Why does the expression i to the power 4n+2 is always equal to -1​

Answers

Answer 1

Answer:

See Below.

Step-by-step explanation:

We are given:

[tex]i^{4n+2}[/tex]

Using exponent properties:

[tex]=i^{4n}\cdot i^2[/tex]

Rewriting:

[tex]=(i^4)^n\cdot i^2[/tex]

Since i⁴ = 1 and i² = -1:

[tex]=(1)^n\cdot -1[/tex]

1 to any power is still 1:

[tex]=1\cdot -1 = -1[/tex]


Related Questions

Which situation is a true statement about payment options?
CLEAR CHECK
A, An advantage of online banking is that you do not need to keep detailed records when paying bills.

B, Paying with a credit card means the amount you spend will be deducted from your checking account.

C, Keeping track of your debit card transactions will help avoid charges resulting from insufficient funds.

D, To avoid paying interest on your credit card purchases, pay on

Answers

Answer:

C. Keeping track of your debit card transactions will help avoid charges resulting from insufficient funds.

Step-by-step explanation:

Correct on TTM

Answer:

C

Step-by-step explanation:

If -3x + 5 > 4, which of the following cannot be a value of x? 7.11B-S)
A -3
B -1
C о
D 4

Answers

Answer:

D

Step-by-step explanation:

Solving the inequality

- 3x + 5 > 4 ( subtract 5 from both sides )

- 3x > - 1

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative value.

x < [tex]\frac{1}{3}[/tex]

The only value not less than [tex]\frac{1}{3}[/tex] is 4 → D

1.1
QUESTION 1
Simplify the following without using a calculator
1.1.1 -4 * (8-(-3)) +7
1.1.2 + 55-20-4​

Answers

Answer:

−36.89

31.22

Step-by-step explanation:

¿si un comedor cuesta 17890, en cuanto se incrementa su precio al agregarle el 16% de iva?

Answers

branly is the best way to clean up the house and I will be there at the same time I don't have a car

Need help on this please help

Answers

do 20 x 3.14 and then youll have your anwser...id use a calculator btw

Then round it to the nearest whole number and BOOM anwser!!

i got 62.8 so round that and youll have ur anwser

-3x-5=16
what is x in the equation

Answers

Answer:

x=−7

Step-by-step explanation:

Step 1: Add 5 to both sides.

−3x−5+5=16+5

−3x=21

Step 2: Divide both sides by -3.

−3x/−3=21/−3

Answer:

x = -7

Step-by-step explanation:

Hello.

I can help.

To solve algebraic equations all you need to do is get rid of everything on the side of the x except the x.

Lets look at your problem.

-3x - 5 = 16

An important thing to note is we are going to get rid of things on the left side of the = by doing the opposite of what they're doing.

If it is addition we do subtraction

If it is division we do multiplication

and so on.

ALSO

Whatever we do on the left side of the = we must do the same thing to the number on the right.

Now, let us start trying to solve this.

You always want to start with the number that is alone without the variable / letter.

So :

-3x - 5 = 16

Since it is -5 lets add 5 to make it 0 and get rid of it.

-3x - 5 = 16

     +5  +5

(Remember to do it to the other side of the = too)

Now we have :

-3x = 21

Now we want to get rid of the 3 attached to the x. And since these two are multiplying we need to divide the -3 by itself to make it 1. Since one number divided by itself is 1.

So like this :

-3x = 21

/-3    /-3

NOTE : When you are dividing or multiplying negative numbers there is an important key to be aware of. Here is a short key to go off of :

- x - = +

- x + = -

So a negative times a negative will be a positive.

While a positive times a negative, the negative will over ride the positive and the answer will be negative.

Going back to the equation, here is what we do :

-3x / -3 = +x (Not negative)

And :

21 / -3 = -7 (Is negative)

So now our equation is :

x = -7

And this is our final answer.

I hope this helped.

If you have any questions or concerns do comment or message me. :)

(-3a^2 + 4a -5 +6a^3) + (-3a + 4 + 10a^2)

Answers

Answer

=6a3+7a2+a−1

Step-by-step explanation:

Let's simplify step-by-step.

−3a2+4a−5+6a3−3a+4+10a2

=−3a2+4a+−5+6a3+−3a+4+10a2

Combine Like Terms:

=−3a2+4a+−5+6a3+−3a+4+10a2

=(6a3)+(−3a2+10a2)+(4a+−3a)+(−5+4)

=6a3+7a2+a+−1

What property is demonstrated in the equation below? 4(5 + 3) = (5 + 34 associative commutative o distributive zero product​

Answers

Answer:

Distributive Property

Step-by-step explanation:

4*(5+3) basically equals 4*5 + 4*3 which is 20 + 12 which is 32.

