Prove that the value of the expression is not divisible by 6 for any whole n:
(2n+1)(n+5)–2(n+3)–(5n+13).

Answers

Answer 1

Answer:

Step-by-step explanation:

(2n+1)(n+5) - 2(n+3) - (5n+13) = 2n² + 4n - 14 (*)

+) if n is divisible by 3 ⇒ n= 3k ⇒ (*)⇔ 2.9k² + 4.9k -14

2.9k² + 4.9k = 3( 2.3k² +4.3k) ║ 3 but  14∦3

⇒ with n =3k, (*)∦ 3 (1)

+) if n = 3k + m (m∦ 3)

⇒ (*) ⇔ 2.(3k+m)² + 4.(3k+m) -14 = 2.9k² + 2.3k.m + 2m² + 4.3k + 4m -14

= 3(2.3k² + 2.km + 4k) +2m² + 4m -14

3(2.3k² + 2km + 4k)║3 but (2m²+4m-14)∦3

⇒ with n = 3k+m, (*) ∦ 3 (2)

(1)(2)⇒ [(2n+1)(n + 5) - 2(n+3) - (5n+13)] ∦ 3

⇒ (2n+1)(n+5)–2(n+3)–(5n+13)   is not divisible by 6 for any whole n

║is divisible∦ is not divisible

Related Questions

The first four terms of a sequence are show below. 3, 9, 27, 81.. Which function models this sequence?
A) 3^n,
B) 3^n-1
C)3n
D)9(-3)^n-1

Please help

Answers

I think either b or d

Please help with this problem

Answers

Answer:

ok its 45

Step-by-step explanation:

No problem

Answer:

the 48 oz becuase it more then the others and its cheaper

Step-by-step explanation:

Solve: - 4x +3<-9

idk tbh

Answers

Answer:

[tex]x > 3[/tex]

Step-by-step explanation:

Luckily for our brains, inequalities work very similar to equations when solving. Let's get on it.

First, we need to subtract 3 from both sides to isolate the -4x (this means we can then divide to get x by itself).

Which leaves us with [tex]-4x<-12[/tex].

Now we need to divide both sides by -4. Here's the thing - with inequalities, when we divide both sides by a negative, the sign flips! So after doing this simplification, our inequality looks like this: [tex]x > 3[/tex]

And there's your answer. :)

Answer:

x>3

Step-by-step explanation:

What is the solution to this system of linear equations?
y − x = 6
y + x = −10

a. (−2, −8)
b. (−8, −2)
c. (6, −10)
d. (−10, 6)

Answers

Answer:

B: (-8,-2)

you add the equation to solve the first variable, then plug in the values to the other equation to find the last variable

good Luck!!!

What is cos(3π)?
1
0
-1
-2

Answers

Answer:

cos(3π) is 0.986 which rounds to 1

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

edge 2020

With the equation 3z + 3 = 22 + 6, the value of z is

Answers

The answer is 25/3 or 8 1/3! Please vove me brainlyist :)

Graph the following system of equations. Click on the graph until the correct one appears.

y > x

y ≤ -x + 2

(look at attached pictures)

Answers

Answer:

pic 2

Step-by-step explanation:

if you are given two coordinate points, you need to first find the?​

Answers

Answer: First you need to find the first point on the coordinate graph..which would be x then y. Remember run before you jump.

Step-by-step explanation:

The first point on the coordinate graph, x, must be identified first. Remember to run before you jump.

What is the coordinate points?

A set of variables that accurately depicts a position. On a graph, the first number represents the distance along, and the second number represents the distance up or down. For example, the point (12,5) is 12 units down and 5 units up.

A coordinate plane is an organizing structure for graphing and describing lines and points. The coordinate plane is made up of a vertical (y) axis and a horizontal (x) axis. The coordinate plane is divided into four quadrants. The origin is where these lines intersect (0, 0).

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x, y).

To learn more about  coordinate points refer to:

https://brainly.com/question/11337174

#SPJ2

what do the differences between the points represent

Answers

Answer:

The point represent the difference between the two sides that what are different between them.

please help me im despreate

Answers

Answer:

The answ is B

Step-by-step explanation:

Remember. Why is it called parallelogram. Look at the first section of the word parallelogram. You can see “parallel.” Rhombus has 4 parallel lines that are diagonal to each other.

