Drag the tiles to the correct boxes to complete the pairs.
Match each power of i to its equivalent expression. 1 -1 i -i
i81
i52
i99
i66

Answers

Answer 1

The Matching is :

1. [tex]i^{81[/tex] = i

2. [tex]i^{52[/tex] = 1

3.  [tex]i^{99[/tex] = -i

4.  [tex]i^{66[/tex] = -1.

What are Complex Number?

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1).

Given:

1. [tex]i^{81[/tex]

= i. [tex]i^{80[/tex]

= i . (i²[tex])^{40[/tex]

= i (-1[tex])^{40[/tex]

Now, the even power of (-1) gives 1.

[tex]i^{81[/tex] = i

2. [tex]i^{52[/tex]

= 1 . (i²[tex])^{26[/tex]

Now, the even power of (-1) gives 1.

=1

3.  [tex]i^{99[/tex]

= i. [tex]i^{98[/tex]

= i . (i²[tex])^{49[/tex]

= i (-1[tex])^{49[/tex]

Now, the odd power of (-1) gives -1.

[tex]i^{81[/tex] = -i

4.  [tex]i^{66[/tex]

= 1 . (i²[tex])^{33[/tex]

Now, the odd power of (-1) gives -1.

= (-1)

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Related Questions

Addition Property of Equality: If m∠ABC=m∠XYZ and m∠PQR=m∠PQR then

Answers

Answer:

A

Step-by-step explanation:

substitution

Answer:

A. m∠ABC + m∠PQR = m∠XYZ + m∠PQR

Step-by-step explanation:

Addition Property of Equality is:

If a = b, then a + c = b + c

Apply to the given:

If m∠ABC = m∠XYZ and m∠PQR = m∠PQR

then

m∠ABC + m∠PQR = m∠XYZ + m∠PQR

When 24 is multiplied by w, the product is 288. What is the quotient when 24
is divided by w? Answer

Answers

Answer:

2

Step-by-step explanation:

24*w = 288

w = 288 /24

w = 12

24 ÷ w = 24 ÷ 12 = 2

1 1/2 - 2/3 = ???
Equivalent fractions.

Answers

Answer:

5/6

Step-by-step explanation:

1 1/2 - 2/3 =

= 1 3/6 - 4/6

We cannot subtract 4/6 from 3/6, so we borrow the 1 as 6/6 and add it to 3/6 to get 9/6. Now we can subtract 4/6 from 9/6.

= 9/6 - 4/6

= 5/6

AUTO RACING At a race car driving school,
there are safety requirements.
UR FAST
DRIVING SCHOOL
RULES TO QUALIFY
18 years of age or older
Good physical condition
Under 6 ft 7 in. tall
Under 295 lb
a. Define the variables, and write a system of
inequalities to represent the height and weight
requirements in this situation. Then graph the system.
b. Name one possible solution.
c. Is (50, 180) a solution? Explain.

Answers

9514 1404 393

Answer:

  a. h < 79; w < 295

  b. (h, w) = (60, 280)

  c. yes

Step-by-step explanation:

a.

We can define h and w to represent the height in inches and the weight in pounds. Then the inequalities representing the given restrictions are ...

  h < 79 . . . . . . . . height is less than 6'7"

  w < 295 . . . . . . weight is less than 295 pounds

The graph is attached. The solution space is the area where the solutions to the inequalities overlap.

__

b.

A 5 ft person weighing 280 pounds would meet the given restrictions.

  (h, w) = (60, 280) . . . . is a possible solution

__

c.

  (50, 180) is a solution. The height of 50 inches is less than 79 inches, and the weight of 180 pounds is less than 295 pounds. (A person with these measurements would be quite obese.)

_____

Additional comments

As a practical matter, healthy 18-year-olds will generally have a height greater than 59 inches and a weight greater than 95 pounds. Less than 3% of the population will be shorter or lighter than that.

"Good physical condition" may require a body mass index within a certain range. This will put additional (rather narrow) limits on height and weight. We have only shown inequalities and a graph for the specific conditions listed in the problem statement.

What is the place value of the first 4 in the decimal 451.48

Answers

Answer:

The values of 4 behind the decimal is 4 tenths and ahead of the decimal is 4 hundred.

-NULL

Brainliest will be appreciated thank you!

just n3d answer fast please ​

Answers

Answer:

Y=-5x-1

Step-by-step explanation:


1) Of the last 100 people who failed the lie detector test, 23 turned out to be telling the truth. What is
the probability that the next person who fails the test is actually telling the truth?
A) 0.23
B) 0
C) 0.5
D) 0.77
Oh

Answers

The probability of those telling the truth is an illustration of experimental probability.