Answer:

distributive

Step-by-step explanation:

i took this test

Segment AB has endpoints A(5, 2) and B(9, 10) that is divided by a point C such that AC and BC form a 2:3 ratio. The distance between the x-coordinates is 4 units. Which of the following fractions represent how far C is on the pathway from A to B? (6 points)

3 over 5
3 over 2
2 over 3
2 over 5

Answers

The answer is D. 2 over 5

Step-by-step explanation:

Took the test.

Last Friday David rented 4 movies from the video store. This Friday he rented 2 movies. Let x represent the cost of renting each movie. Write and simplify an expression for how much more David spent last week renting movies.

Answers

Expression:

4x - 2x

Simplified:

2x

f(x)=|2x+1|+3
g(x)=-2

find (f+g)(x)

Answers

Answer will be : b

hope this help's

For which value of x will the rational expression below be undefined? Check all that apply. (x-5)(x+2)/x+1 A. -5 B. -1 C. 1 D. 5 E. -2 F. 2

Answers

Answer:

B. -1

Step-by-step explanation:

Given expression:

(x-5)(x+2)/(x+1)

This is undefined when the denominator is zero:

x + 1 = 0x = -1

Correct choice is B

Answer:

Answer :-

[tex] \sf \: \dfrac{(x - 5)(x + 2)}{x + 1} [/tex]

Now,

Taking denominator as 0

x + 1 = 0

x = 0 - 1

x = -1

Write an
equation of a line with the given slope and y-intercept.
m=-2, b=3

Answers

Answer:

y=-2x+3

Step-by-step explanation:

y=mx+b

m=-2,b=3

so, y=-2x+3

hopes this helps

In a school contest, each student draws a number from 1 to 5 out of a large basket. The outcomes are shown in the table below.
Number Drawn 1 2 3 4 5
Times Drawn 83 79 88 72 85

Based on the data, what is the expected probability of drawing a 3?

Answers

Answer:

88/407

Step-by-step explanation:

The required, based on the data given, the expected probability of drawing a 3 is approximately 0.216 or 21.6%.

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,

To find the expected probability of drawing a 3, we need to calculate the total number of times any number was drawn and the number of times a 3 was drawn:

Total number of times any number was drawn = 83 + 79 + 88 + 72 + 85 = 407

The number of times a 3 was drawn = 88

The probability of drawing a 3 is then the number of times a 3 was drawn divided by the total number of times any number was drawn:

Probability of drawing a 3 = 88/407 ≈ 0.216

Therefore, based on the data given, the expected probability of drawing a 3 is approximately 0.216 or 21.6%.

Learn more about probability here:

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please help me on this will give you brainliest!!

Answers

the answer should be (13 x n)-8

the 2nd pic is question #1. if i made a mistake in that feel free to correct me

Answers

Answer:

A. x² + 4

Step-by-step explanation:

The second picture has:

1 + 4 = 1² + 44 + 4 = 2² + 49 + 4 = 3² + 4

The pattern is:

y = x² + 4

Correct option is A

Use the dimensions of the rectangular prism to label the indicated dimensions of its net.
Height is 29, width is 16, length is 9.

Answers

Answer:

It will be the 26th divided by 7

Help Please!! Will Give Brainliest to correct answer!

Answers

it’s the third choice

Answer:

It would be the last one square root of 6 over 4

Step-by-step explanation:

In a triangle, the measure of the first angle is 24 degrees more than the measure of the second angle. The measure of the third angle is four times the measure of the second angle. If the total number of degrees in a triangle is 180, what is the measure of the largest angle?
26 degrees
50 degrees
104 degrees
136 degrees

Answers

Here goes the answer. Hope it helps.

Measure of largest angle in a triangle is equals to 104 degrees.

What is triangle?

" Triangle is a 2 dimensional geometrical figure which has three sides and three vertices. Sum of all the angles of triangle is equals to 180°."

According to the question,

x represents the measure of first angle

y represents the measure of second angle

z represents the measure of third angle

Situation 1: First angle is 24 degree more than second angle , it represents the equation:

x = 24 + y               ____(1)

Situation 2: Third angle is four times the measure of second angle, it represents the equation:

z = 4y                       ___(2)

Situation 3: Total number of degree in a triangle is 180, it represents the equation :

x + y + z = 180°           ____(3)

Substitute the value of (1) and (2) in (3) we get,

24 + y + y + 4y = 180°

⇒ 6y + 24 = 180°

⇒ 6y = 180 - 24

⇒ 6y = 156

⇒ y = 26degrees

Therefore,

x = 24 + 26

  = 50 degrees

z = 4 × 26

  = 104 degrees

Hence, measure of largest angle in a triangle is equals to 104 degrees.