Pour tout réel x, on pose : f(x) = -2x²+4x+6. Vérifier que (-1) est une racine de ce polynôme f. On sait que l'axe de symétrie de la parabole qui représente f est la droite d'équation : x=1. Déduire de cette information l'autre racine du polynôme f. Factoriser le polynôme f. Aidez-moi svp meci d'avance

Answers

Explication étape par étape:

Étant donné la fonction polynomiale f (x) = -2x² + 4x + 6. Pour vérifier si f (-1) est un facteur de l'expression, nous devons montrer que f (-1) est équivalent à zéro. S'il est nul, donc x + 1 est un facteur du polynôme.

Preuve

f (x) = -2x² + 4x + 6

f (-1) = -2 (-1) ² + 4 (-1) +6

f (-1) = -2 (1) -4 + 6

f (-1) = -2-4 + 6

f (-1) = -6 + 6

f (-1) = 0

Puisque f (-1) = 0, donc x + 1 est un facteur du polynôme.

Ensuite, il faut obtenir l'autre racine du polynôme. Pour obtenir cela, nous devons factoriser la fonction polynomiale donnée.

Soit f (x) = 0

-2x² + 4x + 6 = 0

multiplier par -1

2x²-4x-6 = 0

diviser par 2

x²-2x-3 = 0

x²-3x + x-3 = 0

x (x-3) +1 (x-3) = 0

(x + 1) (x-3) = 0

x + 1 = 0 et x-3 = 0

x = 1 et x = 3

Par conséquent, l'autre racine du polynôme en dehors de 1 est x = 3

Use the problem 34.65 ÷ 10³

Answers

34.65 / 10^3
34.65 / 1000

0.03465
Answer: when following PEMDAS (parenthesis, exponents, multiplication, division, addition, and subtraction,) the answer comes out to 34.65 / 1000. The answer after that is 0.03465.

HELP PLEASE!!! I dont get this and its due in 5 minutes

If y varies directly with x and y=−54 when x=−20, then which equation best represents this proportional relationship?


1. ) y = 0.37x

2.) y = 2.7x


3.) y = -0.37x


4.) y = -2.7x

Answers

it’s answer 4 i believe

WILL MARK BRAINLIEST
Jerome has read 50 pages of a novel. He plans to read a certain number of pages, p, each day from Monday to Friday. Which inequality shows that Jerome wants to have read at least 85 pages by the end of the day on Friday?

A. 50 + 5p ≥ 85
B. 50 + 5p ≤ 85
C. 5 (50 + p) ≥ 85
D. 5 (50 + p) ≤ 85

Answers

Answer:

There ya go

Step-by-step explanation:

If Jerome wants to have read at least 85 pages by the end of the day on Friday, then the inequality that represents the situation will be 50 + 5p≥ 85

Given that the number of pages he read each day is "p", the number of pages he will read from Monday to Friday is 5p (Monday to Friday is 5 days)

If he has read  50 pages of a novel, the total number of books he has read will be 50 + 5p

If Jerome wants to have read at least 85 pages by the end of the day on Friday, then the inequality that represents the situation will be 50 + 5p≥ 85

Learn more here: https://brainly.com/question/15816805

8 POINTS!! which of the transformations that could take Figure P to Figure Q.

Answers

I believe it’s a single reflection:)

please help this is timed

Answers

Answer:

66 degrees

Step-by-step explanation:

I dont remember the name of this law but ik its right

$haA graph has time (years) on the x-axis and height (inches) on the y-axis. A line goes through points (2, 3) and (4, 6). The graph shows a linear relationship between the height and years of a plant’s growth. Find the rate of change. Select all that apply. The rate of change of a linear function is always the same. The rate of change of a linear function increases as the input increases. The rate of change from 2 years to 4 years on the graph is 1.5 inches per year. The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

Answers

Answer:

The rate of change of a linear function is always the same.

The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

Step-by-step explanation:

Vote brainiest

3x2 + 8x - 10
Please someone help ...

Answers

3x2+8x-10 // the answer is 8x

In math class, you have the following scores: 77, 82, and 73. If the
last test has a maximum of 100 points, what score do you need for
an average of 80?

