/tex]

Mathematics: Conclude.

Therefore, the area of this circle is 28.26 ft.²

the area of the given circle will be 28.27 ft².

What is Area?

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, a circle that has a diameter of 6 ft,

Since, Radius = diameter/2

Thus,

Radius = 6/ 2

Radius = 3ft

From the formula of the area of the circle:

Area = pi* radius *radius

In our case,

Area = pi * 3 * 3

Area = 28.274

Therefore, the area of the given circle will be 28.27 ft².

Learn more about Area here:

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Colin is buying dirt to fill a garden bed that is a 9 ft by 18 ft rectangle. If he wants to fill it to a depth of 4
in, how many cubic yards of dirt does he need? If necessary, round to the nearest cubic yard. If dirt costs
530 per yd, how much will the project cost?
The project will require
|yd of dirt, and will costs

Answers

72 I just did the test

Linear Equation:
4x - 3y = 1
у
X

Answers

confused on what the question is?

Answer:

x (1/4,0) y (0,-1/3)

Step-by-step explanation:

x (1/4,0)

y (0,-1/3)

TERM 2: WEEK 8
CLASSWORK 1
1.
Solve the simultaneous equations using elimination method​
4x - 3y = 1
x + 3y = 19c
a.​

Answers

9514 1404 393

Answer:

  (x, y) = (4, 5)

Step-by-step explanation:

We notice that the coefficients of y are opposites, so we can eliminate y by adding the two equations together.

  (4x -3y) +(x +3y) = (1) +(19)

  5x = 20 . . . . . . simplify

  x = 4 . . . . . . . . .divide by 5

Substituting into the second equation gives ...

  4 +3y = 19

  3y = 15 . . . . . . . subtract 4

  y = 5 . . . . . . . . . divide by 3

The solution is (x, y) = (4, 5).

Find the measure of an angle in standard position for each reference angle.​

Answers

Step-by-step explanation:

1. 90+65= 155°

2. π+ π/6 = 7π/6 or 210°

3. 24+180=204°

4. 3π/2 + 2π/9 = (27π+4π)/18 = 31π/18

or 310°

HELP Ill give brainlist

Answers

Answer:

I think the answer is a

19 POINTS the answer is not the first or second option I’m maybe think the last one

Answers

D) there is almost no connection between US stocks and over seas stocks, since the US economy is different than the North Korean economy (the economy controls the stocks)

Damian has a bag that contains strawberry chews, cherry chews, and peach chews. He performs an experiment. Damian randomly removes a chew from the bag, records the result, and returns the chew to the bag. Damian performs the experiment 48 times. The results are shown below: A strawberry chew was selected 16 times. A cherry chew was selected 10 times. A peach chew was selected 22 times. Based on these results, express the probability that the next chew Damian removes from the bag will be cherry or peach as a fraction in simplest form.

Answers

Answer: 2/3

Step-by-step explanation:

The probability that the next chew Damian removes from the bag will be cherry or peach as a fraction in simplest form is 55/576

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability for the strawberry chews:

P(strawberry chews) = 16/48

Probability for the cherry chews:

P(cherry chews) = 10/48

Probability for the peach chews:

P(peach chews) = 22/48

Now the probability of cherry or peach = P(cherry)×P(peach)

[tex]=\frac{10}{48} \times\frac{22}{48}[/tex]

= 220/2304

= 55/576

Thus, the probability that the next chew Damian removes from the bag will be cherry or peach as a fraction in simplest form is 55/576

Learn more about the probability here:

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Please help which is the greatest one!

Answers

Answer:

the Answer is 2^5

Step-by-step explanation:

Answer:

2^5

Step-by-step explanation:

5^2 = 25

2^5 = 32

3^3 = 27

1^10 = 1

Hope that this helps!

What is the area of the triangle?

Answers

Answer:

Area of triangle 12 ft^2 Area of shaded region 84 ft^2

Step-by-step explanation:

area of triangle 6 x 4 / 2 =12

Shaded region 96-12= 84 ft^2

please help, seventh grade math problem

Answers

Answer:

12

Step-by-step explanation:

divide into two shapes. the first one being 2 x 4 units and the second being 2 x 2.

2 x 4 = 8

2 x 2 = 4

8 + 4 = 12

The answer is 12 square units.

Please mark brainliest if it was correct and helped!

Answer:

12

Step-by-step explanation:

just count the blocks

brainliest please???

Pls help me with this

Answers

Answer:

f(X)=2x is the correct answer

What is the area of AABC?
B
2
X2
O
2
A
6
O A 26
B 13
OC 226
D
26

Answers

Answer:

[tex]Area = 13[/tex]

Step-by-step explanation:

Given

[tex]A = (4,0)[/tex] -- [tex]x1,y1[/tex]

[tex]B =(5,5)[/tex] -- [tex]x2,y2[/tex]

[tex]C =(0,6)[/tex] -- [tex]x3,y3[/tex]

Required

Area of ABC

This is calculated as:

[tex]Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3|[/tex]

This gives:

[tex]Area = \frac{1}{2}|4 * 5 - 5 *0 +5*6 - 0*5 + 0*0 - 4*6|[/tex]

Using a calculator, we have:

[tex]Area = \frac{1}{2}|26|[/tex]

Remove absolute bracket

[tex]Area = \frac{1}{2}*26[/tex]

[tex]Area = 13[/tex]

Please and thank you

Answers

Answer:

[tex]68^\circ[/tex]

Step-by-step explanation:

FGD is congruent to CGE because they are vertical angles.

