The number i can be raised to whole number powers.

Look at the first four powers of i shown, and then use the drop-down menus to evaluate the expressions below.

The Number I Can Be Raised To Whole Number Powers.Look At The First Four Powers Of I Shown, And Then

Answers

Answer 1

Answer:

[tex]i^{8}=1[/tex] and [tex]i^{34}=-1[/tex] will be the answer.

Step-by-step explanation:

Since i = [tex]\sqrt{(-1)}[/tex]

i² = (-1)

[tex]i^{3}=-i[/tex]

[tex]i^{4}=(-1)^{2}[/tex] = 1

[tex]i^{8}=1^{2}[/tex] = 1

[tex](i^{8})^{2}=1[/tex]

[tex]i^{34}=[i^{17}]^2[/tex]

     = [tex](i^{8}\times i^{8}\times i)^{2}[/tex]

     = [1 × 1 × √(-1)]²

     = 1² × 1² × [√(-1)]²

     = (-1)

Therefore, [tex]i^{8}=1[/tex] and [tex]i^{34}=-1[/tex] will be the answer.


Related Questions

I need a fast answer plz!!!


find the slope of the line​

Answers

Answer:

idk

Step-by-step explanation:

Answer:

-4/5

Step-by-step explanation:

over 4 to the left up 5

Please help!
You roll a 6-sided die two times.

What is the probability of rolling a number less than 3 and then rolling a 6?

Simplify your answer and write it as a fraction or whole number.

Answers

Answer:

number less than 3=1 and 2

so 2/6 = 1/3 in lowest terms

then rolling a 6 =

there is only one 6 so it will be 1/6

I hope I helped

Please help me now plz I promise I will mark you brainliest

Answers

Answer:

It should be 72 degrees

Step-by-step explanation:

angle j and h are the same so you just add 63 to 45 and once you get 108, just subtract that from 180 degrees which is the full measure of the triangle.

The mean of 2,4,6,8,10

Answers

Answer:

6

Step-by-step explanation:

to find the mean, you must add all the numbers together and divide by the amount of numbers. for example, 2+4+6+8+10=30. next, you divide 30 by the amount of numbers, which is 5. if you count there are five numbers. so 30÷5=6 :)

For a field trip 5 students rode in cars and
the rest filled ten buses. How many students
were in each bus if 215 students were on the
trip?

Answers

Answer:

21

Plz mark me brainliest

Step-by-step explanation:

Answer:21 students were on each bus.

Step-by-step explanation:

215-5=210

210/10=21 the number of students divided by the number of buses


4. Would a 51-foot ladder be long enough to climb a 50-foot wall? Sketch a graph and find your answer using trigonometric functions

Answers

Answer:

Yes, it is enough to climb.

Step-by-step explanation:

Let suppose that wall is vertical and perpendicular to surface, a right-angled triangle is formed after using the ladder against the wall. (See attachment)

Ladder is useful only if its length is greater than wall length and trigonometrically speaking, the ratio of wall length to ladder length must be less than 1, associated with the definition of sine. That is:

[tex]\sin \theta = \frac{50\,ft}{51\,ft}[/tex]

[tex]\sin \theta = 0.980[/tex]

In a nutshell, the 51-foot ladder is useful to clime a 50-foot wall.

what is the slope of the line ?
please help me fast

Answers

the slope of the line is 3/2 i believe

Help! (Solving quadratic equations by factoring)

m(m-3)=0

Answers

Answer:

m=0 and m=3

Step-by-step explanation:

there are two solutions

The lines below are perpendicular. If the slope of the green line is ą, what is
the slope of the red line?

Answers

Answer:

See below

Step-by-step explanation:

If i recall right when two slopes are perpendicular one slope is supposed to be the negative reciprical of the other slope, because of this I think your answer should be B. -\frac{2}{3}  

Hope this helps

The lines are perpendicular and the slope of the red line is m₂ = -2/3

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = 3/2

So , the slope of the green line is m₁ = 3/2

Since the lines are perpendicular to each other , the product of their slopes will be equal to -1

And , m₁ x m₂ = -1

So , ( 3/2 ) x m₂ = -1

Multiply by ( 2/3 ) on both sides , we get

m₂ = ( -2/3 )

Therefore , the slope of the red line is ( -2/3 )

Hence , the slope of the red line m₂ = ( -2/3 )

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ7

The complete question is attached below :

The lines below are perpendicular. If the slope of the green line is 3/2 what is the slope of the red line?

