Simplify, Show work
1: 2i^20 + i^42
2: i^101 - i^2

Answers

Answer 1

Answer:

1. i^20 X (2+i^22)

2. i² X (i¹¹-1) X (i²² + i¹¹ + 1) X (i^66 + i³³ + 1)

Step-by-step explanation:

1) 2i^20 + i^42

factor out i^20

i^20 X (2 + i^22)

2) i^101 - i²

i²X(i^99-1)

i²X(i³³-1)X(i^66+i³³+1)

Using a³-b³=(a-b)(a²+ab+b²)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

I almost gave up typing. Quite stressful, but its fine


Related Questions


Find the volume of the figure. Round to the
nearest tenth.
1,286.1 units
401.9 units
5,144.6 units
128.6 units

Answers

Answer:

1,286.1 units is the answer

Step-by-step explanation:

your answer may vary depending on what you use for pie, using a calculator with pie on it gave me approx. 1286.79635

volume formula: V=πr^2h

so π*6.4^2*h

π*40.96*10

3.14*409.6

1,286.144

round

1,286.1

roberto earns $5 per hour plus 65% commision on all his sales. if y represents his sales for one day, which expression represents robertos total earnings for a day when he worked 6 hours?

Answers

edit: 5(6)+.65*y

original was wrong I wasn't thinking

four billion, five hundred and seventy million. write this number in figures​

Answers

Answer:

4,575,000,000

Step-by-step explanation:

Answer:

It's 4,570,000,000.

Step-by-step explanation:

The first guy had a typo right after the 7.


PLEASE HELP ME ASAPPPP

Answers

Answer:

The answer is

90 degrees the first one is I don't know about the rest sorry

Step-by-step explanation:

a pair of boots were $45 they were on sale for $38.25 what percent were they off

Answers

Answer:

15% off

Step-by-step explanation:

Answer:

17.2% off

Step-by-step explanation:

45/100 = 0.45

0.45 x 38.25 = 17.2%

Write an equation of the line with a slope of 3 and a y-intercept of 4

Answers

Answer:

y = 3x+4

Step-by-step explanation:

Hope this helps!

Answer:

y=3x+4

Step-by-step explanation:

y=mx+b

m is the slope

b is the y-intercept

y=3x+4

i’ll give brainliest please help!!!

Answers

Answer: The third one.

Step-by-step explanation: The hottest time of the day is around 3 p.m. Heat continues building up after noon, when the sun is highest in the sky, as long as more heat is arriving at the earth than leaving.

Answer: All of them

Step-by-step explanation: I think zll of them

Help needed on this question

Answers

Hope this helps!
I’ve attached a photo

a) 10 - 3(2a + 3) + 4(a - 6)
Simplify

Answers

2becaude 10a -3 =7 colonial

Answer:

-2a - 23

Step-by-step explanation:

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

10-6a-9 + 4(a-6)

10-6a-9 + 4a - 24

-23-6a+4a

-23-2a

Therefore, -2a - 23 is the answer

please help me asap!!!!

Answers

I can't see them clearly....

for number 2 the answer is A
number 3 is B

Which of the following does not have any dimension?
Question 7 options:

A)

Line

B)

Ray

C)

Line segment

D)

Point

Answers

Answer:

D

A point has a dimension of 0.

Hope this helped!

It’s point a line and a line segment and ray have a dimension of 1 :)

HELP ME ASAP

In the following diagram overline DE || overline FG and overline KL perp FG. What is the measure of angle x?

Angle x = _____°​

Answers

Given:

DE||FG and KL is perpendicular to FG.

To find:

The measure of angle x.

Solution:

If two lies intersect each other, then vertical opposite angles are equal.

[tex]m\angle ACB=63^\circ [/tex]         (Vertically opposite angles)

[tex]m\angle BAC=x^\circ [/tex]         (Vertically opposite angles)

KL is perpendicular to FG.

[tex]m\angle ABC=90^\circ[/tex]

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

In triangle ABC,

[tex]m\angle ABC+m\angle BAC+m\angle ACB=180^\circ[/tex]

[tex]90^\circ+x^\circ+63^\circ=180^\circ[/tex]

[tex]x^\circ+153^\circ=180^\circ[/tex]

[tex]x^\circ=180^\circ-153^\circ[/tex]

[tex]x^\circ=27^\circ[/tex]

Therefore, the measure of angle x is 27 degrees.

A window in the shape of a parallelogram has the dimensions given.

What is the area of this window?




20 ft²

24 ft²

28 ft²

40 ft²


i'll give brainlyist

Answers

Answer:

The answer is c, 28 ft! brainliest pls lol

Answer:

20ft

Step-by-step explanation:

I did the quiz and got it right :> (K12)

what is the area of the composite figure ​

Answers

Answer:

132cm

Step-by-step explanation:

will mark brainliest need help with DBA If you had a cube with a side length of 4, how can your write the calculations in exponential form?

