explain why n(n-1) must be an even number​

Answers

Answer 1

n & n - 1 are two consecutive numbers which means one of is surely even and the other one is odd.

_______________________________

Suppose that n is an even number;

So we can right n like this :

n = 2t

Thus :

n - 1 = 2t - 1

_______________________________

n( n - 1 ) = 2t( 2t - 1 ) = 2 ( 2t^2 - t )

= 2 ( q ) = 2q

The number obtained is a multiple of 2, so it is definitely even because all numbers are even multiples of 2.


Related Questions

please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

Answer:

805

Step-by-step explanation:

The answer is V≈201.06in³

please help its easy im just not smart enough to do it lma0

Answers

Answer:

20 feet

Step-by-step explanation:

66/3.3

it's twenty i dont know what else to say

Answer:

20m

Step-by-step explanation:

1m = 3.3ft

66 feet = 20m

 

pliss give me the aswer

Answers

Answer:

AA

Step-by-step explanation:

AA

Answer:

15+ 8d

After d day,she has read 15 +8d pages

Jake draws A POR on the coordinate plane
A. 20.13 units
B. 19.42 unit
C. 18.71units
D. 18 units

Answers

the answer is c18.71

Jean walks forward 80 feet to his mailbox. He then walks the 80 feet
back. Does Jean end up back where he started?

Answers

Answer:

yes

Step-by-step explanation:

2w^2-9w+3=-4w solve the equation for all real solutions

Answers

Answer:

w= 1

w= 3/2

Step-by-step explanation:

x) sec’A + cosec?A
secA. cosecA​

Answers

Answer:

(Sin A + Cos A)/Sin A. Cos A

Step-by-step explanation:

As we know

Sec A = 1/Cos A

and Cosec A = 1/Sin A

Given Equation

Sec A + Cosec A

Substituting the given values, we get -

1/cos A + 1/Sin A

(Sin A + Cos A)/Sin A. Cos A

please help i give all my points

Answers

where is the drip at?

How do I solve this?
Please help

Answers

Filling in the boxes:
Top row outside box: 3c and 8
Second row outside box: - or -1
Inside box: -3c and -8

Expanded: -3c - 8

Helppp easy math please !!!!

Answers

Answer:

x=5      x=1

Step-by-step explanation:

To find the x intercepts, set y=0

(x-5) (x-1) =0

Using the zero product property

x-5 =0   x-1 =0

x=5      x=1

Dr. Porterfield has a choice of bread (pink, purple), meat (ham, turkey, beef) and Cheese (American, Swiss, Portugues, Japanese) at a sandwich shop. What is the probability he will select a sandwich on purple bread with either beef or turkey and has Japanese cheese

Answers

Answer:

The probability is 0.08[tex]\overline 3[/tex]

Step-by-step explanation:

The choice of bread Dr Porterfield has = Pink, purple

The number of types of breads = 2

The choices of meat = Ham, turkey, beef

The number of types of meat = 3

The choice of cheese = American, Swiss, Portuguese, Japanese

The number of types of cheese = 4

The probability of selecting purple bread from pink or purple = 1/2

The probability of selecting beef or turkey from the 3 choices of meat = 2/3

The probability of selecting Japanese cheese from the fourvtypes of cheese = 1/4

Therefore, the probability he will select a sandwich on purple bread with either beef or turkey and has Japanese cheese = (1/2) × (2/3) × (1/4) = 2/24 = 1/12 = 0.08[tex]\overline 3[/tex]

Niall has half dollar mary has a tenth of a dollar and jack has a hundredth of a dollar if they combine their money do the 4 students have more or less than a dollar

Answers

Answer: Students have less than a dollar.

Step-by-step explanation:

Niall has $1/2

Mary has $1/10

Jack has $1/100

Add these up to see if they reach 1.

= 1/2 + 1/10 + 1/100

Convert to decimals by dividing the numerator by the denominator:

= 0.5 + 0.1 + 0.01

= $0.61

Students have less than a dollar.


[tex] {x}^{2} + 16x + 10 = 0[/tex]Split the middle term.​

Answers

Answer :-0.65 , -15.34

what is the answer to −5/12−3/10

Answers

Answer:

The answer is -0.71666666666 in decimal form.

In fraction form it is -43/60.

Step-by-step explanation:

please help. It’s due tomorrow.

Answers

Answer:

It is assumed you need to find the area of shaded region.Results rounded to the nearest hundredth.

#1

Shaded area:

A = 32² - 16*π*(32/8)² = 219.75 cm²

#2

Shaded area:

A = π*2² - 2*π*(2/2)² = 6.28 cm²

219.75cm²

3.14cm²

Answer:

Solution given:

1.