A certain car's windshield wiper has a total length of 22 inches. As the wiper pivots it clears a sector with a central angle of 120 degrees. If only 18 inches of the wiper cleans the windshield, what is the area (in exact form) of the windshield that is wiped during each swing? 468π inches squared 156π inches squared 160π inches squared 108π inches squared

Answers

Answer: 108π inches squared

Step-by-step explanation:

Formula : Area of sector = [tex]\dfrac{\theta}{360^{\circ}}\times\pi r^2[/tex]

where , r= radius and [tex]\theta =[/tex]

Given : A certain car's windshield wiper has a total length of 22 inches. As the wiper pivots it clears a sector with a central angle of 120 degrees.

If only 18 inches of the wiper cleans the windshield, then we take radius of the range of wiper cleaining = 18 inches

The area of the windshield that is wiped during each swing = Area of the sector made by wiper of  with a central angle of 120 degrees.

[tex]=\dfrac{120}{360}\times\pi (18)^2\\\\=\dfrac{18^2}{3}\pi=\dfrac{18\times6}{1}\pi=108\p\text{ inches}^2[/tex]

Hence, the area (in exact form) of the windshield that is wiped during each swing is 108π inches squared.

% of 10 = 10
I need help with this

Answers

Answer:

100 percent

Step-by-step explanation:

if x of y is y....

x is always 100!

The rectangle below has an area of x^2-6x-7 sq meters and a width of x-7 meters.


What expression represents the length of the rectangle?


Length=______ meters

Answers

Answer:

Length = ( x - 1 ) ( m)

Step-by-step explanation:

Area of rectangle is:

A(r) = l*w ( in m² )    where l is the length in m   and w is the width in m

If we have:  A(r)  =  x² - 6*x  - 7 (m²), as an area of a rectangle, then we can factoring the equation, and get the rectangle dimensions, then:

x²  - 6*x  -  7  =  ( x  - 1 ) * ( x - 7 ) = area of the rectangle in m²

As problem statement establishes that ( x - 7 ) ( m)  is the width, then

( x - 1 ) ( m) is the length

Workers have packed 1,400 glasses in 7 boxes. If they pack 3 more boxes, how many glasses will they have packed in all?

Answers

2000


1box = 1400/7 = 200
200×3=600
1400+600=2000


Step-by-step explanation:
Given :Workers have packed 1,400 glasses in 7 boxes.
To Find :If they pack 3 more boxes, how many glasses will they have packed in all?
Solution:
Workers packed no. of glasses in 7 boxes = 1400
Workers packed no. of glasses in 1 box =
Workers packed no. of glasses in 3 boxes =
                                                                      =
So, initially they packed 1400 glasses
If they pack 3 more boxes so, the pack 600 glasses more
So, The total no. of glasses have packed by workers = 1400+600 = 2000
Hence they have packed 2000 glasses in all.

4(x + 2) = 4x + 2
Are these two Equivalent

Answers

Answer:

no they're not

Step-by-step explanation:

4(x+2) = 4x +8

4x+2= 4x+2

Answer:

No they are not equivalent

First we would have to solve 4(x+2)

In order to solve this we need to multiply. So 4×X is equal to 4x. 4×2=8 Therefore when solving Its 4x+8..and 4x+8 is not equivalent to 4x+2

4 x^{2} -12 x +9 = 0
Rewrite the equation by completing the square.

Answers

Answer:

Step-by-step explanation:

[tex]4x^2-12x+9=0\\4*9=36\\6+6=12\\6*6=36\\4x^2-(6+6)x+9=0\\4x^2-6x-6x+9=0\\2x(2x-3)-3(2x-3)=0\\(2x-3)(2x-3)=0\\(2x-3)^2=0[/tex]

Answer:

[tex](x-\frac{3}{2}) ^{2}[/tex]

Step-by-step explanation:

When we complete the square, we take the b value from the equation:

a[tex]x^{2}[/tex] + bx + c = 0, and plug it into [tex](\frac{b}{2})^{2}[/tex] ..

First step is to make the coefficent of x go away. By dividing by 4.

x^2 - 3x + 9/4 = 0

now plug into the equation

(-3/2)^2 = 9/4 <-- because the square is parantheses, the negative goes away. Notice how there is a 9/4 already in our equation, meaning we dont have to do anything and simply can find the answer!

(x - 3/2)^2 = 0

A biologist tags 25 birds with a band on their foot and lets them go back into the wild. The next year 100 total birds are captured and 5 of them have the foot bands. Enter an estimate of the total bird population. 20

Answers

Answer:

We can estimate a population of 500 birds.

Step-by-step explanation:

We can estimate the total bird population using a rule of three with the information given:

If we find 5 birds with the foot band among 100 birds captured, how many birds there are in total if inicially we put foot bands in 25 birds?