Answers

Answer: 88

Step-by-step explanation: 77+82+73= 232. So you need an 80 for average. So what you have to do is 80x4 and that equals to 320. last step is to subtract 320-232 and you get 88. 77+82+73+88=320.

Answer:

Did you actually get that score???

Actually, it is none- of my buisness, but no one will judge

and probably not for the 77 and 73 your grade just go's up 2 points if you get a 100

Which of the following is a line that is
perpendicular to y
2 and passes
through the point (-2,4)?

y - 4= 1/3 (x + 2)
y - 4= -3(x+2)
y - 4= -3(x - 2)
y - 4= 3(x + 2)

Answers

Answer:

y - 4= -3(x - 2)

I'm 101% sure

Y-4=-3(x-2) your welcome

(3) (-9) what is the answer

Answers

Answer:

-27

Step-by-step explanation:

Positive times negative is always a negative or use a calculator

I NEED HELP PLEASE HELP ME

Answers

Answer:

4 squares?

Step-by-step explanation:

Find the next two numbers in the pattern.

−12,60,−300,1500

Answers

the pattern is

multiplied by -5

so...

1500 *-5 = -7500

-7500*-5 = 37500

hope this helps

Answer:

-7500,37500 are next two numbers in the pattern

PLEASE HELP THIS IS OVER DUE.

Answers

Answer:

(-2,-4)

Step-by-step explanation:

Cant explain but its that one.

x + y = -7
-x+ 4y = 17
X=
y =

Answers

Answer:

x= -9,  y= 2

Step-by-step explanation:

5y=10

y=2

x+2=-7

x=-9

Answer:

x=-9y=2

Step-by-step explanation:

[tex]x + y = - 7[/tex]

[tex] - x + 4y = 17[/tex]

[tex]y = - 7 - x[/tex]

[tex]x = 4y - 17[/tex]

[tex]y = - 7 - 4y + 17[/tex]

[tex]5y = 10 \\ y = 2[/tex]

[tex]x = 4y - 17 = 4 \times 2 - 17 = 8 - 17 = -9 \\ x = -9[/tex]

You buy a sandwich for ​$​ 3.55 an apple for ​$​0.65 and a bottle of juice for ​$2.45.What is the total​ cost?

Answers

$3.55 + $0.65 + $2.45 = $6.65

The total cost is $6.65.

The total cost of your items is $6.65. When asking for the total cost, they are asking you to add the values.

3.55 + 0.65 + 2.45 = 6.65.

Carrie needs to determine the number of towels that will fit each row along the back of the shower if the back of the shower measures 6 feet long and each towel is 2/3 a foot long which equation shows how to determine the number of tiles that will fit in each row

Answers

Answer:

6 / 2/3 = 9

Step-by-step explanation:

Carrie want to find out the number of towels that will fit each row along the back of the shower

The back of the shower measures 6 ft long

Each towel is 2/3 foot long

Therefore the equation which shows how to determine the number of tile that will fit in each row is

Since 1 tile is 2/3 foot long then the number the number of tile in each row is

= 6 / 2/3

= 6 ×3/2

= 18/2

= 9

Which of the following numbers is a composite number?
OA) 13
OB) 31
OC) 49
OD) 67

Answers

Step-by-step explanation:

First you will need to know what a composite number is.

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.

see pic below

I think it would be OC) 49

(Because that is a composite number.)

[tex]hopethis helps[/tex]

Please help! i dont understand

Answers

Answer:

3x2>n+2x7>n

Step-by-step explanation:

from what I understand, you're suppose to write what's its saying in numbers. so you have to write three times two more than the number n in numbers then add that expression with two times seven more than the number n. I hope I helped

please help urgent easy 8th grade math

Answers

Answer:

No Solution

Step-by-step explanation:

8x-3(1+6x) -2>5(1+2x)

-10x-5>-5-10x

(Add 5 to both sides)

-10>-10x

(Add 10x to both sides)

-10x+10x>-10x+10x

Therefore , this equation has no solutions.

Answer:

-1=x

Step-by-step explanation

8x-3(1+6x)-2> 5(1+2x)

   8x-3(7x)-2>5(3x)

      8x-21x-2>15x

            13x-2>15x

           -13       -13

             -2     2x

            2         2

            -1        x

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