The probability that the next person tells the truth is 0.23

The given parameters are:

[tex]\mathbf{n = 100}[/tex] -- sample size

[tex]\mathbf{x = 23}[/tex] -- those telling the truth

So, the probability that the next person tells the truth is:

[tex]\mathbf{Pr = \frac xn}\\\\\\[/tex]

Substitute values for x and n

[tex]\mathbf{Pr = \frac{23}{100}}[/tex]

Divide 23 by 100

[tex]\mathbf{Pr = 0.23}[/tex]

Hence, the probability that the next person tells the truth is 0.23

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If g(x) = 2(x − 4), find the value of x if g(x) = 20. (2 points) a 32 b 12 c 14 d 10

Answers

Answer:

45/56=678_78÷65×56+63×568=466

In the given figure find the value of the unknown interior angle x in the following figure.​​

Answers

Answer:

Therefore, the measure of angles x is 70°.

Step-by-step explanation:

From the given figure ,

115° is the exterior angle

x° and 45° are the two interior opposite angles to 115°

We know that

An exterior angle formed by extending the side of a triangle is equal to the sum of the two interior opposite angles

⇛ x° + 45° = 115°

⇛ x° = 115°-45°

⇛ x° = 70°

Therefore , x = 70°

6. The cost C of hiring a taxi is given by the formula C = 4 + 1.25m where m is the number of miles driven. Make a table showing the cost of hiring the taxi to drive 1, 2,3, and 4 s, Dete whether the cost of the taxi is proportional to the number of miles driven. Explain your reasoning.

Answers

The ratios are not all equal, we can conclude that the cost of the taxi is not proportional to the number of miles driven.

What is proportional?

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)

To find the cost of hiring a taxi to drive 1, 2, 3, and 4 miles, we can use the formula:

C = 4 + 1.25m

For m = 1, we have:

C = 4 + 1.25(1) = 5.25

For m = 2, we have:

C = 4 + 1.25(2) = 6.5

For m = 3, we have:

C = 4 + 1.25(3) = 7.75

For m = 4, we have:

C = 4 + 1.25(4) = 9

So the table of costs for driving 1, 2, 3, and 4 miles is:

Miles (m) Cost (C)

       1 5.25

       2 6.5

       3 7.75

       4 9

To determine whether the cost of the taxi is proportional to the number of miles driven, we can check whether the ratios of cost to distance are equal. If they are, then the cost is proportional to the number of miles driven.

Let's check the ratios:

C(1)/1 = 5.25/1 = 5.25

C(2)/2 = 6.5/2 = 3.25

C(3)/3 = 7.75/3 = 2.58333...

C(4)/4 = 9/4 = 2.25

Hence, the ratios are not all equal, we can conclude that the cost of the taxi is not proportional to the number of miles driven.

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please help me, i will mark the brainliest pls!

Answers

No because if you could use distributive property you would do 5*7 then 5*10 then you would get 35*50 which equals 1,750 and if you do it like it’s set up you would do 7*10 first cause PEMDAS so parentheses first so 7*10 is 70 then 70*5 is 350 and that’s not even close to the other answer so no you can’t .

Hey guy don’t you hate does people that said here is the link to your answer

Answers

Answer:

Thats not the way to give an answer..should write it properly

its just similar to..someone asked your name and you say this is the link and you give him the link of the ppt you made of your name

Plz Help!!! ID.K !! HELPPPPPPPPPPP!

Answers

Answer:30m

Step-by-step explanation:

15m/s x2 is 30m

Please help !! im struggling with this question ! thank you

Answers

Answer:

Diagnols of a rectangle are always congruent.

Step-by-step explanation:

1 point
Which graph represents the solution to 5+ 83 <3(2x +4) ?
A:
-10 9 8 7 6 5
4
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
B:
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
G
-10 -9 -8 7 6 5 4 3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
D:
-10 9 8 7 6 5 4 3 -2 -1 0 1 2 3 4
5
6 7 B 9 10
O
A
B
О
О
О
С
D

Answers

Answer:

adc

\Step-by-step explanation:

thanks for ur wait

The graph of the inequality is graph (B)

How to determine the graph

The inequality is given as:

[tex]5 + 8x < 3(2x + 4)[/tex]

Start by expanding the bracket

[tex]5 + 8x < 6x + 12[/tex]