[r]radius of each circle =32/8=4cm

[l]length of square=32cm

Area of shaded region =area of square- area of 16 circle=l²-11*πr²=32²-16*π*4²=219.75cm²

Step-by-step explanation:

radius for big circle [R]=2cm

radius for small circle [r]=1cm

area of shaded region=area of big semi circle -2 area of semi small circle

=½πR²-2*½πr²

=½*π*2²-π*1²

=2π-π

=π=3.14cm²

Which expression would you use to determine the missing number in the sequence? 11, ____, 25, 32, 39

Answers

The number is 18 ………,,……..
18 because if it’s jumping by 7 you would just add seven

A movie begins at 4:40 pm and it’s last 2 housers and 20 minutes

Answers

Answer: 7:00

Step-by-step explanation:

hope that helps

its 7:00, hope that helps you out!

Please help!!!!!!
BRainliest.

Answers

Answer:

4.974

Step-by-step explanation:


I need help plss!! Thankyou in advance!!

The sum of Bill's age and
Nancy's age is 45. In three years, bill will be three times as old as Nancy
was four years ago. Create a system of linear equations to represent the relationship between
Bill's age and Nancy's age. Solve the system graphically to determine how old Bill and Nancy are
today?

Answers

Answer:15

Step-by-step explanation:

Find the area of the figure below

Answers

Answer:

the answer 240

Step-by-step explanation:

times 24 and 10 to get 240 m

Skyler has 20 comic books about the Avengers. He goes to the comic book
store and after he leaves, he now has 26 Avengers comics. What is Chris'
percent increase in Avenger comics? *

Answers

I love Marvel but anyways i think it’s 6%

Answer:

6%

Step-by-step explanation:

In your wallet you have the following paper money: 2 singles, 4 fives, 3 tens, and 6 twenties. What is the probability that you will draw a 5 and then a 10?

Answers

Answer:

Step-by-step explanation:

will give brainlist, pls help lol

Answers

Answer:

D, 144

Step-by-step explanation:

Find x first by solving 9x+27=6x+66, and plug x in to the angle RSL.

what is 13 over 4 multiplied by 3 over 2

Answers

Answer:

so this is the correct answer right

Answer:

[tex]\frac{39}{8}[/tex]

Step-by-step explanation:

Multiply the numerators: [tex]13*3= 39[/tex]

Multiply the denominators: [tex]4*2=8[/tex]

Final answer: [tex]\frac{39}{8}[/tex]

It is in simplest form, by the way.

What is the area of the triangle?
10
8
6

Answers

Answer:

10

Step-by-step explanation:

An isosceles triangle has base angles that each measure 42°. Which equation can be used to find z, the measure of the third angle of this isosceles triangle in degrees? \

Answers

Answer:

42 + 42 + z = 180

Step-by-step explanation:

Note that:

Base angles in an isosceles triangle are equal in measure.

The sum of angles in a triangle is 180°.

Thus, the equation would be

42 + 42 + z = 180

Arrange the matrices in increasing order of their determinant values.

Answers

Answer:

c, a, b

Step-by-step explanation:

Given

See attachment for matrices

(a)

[tex]D = \left[\begin{array}{cc}\cos\theta &\sin\theta\\ -\sin\theta& \cos\theta\\\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D |= (\cos\theta * \cos\theta - \sin\theta *- \sin\theta)[/tex]

[tex]|D | = \cos^2\theta + \sin^2\theta[/tex]

Using trigonometry ratio, we have:

[tex]|D | = 1[/tex]

(b)

[tex]\left[\begin{array}{ccc}2&0\\0&2\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D| = 2 * 2 - 0 * 0[/tex]

[tex]|D| = 4 - 0[/tex]

[tex]|D| = 4[/tex]

(c)

[tex]\left[\begin{array}{ccc}0&i\\-i&0\end{array}\right][/tex]

The determinant of the matrix is:

[tex]|D| = 0 * 0 -(-i * i)[/tex]

[tex]|D| = 0 +i^2[/tex]

[tex]|D| = i^2[/tex]

In complex numbers

[tex]i^2 = -1[/tex]

So:

[tex]|D| = -1[/tex]

So, the order of the determinants is: c, a, b

40:√100 + √9.√36

????​

Answers

Answer:

28

Step-by-step explanation:

[tex]\sqrt{100} + (\sqrt{9} \cdot \sqrt{36}) = 10 + (3 \cdot 6) = 10 + 18 = 28[/tex]

it’s two different answers but i need help !!

Answers

Answer:

use this to help you determine your answer

Step-by-step explanation:

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. ... and another pair of corresponding sides are equal in two right triangles.

(7x-3y)/(y-2x) = -(3/5).
Find the value of x/y. ​

Answers

Answer:

x =  12 y       y = 29x

     29             12

Step-by-step explanation:

x / y = 12 / 29

Cross multiply to get
5(7x - 3y) = -3(y - 2x)
35x - 15y = -3y + 6x
35x - 6x = -3y + 15y
29x = 12y
x = 12y / 29
x/y = 12 / 29
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