Answers

4^3

you can write it like 4 × 4 × 4

you can also call it "Four to the Third power".

Find the value of x

I tried to solve, but ny answer did not make any sense do Im not sure how to ;-; Some help would be lovely :)​

Answers

Answer:

x = 25

Step-by-step explanation:

A quadrilateral is inscribed in a circle, so it is a cyclic Quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

3x + 21y = 180°.....(1)

2x + 26y = 180°.....(2)

From equations (1) & (2)

3x + 21 y = 2x + 26y

3x - 2y = 26y - 21y

x = 5y

y = 1/5 x

Plug y = 1/5 x in equation (1)

3x + 21*1/5x = 180

15x + 21x = 180*5

(Multiplying both sides by 5)

36x = 900

x = 900/36

x = 25

what fraction repsents 0.64​

Answers

Answer:

64/100 = 16/25

Answer:

0.64 in fraction

= 64/100 = 16/25

because each decimal equal to one zero

hope it helps

Anyone knows this one ?

Answers

Answer:

looks like it might be 4 but I'm not a 100% sure

0.5(12n – 8) = 26
show your work

Answers

Answer:

n=5

Step-by-step explanation:

divide by 0.5

6n-4=26

(add 4 to both sides)

6n=30

Divide both sides by 6

n=5

Write the equation of the line in fully simplified slope-intercept form?​

Answers

Answer:

ok

Step-by-step explanation:

Answer:

y=-1/2x-1

Step-by-step explanation:

circus has 20 performers, of which 6 are dancers.

What is the probability that a randomly selected performer will be a dancer?

Write your answer as a fraction or whole number.

Answers

Answer: 1/4

Step-by-step explanation:

A pair of Descartes jeans costs $120. If the tax is 13%, how much does the pair of jeans cost including tax?

Answers

Answer:

$135.60

Step-by-step explanation:

120*13%=15.6

15.60+120.00=$135.60

The answer is 135.60 dollars

if a = 5, what is the value of a-3?​

Answers

Answer:

2

Step-by-step explanation:

5-3=2

Answer:

2

Step-by-step explanation:

5 - 3 = 2

hello pls help besties (o˘◡˘o)

Answers

Hello bestie I cannot help you
21 or 69

Louis Partridge
Draco Malfoy
Blaise Zabini
Etc....

Which of the following is a solution of x^2+6x=-18

Answers

We are provided with a quadratic equation , and we have to find it's roots , but let's recall some things

The Standard Form of a quadratic equation is ax² + bx + c = 0

If D > 0 , then the equation have two real and distinct roots/zeroes .

If D = 0 , then the equation have two equal roots/zeroes .

If D < 0 , then the equation have two imaginary roots/zeroes or you can say that no real roots

Where , D is the Discriminant whose value is b²- 4ac and the roots of the equation are given by a very famous formula called The Quadratic Formula , which is as follows ;

[tex]{\quad {\boxed{\pmb{\bf x = \dfrac{-b \pm \sqrt{D}}{2a}}}}}[/tex]

Now , coming back on the question ;

We are provided with the equation x² + 6x = -18 , so on comparing this equation with the standard form of quadratic equation , we have , a = 1 , b = 6 and c = 18 . Now calculating the Discriminant ;

[tex]{: \implies \quad \sf D=(6)^{2}-4\times 1 \times 18}[/tex]

[tex]{: \implies \quad \sf D=36-72}[/tex]

[tex]{: \implies \quad \sf D=-18}[/tex]

As , D < 0 , so two imaginary roots exist . Now by quadratic formula ;

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm \sqrt{-36}}{2\times 1}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm \sqrt{\underline{6\times 6}\times -1}}{2}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm 6\sqrt{-1}}{2}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm 6\iota}{2} \quad \{\because \sqrt{-1}=\iota\}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{2(-3\pm 3\iota)}{2}}[/tex]

[tex]{\quad \qquad \boxed{\bf \therefore \: x=-3 \pm 3\iota}}[/tex]

3. Reason quantitatively. A figure has vertices P(-3, 1), Q(9, 1), R(3, —7), and S(-9, -7).
a. What is the most specific name that can be given to PQRS? Explain how you know.
b. Find PQ, QR, RS, and SP.
c. What is the perimeter of quadrilateral PQRS?
d. What is the area of quadrilateral PQRS?

