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

Write the equation of the line that has a slope of 10/3 and the y intercept of 12

Answers

                 y=10/3x+12

The x is after the fraction

how do I explain this?​

Answers

Answer:

Step-by-step explanation:

To do this, we have to prove that ∠1=∠5. We can do this using the corresponding angles theorem, which states that these two angles are congruent. Since ∠G=∠1, we can say ∠G=∠1=∠5, and as this, ∠G=∠5

the monthly revenue for printer ink for a large office supply store is r(x) =-x^2 +12x+13, where x is the price of an ink cartridge in dollars and r(x) is in hundreds of dollars. what is the maximum monthly ink revenue​

Answers

Answer:

6u77vhy46yvt g vgj v6. hy

Step-by-step explanation:

guv yg

Evaluate the expression 9z – 4 for z = 3.

Answers

Answer:

27 is the final answer

Step-by-step explanation:

9z-4=

9(3)-4=

27-4=

I WILL AWARD BRAINLIST PLS SOLVE

Answers

Answer:

Ah yes rsm.

Anyways, AB is parallel to DE so 72= angle BDE. So BDE+2x+2x=180

72+4x=180

108=4x

x=27

4x – 8 = 32
How do I solve this

Answers

Answer:4

x

+

8

=

32

Step-by-step explanation:Isolate for

x

. Start by subtracting

8

from both sides of the equation.

4

x

+

8

8

=

32

8

4

x

=

24

Divide both sides of the equation by

4

.

4

x

4

=

24

4

x

=

6

Answer:

10

Step-by-step explanation:

4x-8=32

4x=32+8

4x=40

x=40/4

x=10

A village is 10km on a bearing 050° from a point O. Calculate how far the village is north of O.

Answers

Answer:

7.66 km

Step-by-step explanation:

Let distance village is ; north of O = x

Using Pythagoras rule :

Sinθ = opposite / hypotenus

Opposite = x

Hypotenus = 10

θ = 50°

Sin50 = x / 10

0.7660444 = x / 10

x = 0.7660444 * 10

x = 7.6604444

x = 7.66

Help please I don’t get it

Answers

Answer:

B

Step-by-step explanation:

when the arrow is pointing toward the left side that means less than side. When the arrow is pointing towards the right side that means greater than.

Answer:

B, because that symbol means at least so you would go to the negative side which is on the left it has to start from 4 which is correct and this means negative: - The 0 is the origin so from the origin to the left side is negative from the origin to the right side is positive you want to look for negative because it's negative 4.

y = 3.2 – 24
5x - y = 8
The solution is

Answers

X= -8
Y= -48

Explanation:
Since we know that 3x-24 is equal to y, we can plug that in for y in the equation 5x-y=8. That would look like 5x-(3x-24)=8. Distribute the -1 and you will get 5x-3x+24=8. Subtract 24 from both sides and get 2x=-16. Divide both by 2 and get x=-8. Than plug in -8 for y in one of the equations to get the y. You will get -48.

7x+3(-4x-2)=-6 how do i solve

Answers

Answer:

Step-by-step explanation:

7x+3  (-4x-2)=-6

remove the parenthesis

7x-12x-6=-6

-5x=0

x=0

How to solve your question- 7

In the diagram, which pair of angles are vertical angles?
•<1 and <2
•<4 and<6
•<6 and <8
•<5 and <3

Answers

angle 6 and angle 8 because they’re across from each other

ILL GIVE BRAINLIESTTTTTT
help!!! use proportional reasoning to find 65%of 200.... also whats the part and wholeeeeeee thanks

Answers

Answer:

130

Step-by-step explanation:

65*2=130

Solve the system of equations by graphing. [x+y=4 7x-6y=54​

Answers

Answer:

(x,y)=(6,-2)

Step-by-step explanation:

to understand thisyou need to know about:linear equationsystem of linear equationsolving system of linear equation by graphingPEMDASgiven:[tex] \begin{cases} \sf x + y = 4 \\ \sf7x - 6y = 54 \end{cases}[/tex]tips and formulas:to solve system of linear equation by graphing we have to simplify the linear equations to slope-intercept formslope intercept form:y=mx+blet's solve:

let's simplify first linear equation to slope -intercept form

x+y=4

y=-x+4

table for this equation

see the first attachment picture

let's simplify first linear equation to slope -intercept form

[tex] \sf7x - 6y = 54[/tex]

[tex] \sf - 6y = - 7x + 54 \\ \sf \frac{ - 6y}{ - 6} = \frac{ - 7}{ - 6} x + \frac{54}{ - 6} \\ \sf y = \frac{7}{6} x - 9[/tex]

table for this equation

see the second attached picture

solutions by graphing the system of linear equation

see the last attached picture

note: the red line is for first equation as well as the green line is for second equation and the black dot is the coordinates of the solutions of x and y

Jasmine ran 5 miles in 42 minutes.

Part A

At what rate did Jasmine run?

Jasmine ran at a rate of _____ minutes per mile.



Part B

Katie ran 4 miles. She ran at a rate that was 1.1 minutes per mile slower than Jasmine.

For how many minutes did Katie run? Explain how you determined your answer.

Answers

Answer:

part A 210 Part B  4.4

Step-by-step explanation:

PART A    42 TIMES 5   210

that will be the rate she ran.

PART B 1.1 times 4 that will be the minute.

The line models the cost of renting a bike. It costs ​$2 per hour plus a ​$4 deposit. Write an equation in​ slope-intercept form for the line where x is the number of hours a bike is rented and y is the total cost of renting a bike. How much does it cost to rent a bike for 3 ​hours?