Learn more about triangles here

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Standard
Expanded
Written
6000 + 900 + 10 + 5

Answers

Answer: This is written in Expanded form.

Step-by-step explanation: The number is 6,915, to write a number in expanded form, write it's place values by the number it's in.

Ex: Expanded form of 5,731: 5,000 + 700 + 30 + 1

A petting zoo has 7 lambs, 12 rabbits, 6 goats, and 3 piglets. Find the
ratio of rabbits to the total number of animals. Write the ratio in
simplest form.

Answers

Answer:

3:7

Step-by-step explanation:

The number of rabbits is 12 while the total number of animals

7 + 12 + 6 + 3 = 28

So the ratio of rabbits to animals is 12:28 = 3:7

please helpppppp

Does the equation 5(x – 3) = 10x–15 have one solution, infinitely many solutions, or no solution?​

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

The equation 5(x - 3) = 10x - 15 has one solution, which is x = 0.

Let's simplify the given equation:

5(x - 3) = 10x - 15

Distribute the 5 on the left side:

5x - 15 = 10x - 15

Now, let's isolate the variables on one side by subtracting 5x from both sides:

-15 = 5x - 15

Next, add 15 to both sides:

0 = 5x

Divide both sides by 5:

0/5 = 5x/5

0 = x

Therefore, the equation simplifies to 0 = x. This means that x is equal to 0.

So, the equation 5(x - 3) = 10x - 15 has one solution, which is x = 0.

Learn more about equation click;

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solve each system by elimination.
-20x - 16y = -20
10x + 8y = 10​

Answers

Answer: None

Step-by-step explanation:

You have to either solve for x or y by getting x/y in both equations the same value to cancel them out. In my steps I will solve for x:

-20x - 16y = -20

10x + 8y = 10

----------

1.) Multiply 10x + 8y = 10 by 2

-20x - 16y = -20

20x + 16y = 20

2.) Cancel out values

All parts cancel out.

Answer: No solution

Please help the question is in the picture

Answers

Answer:

(1,-4)

Step-by-step explanation:

the solution is

(1, -4)

Shavon has a gift box shaped like a rectangular prism. The box is 12 inches long, 8 inches wide, and 3 inches high. What is the surface area if the gift box?

A. 156 in
B. 184 in
C. 312 in
D. 288 in

Answers

i believe that it’s C: 312 inches

Given the equation 25 + 7x = 11
x = -2
x = 2
X = -14
x = 14

Answers

Answer:

x = -2

Step-by-step explanation:

Isolate the variable (or x) by subtracting 25 from both sides.

We do this and get 7x = -14

Divide both sides by 7 and we get x = -2

I will give BRAINLIEST:)

Answers

Answer:

A'C'=AC=3

Step-by-step explanation:

Answer:

C: 3 units

Step-by-step explanation:

Just think about it... 180 degrees rotated is exactly opposite rotation degree.

If you rotate 90 degrees, the triangle will end up on quadrant 4.

Rotate 360 degrees, the triangle will stay in the same quadrant.

In conclusion, C is the best option

Super bowl reflection ( has to be about bucs because this is a question my teacher is asking for a grade and I didn’t watch it and we live in the bucs city so uh yea)

Favorite play?
Favorite commercial?
Favorite entertainer?

Answers

i didn't watch it but i liked that men's soap commercial

the owner of a pet shop buys budgie bells in packs of 30 bells. she pays 12p per bell. She sells 3/5 of the bells for 50p each and the rest for 40p each. How much profit does she make on the whole pack of budgie bells?

Answers

Answer: 1020p

Step-by-step explanation:

The total cost of the bells will be:

= 12p × 30 = 360p

She sells 3/5 of the bells for 50p each. This will be:

= (3/5 × 30) × 50

= 18 × 50p

= 900p

She sells the remaining 2/5 for 40p each. This will be:

= (2/5 × 30) × 40

= 12 × 40

= 480p

Then, total revenue will be:

= 900p + 480p

= 1380p

Profit = Revenue - Cost

= 1380p - 360p

= 1020p

So I need 20 words but I don’t get why so here’s this useless sentence

Answers

14(10) + 2, 14x10 is 140 plus 2 = 142
2(7(10) + 1) 7x10 = 70 + 1 = 2(71) = 142
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