5 birds with foot band -> 100 birds captured

25 birds with foot band -> X total birds

X * 5 = 25 * 100

X = 25 * 100 / 5 = 500 birds

We can estimate a population of 500 birds.

I need helppp!!! Please

Answers

Answer:

18 ft^2

Step-by-step explanation:

1^2=1

1*6=6

6*3=18

Answer: 18 square feet.

Step-by-step explanation:

You can find the surface area of the ice cubes by taking the area of each square side and multiplying it by 6.

1 * 1 = 1, so each side is 1 square foot.

There are six sides on a cube, so each ice cube has a surface area of six feet squared.

There are three ice cubes there, so 3 * 6 = 18 square feet.

Three ice cubes have a surface area of 18 feet squared.

A cylinder has a diameter of
5.8 cm and is 8.4 cm high. Calculate the
volume of the cylinder.

Answers

Answer:

887.74

Step-by-step explanation:

What is important to keep in mind when selecting a sample?
a. The sample should be chosen based on specific criteria, such as the youngest students in the
class.
b. The sample should be chosen at random so that it is fair.
c. The sample should consist of every person in the population being studied.
d. The sample size should always be exactly one person or piece of data.

Answers

Answer: b. The sample should be chosen at random so that it is fair.

Step-by-step explanation:

Looking at the options:

a. The sample should be chosen based on specific criteria, such as the youngest students in the  class.

This is false. Choosing a sample size based on specific criteria may skew the data unfairly. For example, in a survey on students' studying habits, choosing only the students with lowest grades would be an inaccurate representation of the data.

b. The sample should be chosen at random so that it is fair.

This is true. Randomizing a sample eliminates any bias, whether intended or unintended.

c. The sample should consist of every person in the population being studied.

Although it is ideal to survey every person in order to get the most accurate data, doing so is often impossible given the scope of a data set. Doing a survey on high schooler's study habits cannot possibly get data from every person in the population, as there are high school students across the world.

d. The sample size should always be exactly one person or piece of data.

One person's data is not a survey, it is just an opinionated study. Sample size should always be large enough to eliminate any accidental bias.

The correct choice is B.

answer these 12 questions


SOLVE these

(1. 7x - 14 = 2x + 11) (5. 5x + 3 = x + 11) (9. 16x - 35 = 7x - 8)

(2. 6x + 5 = 3x + 14) (6. 7x + 2 = 5x + 14) (10. 6x - 5 = 13 - 3x)

(3. 12x + 5 = 4x + 37) (7. 13x - 15 - 12x + 16) (11. 4x - 9 = 6 - x)

(4. 3x + 8 = 2x +21) (8. 9x - 19 = 2x - 5) (12. 5x - 2 = 10 - x)

Answers

Answer:

Step-by-step explanation:

1) 7x - 14 =  2x + 11    {Add 14 to both sides}

  7x - 14 +14 = 2x + 11  +14

7x  = 2x + 25

7x - 2x = 2x + 25 - 2x

5x = 25           {Divide both sides by 5}

5x/5 = 25/5

x = 5

 

2) 6x + 5 = 3x + 14

6x = 3x + 14 - 5

6x = 3x + 9

6x - 3x = 9

3x = 9

x = 9/3

x = 3

3) 12x + 5 = 4x +37

12x = 4x + 37 - 5

12x = 4x + 32

12x - 4x = 32

8x = 32

x = 32/8

x = 4

4) 3x + 8 = 2x + 21

3x  = 2x + 21 - 8

3x = 2x + 13

3x - 2x = 13

x = 13

5)  5x + 3 = x + 11

5x = x + 11 -3

5x = x + 8

5x - x = 8

4x = 8

x= 8/4

x = 2

Answer: Step-by-step explanation:

1) 7x - 14 = 2x + 11 {Add 14 to both sides}

7x - 14 +14 = 2x + 11 +14

7x = 2x + 25

7x - 2x = 2x + 25 - 2x

5x = 25 {Divide both sides by 5}

5x/5 = 25/5

x = 5

2) 6x + 5 = 3x + 14

6x = 3x + 14 - 5

6x = 3x + 9

6x - 3x = 9

3x = 9

x = 9/3

x = 3

3) 12x + 5 = 4x +37

12x = 4x + 37 - 5

12x = 4x + 32

12x - 4x = 32

8x = 32

x = 32/8

x = 4

4) 3x + 8 = 2x + 21

3x = 2x + 21 - 8

3x = 2x + 13

3x - 2x = 13

x = 13

5) 5x + 3 = x + 11

5x = x + 11 -3

5x = x + 8

5x - x = 8

4x = 8

x= 8/4

x = 2

Step-by-step explanation:

Find the area of the circle below.
12 cm

Answers

Answer:

About 113.1

Step-by-step explanation:

Area of a circle= πr2

Radius= 6

6x6=36

36π= About 113.1

Answer:

work is shown and pictured

can you please help me.