Because AB is a line and AGC makes a right angle, then CGB is also a right angle. Thus [tex]\angle{EGB} = \angle{CGB}-\angle{CGE}[/tex], or [tex]\angle{GCE} = 68^\circ[/tex]


. if 3, 2, y, 10 are in proportion, find the value of y​

Answers

Answer:

y = 15

Step-by-step explanation:

Given :

3, 2, y, 10

If the numbers are in proportion :

We can thus say :

3/2 = y/10

Cross multiply

3 * 10 = 2 * y

30 = 2y

Divide both sides by 2

30 / 2 = 2y / 2

15 = y

Help will give 20 points

Answers

Answer:1/3 divided by 6 equals 18

Step-by-step explanation: If you have a cloth that is 1/3 long then divide it by 6 it would look like 1/3 divided by 1/6 which would then equal 1/18.

I need help with this question and no links or I will report you

Answers

A: 0.748≈0.75(.88x.85)
B.1.63 (.88x1.85)


The estimated difference of 3209 and 1893, when rounded off to the nearest ten is
o(a) 1300
(b) 1310
(c) 1320
0 (d) 1000

Answers

Answer:

[tex] = (3209) - (1893) \\ = 1.32 \times {10}^{3} \\ = 1320[/tex]

[tex] \small{ \star{ \underline{ \blue{becker}}}}[/tex]

Answer:

1320

Step-by-step explanation:

round off

3209 ≈ 3210

1893 ≈ 1890

estimated difference = 3210 - 1890 = 1320

Jeb's weight w is 1/3rd of lago's weight a. Which equation could
be used to find Jeb's weight?
F: w=a-1/3
G:w=1/3(a)
H:w=1/3+a
J:w=a divided by 1/3

Answers

Answer:

:w=1/3(a)

Step-by-step explanation:

w = 1/3 × a

If Lago is 150lb, Jeb's  =

1/3 x 150 = 50 lb

If Lago is 60lb, Jeb's  =

1/3 x 60 = 20lb

please help will mark brainlist!!​

Answers

Answer:

x=28

y=28

Step-by-step explanation:

Equation 1:

Dived both sides by 0.75 to remove 3/4 from x.

(x-12)=16

Now, add 12 to both sides.

x=28

Equation 2:

Same here, divide both sides by 0.75.

y-12=16

Add 12 to both sides.

y=28

Help PLZZ NO FILES NO FILES

Answers

Answer:

A.) you multiply the 3 and 2

A.
The answer is A lol

Express the series using sigma notation. 1 + 4 + 16 + ... + 256.
a.

c.

b.

d.



Please select the best answer from the choices provided

A
B
C
D

Answers

Answer:

D

Step-by-step explanation:

By looking at the terms, we can notice that each term is 4 times the previous term. This means the series is geometric and we can rule out options A and B because of this. We can find the first terms of both options C and D to get:

first term c: 4

first term d: 1

The first term of our series is one, so that must mean D is the answer.

PLEASE HELP ME
Arnold deposits $6,000 into a certificate of deposit that pays 8% interest compounded quarterly . How much interest does his account earn in the first 3 years?

Answers

Answer:

8

Step-by-step explanation:

Tap A can fill 8 pails of the exact capacity in 5 minutes.
Tap B can fill 7 of the same pails in 4 minutes.
Tap A and B are turned on together to fill a total of 16 pails.
How long will it take the two taps to fill the 16 pails together? Give your answer in minutes and seconds to
the nearest second.​

Answers

Answer:

4min 47 seconds

Step-by-step explanation:

Together

8pails/5min + 7pails/4min = x

Use common denominator of 20

32/20 + 35/20 = 67pails/20min = 3.35pails/min

16/3.35 = 4.776119403 minutes

4min  60*0.776119403sec

4min 47 seconds

what is a lineary equation

Answers

Answer:

In mathematics, a linear equation is an equation that may be put in the form are the coefficients, which are often real numbers.

Step-by-step explanation:

Hope this helped Mark BRAINLIEST!!!!

What is the shape of the cross-section formed when a cylinder intersects a
plane as shown in the drawing?
O A. circle
B. oval
C. rectangle
OD. square

Answers

Answer: circle

Step-by-step explanation:

The shape of the cross-section is formed when a cylinder intersects the plane is a circle option (A) is correct.

What is a cylinder?

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we know, the circle is a set of points, where each point is at the same distance from a fixed point (called the center of a circle)


As we can see in the picture the cylinder is cut by a plane that is parallel to the base of the cylinder.

The base of the cylinder is a circle.

the shape of the cross-section is formed when a cylinder intersects a

the plane is a circle.

Thus, the shape of the cross-section is formed when a cylinder intersects the plane is a circle option (A) is correct.

Learn more about the cylinder here:

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e is 150% more than d . what is the ratio d:e in its simplest form? what is the ratio e:d in the form 1::n​

Answers

Answer:

d:e is 2:3

Step-by-step explanation:

if 'e' is 150% more than 'd' we can say that 'e' is 1.5 and 'd' is 1

ratio of 1/1.5 or 1÷3/2 is 2/3

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