Answers

don’t listen to them

given the following in a right triangle the hypotenuse is 200 cm and one of the legs is 45cm what is the lenght of the other leg

A: 194.9 cm
B: 12.4 cm
C: 155 cm
D: 245 cm

Answers

Step-by-step explanation:

Hence the length of other side is 194.87 I.e.194.9 cm

17x(8-5)x5 plz help me by solving this plz

Answers

Answer:

255

Step-by-step explanation:

so you first do the bracket so 8- 5 = 3

then 17 × 3 =51

and 51× 5 = 255

17 x (8-5) x 5

= 17 x (3) x 5

= 17 x 3 x 5

= 17 x 15

= 255

URGENT HELPPP !!!!!! Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!

Answers

Answer:

(8,-3)

Step-by-step explanation:

I just added 1 to the x value and added 2 to the y value because that was the difference between point A and the midpoint of the segment.

Hope this helps!

Which point is a solution to ys 3x – 4?

Answers

Answer:(3,1)

Step-by-step explanation:

Other Questions
How many liters are equal to 2,396 milliliters? Use the placement of the decimal point when dividing by a power of 10 to help you solve. 2.396 liters 239.6 liters 23.96 liters 23,960 liters P = 30x + 50y Corner that maximizes profit: (0, 6) What is the profit? No person shall...be deprived of life, liberty, or property, without due process of law. How would this amendment sound if it described the way things really were? What is the subject in this sentence? ---At the front of the room jumpedthe frog. *AtO jumpedroomthefrontfrog A piece of wire is 240 cm long.Peter cuts two 45 cm lengths off the wire.He then cuts the rest of the wire into as many 40 cm lengths as possible.Work out how many 40 cm lengths of wire Peter cuts. Please somebody answer this question fast A. Exports of U.S agriculture goods to postwar Europe B. Resistance to the soviet blockade of west BerlinC. Economic aid to Europe under the Marshall planD. U.S air power over Germany during the World War II If each image represents one mole of the substance pictured, which contains the greatestamount of substance?A)moleculesB) atomsC)formula unitsD)none; all amounts are the same why a small car can stop easier than an 18 wheeler while traveling at 70 mph down the interstate? Brianna has 6 bags of soil. Filling one flowerpot requires 1/3 of a bag of soil. How many flowerpots can be filled with these 6 bags?A.1/2B.2C.18D.24Help I suck at math 0-0 Number the events from earliest (1) to most recent (6) to outline the development of the cell theory. If 7.0 moles of HCl is added to enough iron that the HCl is completely used up, how manymoles of hydrogen gas will be produced? School debates aren't the only forum for rhetoric. Explain the role of rhetoric in legislative bodies like Congress or Parliament. Brainpop Debate(someone please help) Which of the following statements is evidence in the form of an example? A: I strongly believe that breakfast is the most important meal of the day.B: After Susan began eating breakfast every day, she noticed she was much more alert and ready to participate in her morning classes.C: A study of 500 middle-school students in Virginia showed that test scores improved by 15 percent when students ate breakfast.D: An example of a healthy breakfast is an omelet with vegetables, whole grain toast, and orange juice. A line passes through the point (0,-5). The gradient of this line is 3.Write down the equation of this line Which of the following statements are true of cartilaginous joints?A) The spine contains many cartilaginous joints.B) They are the most flexible type of joint.C) They contain cartilage between the bonesD) They are wrapped in ligaments. Jamie took a test. She got 31 correct, and 13 incorrect. Find the percentage of incorrect answers to correct answers. Explain with all steps. Please help test due in 1 hour and its a grade! Will give good review and brainliest! Suppose 7x-5 M=- 3 x-8 and NE 2 2 x - 5 x - 50 X - 14 x +40 and you want to add the fractions M and N, in other words you want to compute 7x-5 3 x - 8 2 x - 5 x - 50 x - 14 x + 40 and simplify the result. We know that, before you can add the fractions, you must find a common denominator and rewrite each fraction so it has that common denominator. Once the rewritten fractions have the same denominator, you can add them and simplify the result. There are four text boxes below. In the first text box, enter a common denominator for the two fractions. In the second text box, rewrite M so that it possesses the common denominator you found. Note that your entry in this text box should equal M, however it should have the common denominator you found. In the third text box, rewrite N so that it possesses the common denominator you found. In the last text box, compute your simplified answer for M N . Make sure that your answer is simplified; the numerator and denominator of your answer for M N should not have common factors. Note that your entry for the common denominator should be a polynomial with integer coefficients. Your other three entries should be fractions that contain polynomials. All of your answers should contain no letters other than the variables that appear in M and N. Do not include an equals sign with any of your answers. All of your expressions should be mathematically correct and not contain non-mathematical symbols. After entering your answers, click the Save Answer button. Your computer will display how your answers were interpreted, and you will have the opportunity to accept these answers or modify them.Enter a common denominator for M and N here: Enter M rewritten here: Enter N rewritten here: Enter your simplified result here: Differentiate between solar dryer method and electric dryer method in 4/4 point. A shirt costs 20$ if it was on sale for 75 percent off what is the discount