Next, we collect the like terms

[tex]8x - 6x < 12 - 5[/tex]

Evaluate the like terms

[tex]2x < 7[/tex]

Solve for x

[tex]x < 3.5[/tex]

The above means that, the values of x are less than 3.5

Hence, the inequality is graph (B)

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Please help me solve for x in this picture, thank you

Answers

Answer:

x = –10

Step-by-step explanation:

The angles are supplementary

(x + 75) + (x + 125) = 180

Combine like terms

2x + 200 = 180

Subtract 200 from both sides

2x = -20

divide both sides by 2

x = –10

Answer:

x = -10

Step-by-step explanation:

These are known as same-side interior angles and they are supplementary.

[tex]x+125+x+75=180\\\\2x+200=180\\\\2x=-20\\\\x=-10[/tex]

Miguel takes $50 to the mall. He buys a shirt for $18.99 and a hat for $12.49. On his way home, he stops at the bank and withdraws $25. How much money does he have now?
I REALLY NEED HELP PLEASE!

Answers

Answer:

50 - 18.99 = 31.01 - 12.49 = 18.52

18.52 + 25 = 43.52$

Miguel's got 43.52$ now.

What is the slope of a line parallel to the line whose equation is y- x= 5?
O-1
0 1
5.
01
05

Answers

Answer:

Slope = -1 .     Parallel lines have the same slope.  The slope is a coefficient of the x-term.

Step-by-step explanation:

y - x = 5

y = x + 5    slope = 1

The slope of the line parallel to the given line is 1.

What is slope?

Slope is a value that describes the steepness and direction of a line. In variable format, it is commonly represented by the letter m.

The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run.

Given that the equation of a line y - x = 5, we need to find the slope of the parallel to the same,

Converting the equation in slope-intercept form,

y - x = 5

y = x + 5

Comparing with standard form of the equation of the line y = mx + c, where m is the slope,

Hence, the slope of the given line is 1,

We know that the slopes of the parallel lines are equal.

So, the slope of the asked line is 1.

Hence, the slope of the line parallel to the given line is 1.

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6. The sum of three numbers A, B, and C, is $840. A is 2 times of B and C is half of B. Find the values of each number.​

Answers

This is what i got, hope it helps :)

LOOK AT ATTACHED IMAGIE! Make a two-column proof showing statements and reasons to prove that triangle ABD is similar to triangle ACB.

Answers

angle ABD is 45 degrees
angle ACB is also 45 degrees
only similar triangles have the same angles yet different sizes.
if they are the same size, they would be congruent, but in this case they are only similar because AB is not equal to AC, which shows that one triangle is bigger than the other.
hope this helped :D

Heather's employer pays 80% of her health insurance premium. If the annual premium is $2447.25 and she is paid weekly, how much is deducted from each paycheck?
$1957.80
$75.30
$37.65
$9.41

Answers

Answer:

37.65

Step-by-step explanation:

Take 2447.25, divide by 52 (there are 52 weeks in a year) and mutiply by 0.8 (80%), and then you have the answer!

The amount of money deducted from each payback will be $37.65.


What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Heather's employer pays 80% of her health insurance premium. If the annual premium is $2447.25 and she is paid weekly.

The payment will be calculated as,

Pay = ( 2447.25 / 52 ) x 0.8

Pay = $37.65

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Find the other endpoint of the line segment with the given endpoint and midpoint.
Endpoint (8,-2) and Midpoint (3, 10)
0 (3,6,5)
0 (-2,22)
O (2.5, -6)
0 (0.5, -1.5)

Answers

Answer:

Step-by-step explanation:

The endpoint x value of 8 must be reduced by 5 to get to the mid point x value of 3. We reduce 3 by another 5 to get the opposite end x value of -2

The endpoint y value of -2 must be increased by 12 to get to the mid point y value of 10. We increase 10 by another 12 to get the opposite end y value of 22

(-2, 22) endpoint

this is my final, this thing is hard

Answers

Answer: graph 1:no graph 2:no graph 3: yes graph 4: yes graph 5: no

graph 6: no

Step-by-step explanation:

Answer:

Graph 1 I think is yes because when determining if a function, you do the vertical line test meaning you place an imaginary vertically on the graph and if there is 2 points on the line at once, like for graph 5 or 6, then it isn't a function.

Therefore,

Graph 1: Yes

Graph 2: No

Graph 3: Yes

Graph 4: Yes

Graph 5: No

Graph 6: No

For graph 1, it is way to close to tell if a function or not. So, I would say go with your gut.