Answers

Answer:

Step-by-step explanation:

2 votes

Which three lengths CANNOT be the lenghts of the sides of a triangle? A. 16m, 5m, 10m B. 15m, 11m, 10m C. 23m, 20m, 13m D. 5m, 8m, 9m

Answers

Answer:

C. 23m, 20m, 13m

Step-by-step explanation:

Hope it help

Sorry if my answer is wrong

Help please! I really need it! please dont guess if you dont know, dont answer.....( this is basic geometry im just dum'b) part 4

Answers

Answer:

m<2 = 120

Step-by-step explanation:

When two lines are parallel and are intersected by a transversal, same side exterior angles are supplementary, meaning that their angle measures add up to 180 degrees.

Using this, one can form the equation;

m<8 + m<2 = 180

Substitute,

60 + m<2 = 180

Inverse operations,

60 + m<2 = 180

-60              -60

m<2 = 120

Answer:

Step-by-step explanation:

Solution

<8 = 60 degrees.

<6 is <8s supplement

<6 + <6 = 180

60 + <6 = 180

<6 = 180 - 60

<6 = 120

<2 and <6 are corresponding angles and are therefore equal.

<2 = 120

The table shows the relationship between the number that fit into given number of boxes from a bakery . What is the missing value in the table

Answers

Answer:

The missing value should be 48 because between the two numbers of each group. They are multplied by 6

Step-by-step explanation:

Hope this Helped!

Answer:

yeah 48 is the answer

you're correct

Help me !!!!!!!!!!!!!!!!!

Answers

Answer:

D. Neither

Step-by-step explanation:

Ok so,

lets plug in the ordered pairs to see if the answer matches up. It should look like this:

7 = -2 - 5

7 = -7      DOES NOT MATCH; INCORRECT

now lets do it with the other ordered pair

-7 = -4 -5

-7 = -9        DOES NOT MATCH; INCORRECT

hope this helps, have a good day!

please mark brainliest if possible!!! :)

Answer:SEARCH UP ON THE INTERNET HEHEH

Step-by-step explanation:

Help I need to submit soon

Answers

Answer:

4

Step-by-step explanation:

I don't know if u want the explanation

i got 4 as the answer

Please help and make it right.....

Answers

Answer:

-1

Step-by-step explanation:

6/7-1=11/14 11/14-1=5/7 and so on.

12/14, 11/14, 10/14, 9/14, next term is 8/24 which is simplified to 1/3

In ΔFGH, g = 7.6 inches, h = 3.2 inches and ∠F=160°. Find the length of f, to the nearest 10th of an inch.

Answers

In ΔFGH, g = 7.6 inches, h = 3.2 inches and ∠F=160°. Find the length of f, to the nearest 10th of an inch.

=10.7

The length of f from the given triangle FGH is 10.7 inches.

What is cosine rule?

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine states that: a² = b² + c² − 2bc·cosA.

Given that, in ΔFGH, g = 7.6 inches, h = 3.2 inches and ∠F=160°.

Here, f² = 7.6² + 3.2² − 2×7.6×3.2×cos160°

f² = 57.76+10.24-48.64×(- 0.9396)

f² = 68+45.70

f² = 113.7

f = √113.7

f = 10.7 inches

Therefore, the length of f is 10.7 inches.

Learn more about the cosine rule here:

https://brainly.com/question/28716982.

#SPJ3

An isosceles triangle has an angle that measures 78.Which other angles could be in that
isosceles triangle? Choose all that apply.
HELP PLEASE

Answers

Answer:

78, 51, 51

or

78, 78, 24

Step-by-step explanation:

78, 51, 51

or

78, 78, 24

Shoes cost $135. If you save $27 with a sale, what is the percent discount?

Answers

Answer:

the precent discount is 20%

(27 / 135) x 100 = 20%

I hope this helps! ^^

☁️☁️☁️☁️☁️☁️☁️

pa help po pls ASAP plssss​

Answers

On A type Fa,La,Do on B Type Mi,So,Ti

Given 2 points find the slope using the slope formula. Show all work.
12-Y
me
Xzx,

Answers

What are the coordinates of the 2 points?

The distance from Charles's house to his school is 3 miles. His father gave him a ride for 1,760 yards, and he walked the rest of the way. The distance that Charles walked is miles or yards. (Hint: 1 mile = 1,760 yards.)

Answers

Answer:

2 miles or 3520 yards

Step-by-step explanation:

The distance from Charles's house to his school is 3 miles. His father gave him a ride for 1,760 yards, and he walked the rest of the way. The distance that Charles walked is miles or yards. (Hint: 1 mile = 1,760 yards.)

From the Question, we know that

1 mile = 1,760 yards..

His father gave him a ride for 1,760 yards,

Hence, the number of miles Charle's father drove him was 1 mile

The distance that Charles walked in miles is calculated as:

3 miles - 1 mile

= 2 miles

Converting to yards

1 mile = 1,760 yards..

2 miles = x

Cross Multiply

x = 2 × 1760 yards

= 3520 yards

Write an equation, slope of -7 y-intercept of 5

Answers

y=-7x+5

(y=mx+b)
m- slope
b- y-intercept

Name the ordered pair for Q

Answers

0,8 because you have to do x,y and x=0 and y=8
C. (0, 8). Next time just know that the first number in a ordered pair is on the X-axis and the second number is the Y-axis

what is slop intercept from​

Answers

Answer:

Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line. Watch this video to learn more about it and see some examples.

Step-by-step explanation:

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