Answers

Answer:

Answer is D.

6 x 3 =1 8

9 x 3 = 27

11 x 3 = 33

14 x 3 = 42

18 x 3 = 54

c = 3 x w

Step-by-step explanation:

The answer for this question is a

The average mark of candidate in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are 148, 102,152. What is the average of the extracted scores t hat are extreme values (outliers)?

Answers

Answer:

Step-by-step explanation:

Given that  : The average marks of candidates in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are; 148, 102 and 152.

The objective here is to determine the average of the extracted scores that are the extreme values (outliers)

NOW:

The average marks of candidates in an aptitude test was 128.5

i.e the Mean = 128.5

Standard Deviation = 8.2

outlier will be outsides;

then the range  will be    Mean  ± 3 × SD

= 128.5 ± 8.2 × 3

= 128.5 ± 24.6

Range is  ( 103.9  ,  153.1)

102 is outside this range

Hence, the average of the extracted scores that are extreme values (outliers) will be 102 only

The slope of the graph of the equation y = 2 x minus 2 is 2. What is the y-intercept? y-intercept =

Answers

Answer:

(0, -2)

Step-by-step explanation:

y= 2x - 2

To find the y-intercept, or where the graph hits the y-axis, you plug 0 in for x

y= 2(0) - 2

y= -2

because 2 times 0 is 0, then 0 - 2 is -2

If they ask for just the value, it is -2

If they ask for the coordinate, it is (0, -2)

Answer:

the answer is -2

Step-by-step explanation:

Today is your lucky day! You have just won a contest, and they can pay you your prize in two different ways.

Option one is to pay you $10,000 every 10 days, for 30 days.

Option two is a prize of a penny that doubles every day, for 30 days.

Which option would you choose?

Answers

Answer:penny

Step-by-step explanation:

Answer:

I would choose option two. Option one will make me a total of $30,000. Option two will make a total of $5,368,709.12.

Please someone help me I’m confused

Answers

Answer:

a2 =14

a4 = 22

a11 = 50

Step-by-step explanation:

an = 10 + (n-1) *4

n is the term number

Let n =2

a2 = 10 +(2-1)*4 =10 +(1)*4 = 14

Let n =4

a4= 10 + (4-1)*4 = 10 *3*4 = 10+12 = 22

Let n = 11

a11 = 10 +(11-1)*4 = 10 *10*4 = 10+40 = 50

Nine times a number is -63

Answers

Answer:-7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

Correct answers only please!

To the nearest cent, how much will she have in 3 years?

Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Answers

Answer:

$125.97

Step-by-step explanation:

They have given you everything you need.

p = 100

r = 0.08

t = 3

B = final amount

B = 100(1 + 0.08)^3

B = 125.9712

since you're dealing with money you have to round to the nearest cent

B = $125.97

Please brainlist if I helped

2006-1-2-3-4-...-48-49-50

Answers

Answer:  What is the "..." for?

Step-by-step explanation:

Help NEEDED asap if you dont know atleast comment

Item 11
MODELING REAL LIFE The stem-and-leaf plot shows the number of confirmed cases of a virus in 15 countries.

A stem and leaf plot. A vertical line separates each stem from its first leaf. The first row has a stem of 4 and leaves 1, 1, 3, 3, and 5. The second row has a stem of 5 and leaves 0, 2, 3, and 4. The third row has a stem of 6 and leaves 2, 3, 3, and 7. The fourth row has a stem of 7 and leaf 5. The fifth row has a stem of 8 and no leaves. The sixth row has a stem of 9 and leaf 7. The key shows 5 vertical bar 0 is equal to 50 cases.

Find the mean, median, mode, range, and interquartile range of the data. Round your answers to the nearest tenth, if necessary.

The mean is
.

The median is
.

The modes from least to greatest are
,
, and
.

The range is
.

Answers

I tried to do it and this is what i got

mean - 4.19

median - 3 or 4

Modes L to G - 0,1,1,2,2,3,3,3,3,3,4,4,5,5,5,6,7,7,7,8,9 and the most occuring number is 3

Range - 9

I tried i hope this can help, i'm sorry if not.

As always i would appreciate a brainliest

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