(-3.2)^0 write two expressions equivalent to the given expression

Answers

Step-by-step explanation:

First expression

[tex] = {( - 3 \times 2)}^{0} [/tex]

[tex] = { - 3}^{0} \times {2}^{0} [/tex]

[tex] = 1 \times 1[/tex]

[tex] = 1[/tex]

[tex] \: [/tex]

Second expression

[tex] = {( - 3 \times 2)}^{0} [/tex]

[tex] = { - 6}^{0} [/tex]

[tex] = 1[/tex]

[tex] \: [/tex]

third expression

[tex] = {( - 3 \times 2)}^{0} [/tex]

[tex] = {( - 3 \times 2)}^{1 - 1} [/tex]

[tex] = \frac{ - 3 \times 2}{ - 3 \times 2} [/tex]

[tex] = \frac{ - 6}{ - 6} [/tex]

[tex] = 1[/tex]

The equivalent expressions are;

1.  ( -32/10 ) ⁰

2. ( - 2 × 1.6 )⁰

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is given as;

( -3.2 ) ⁰

Now,

First equivalent expression is;

( -3.2 ) ⁰ = ( -32/10 ) ⁰

            = ( -32 )⁰ / (10) ⁰

            = 1 / 1

            = 1

Second equivalent expression is;

( -3.2 ) ⁰ = ( - 2 × 1.6 )⁰

            = (-2)⁰ × (1.6)⁰

            = 1 × 1

            = 1

Thus, The equivalent expressions are;

1.  ( -32/10 ) ⁰

2. ( - 2 × 1.6 )⁰

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Is the ordered pair (4,3) a solution to the equation below?
y = 2x – 5

no
yes

Answers

Answer:

Yes

3 = 2(4) - 5

This is true

Answer:

Yes

Step-by-step explanation:

Since y is 3 and x is 4 plug those into equation

3=2(4)-5

3= 8-5

3=3

2 short questions 100 point pls help

Answers

So

Common difference

t_3-t_26.8-51.8

#4

The formula is

a_n=10n-14

Put n=8

a_8=10(8)-14=80-14=66

Answer:

3)  d = 1.8

4)  a₈ = 66

5)  a)  138  

    b)  55

    c)  [tex]a_n=55n+83[/tex]

Step-by-step explanation:

Question 3

The common difference of an arithmetic sequence is the difference between consecutive terms.

Therefore, to find the common difference, subtract one term from the next:

⇒ d = 5 - 3.2

⇒ d = 1.8

Question 4

Given arithmetic sequence:   [tex]a_n=10n-14[/tex]

To find the 8th term, substitute n = 8 into the equation:

[tex]\implies a_8=10(8)-14[/tex]

[tex]\implies a_8=80-14[/tex]

[tex]\implies a_8=66[/tex]

Question 5

General form of an arithmetic sequence:

  [tex]a_n=a+(n-1)d[/tex]

where:

[tex]a_n[/tex] is the nth terma is the first termd is the common difference between terms

a)  The first term is the initial amount Mrs Speas has in her bank account:

a = 138

b) The common difference is the amount she deposits each week:

d = 55

c) The iterative rule for the amount of money she has after n weeks is:

    [tex]\implies a_n=138+(n-1)55[/tex]

    [tex]\implies a_n=138+55n-55[/tex]

    [tex]\implies a_n=55n+83[/tex]

help here ASAP

which one is true?

Answers

Step-by-step explanation:

9π > 27

π > 27/9

π > 3

Option B

We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 13.5, what is a 99% confidence interval for the population mean

Answers

Answer:

hgggy7sid8e6r7r6d66yw7e7e56

There are 20 dogs at the park on a busy Saturday.
9 of them are springer spaniels, 7 of them are labs
and 4 of them are bulldogs. What is the
probability that a randomly selected dog in not a
springer spaniel?

Answers

We know that 9/20 dogs are spaniels, so 11/20 of the dogs will not be spaniels. That would be your probability in fraction form, but if you need percentage, remember that you can find percentage of something by multiplying the fraction by 100 and evaluating, so [tex](\frac{11}{20} )*100= 0.55*100= 55[/tex]. So, the percentage of dogs that are not spaniels would be 55%.

If you could mark brainliest, that would be much appreciated as I'm trying to rank up!

5 is 7 less than twice a number
translate into algebra

Answers

Step-by-step explanation:

2x-7=5

is it shown numbers

This is The correct answer 2x-7=5









X=6
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