Convert the polar representation of this complex number into its rectangular form: z=4(cos120 + isin 120)

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Convert The Polar Representation Of This Complex Number Into Its Rectangular Form: Z=4(cos120 + Isin

Answers

Answer 1

Answer:

The answer is D

Step-by-step explanation:

took the test

Answer 2

The polar expression of a complex number in its rectangular form 4(cos120° + i sin120°) = -2 + 2√3 i.

What is the polar form of a complex number?

Let Z = a + ib be a complex number in the cartesian form represented by point P(a, b) in the complex plane then Z = r cos∅ + i r sin∅ =r is called the polar form of a complex number.

We have.

z = 4(cos120° + i sin120°)

z = 4(cos(90 + 30)° + i sin(90 + 30)°)

Using trigonometry

cos (90 + ∅) = -sin ∅ and sin (90 + ∅) = -cos ∅

So, 4( -sin (30)° + i cos (30)°)

= 4 ( -1/2 + i √3/2)

= -4(-1/2) + i 4(√3/2)

= -2 + 2√3 i

Thus, the rectangular form is 4(cos120° + i sin120°) = -2 + 2√3 i.

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In order to find the measure of each angle, it is important to remember that the sum of the interior angles of a triangle is 180 degrees.

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[tex]1000ml = 1l \\ 5000ml = \frac{5000}{1000} l = 5l[/tex]

So option C, 5 litres.

Answer:

5 liters

Step-by-step explanation:

So, lets go over what we know:

There is 5000 milliliters.

There are 1000 milliliters in a liter.

To find the amount of liters, we have to divide 5000 by 1000, or total millilileters by millilileters per liter:

5000/1000

=

5

Hope this helps!

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Classify the solid.
Your answer

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Answer:

Square pyramid

Step-by-step explanation:

Hope this helps

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Answers

Answer:

5.66

Step-by-step explanation:

c^2= a^2 plus b^2

c^2 = 16 plus 16

c^2 = 32

c = 5.6568

Kaylah's cell phone has a mass of 58,000 centigrams What is the mass of her phone in grams? The mass of Kaylah's cell phone is ? grams.​

Answers

The answer is 580 grams.

Figures A and b are similar. Figure A has an area of 18 square feet. Figure b has an area of 98 square feet and one of the sides lengths is 14 feet find the corresponding side length

Answers

Answer:

6 ft

Step-by-step explanation:

The ratio of the square of the sides of two similar figures = the ratio of their area

Let x represent the missing side corresponding side length

Therefore,

Area of figure B/area of figure A = square of side length of figure B/square of the side length of figure A

Thus:

98/18 = 14²/x²

98/18 = 196/x²

Cross multiply

98*x² = 196*18

98x² = 3,528

Divide both sides by 98

x² = 3,528/98

x² = 36

x = √36

x = 6

Therefore, missing corresponding side length = 6 ft

The corresponding side length is 2.57 feet

Similar shapes

Given that figures A and b are, hence the ratio of the area to the length is equal to a constant as shown:

[tex]\frac{A}{L} = \frac{a}{l}[/tex]

Substitute the given parameters into the formula to have:

A = 98 square feet

L = 14 square feet

a  18 square feet

[tex]\frac{98}{14} = \frac{18}{l}\\98l=252\\l = 2.57 feet[/tex]

Hence the corresponding side length is 2.57 feet

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Solve the inequality: -16< 4(2x + 8) <40

Answers

Answer:

-6 < x <1 , (-6, 1)

Step-by-step explanation:

Can someone solve this please? Thank you!

Answers

Answer:

.125

Step-by-step explanation:

1/4 times 1/2 equals .125.

Answer:

Total area of the box is 1 ft squared

Area of the shaded box is .125 ft squared

Area of the non - shaded box is .875 ft squared

Step-by-step explanation:

To find the total area, we can multiple the length * height, 1 * 1 = 1.

To find the shaded area, we can multiple the length * height, .5 * .24 = .125.

To find the total area, we can multiple the length * height of the box minus the shaded area, 1 * 1 - .125 = .875.

6) What is the value of digit 7 in 0.057 *.///what is the answer _____________________
7/10
0.07
7/1000

Answers

Answer:

7/1000 thousandths for place value

PLSSSS HELP WILL GIVE BRAINLIEST

NO LINKS OR BANNED

Tina is constructing an angle congruent to ZABC.
What is her next step?
A. Using MN as the radius, place the center of the
compass on P and construct an intersecting arc.
B. Using MB as the radius, place the center of the
compass on P and construct an intersecting arc.
C. Using MN as the radius, place the center of the
compass on Y and construct an intersecting arc.
D. Using MN as the radius, place the center of the
compass on X and construct the intersecting
arc.

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Answer:

C

Step-by-step explanation:

C Whausygwvwiayabwoauhebtkziywgwvykofusgwbek

Which inequality represents the phrase "a number b is at least -16"?

Answers

Answer:

[tex]b \leqslant - 16[/tex]

Only x = -3 is less than -2.

What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following statement -

"A number b is at least -16"

Given is the following statement -

"a number b is at least -16".

We can write the given inequality as -

b ≥ - 16

Therefore, we can write the given statement as -

b ≥ - 16

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Answer:

multiply the two numbers on a calculator

Step-by-step explanation:

give brainlest please

Answer:

Using Pythagorean Theorem: a^2 + b^2 = c^2

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A kite is flying 95 feet off the ground in a string is pulled toward the angle of elevation of the kite is 40° find the length of the string.

Answers

Answer:

It is 127.5 feet

Step-by-step explanation:

[tex] \sin(40) = \frac{95}{x} \\ x = \frac{95}{ \sin(40) } \\ x = 127.5 \: feet[/tex]

I hope that is useful for you :)

A prism _____has two congruent, parallel bases.
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B never
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Answers

A prism Always has two congruent, parallel bases.

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Answers

Answer:

i, n, e, q, u, a, l, t, y

Step-by-step explanation:

You repeated some letters.

pls give me brainliest and have a nice day! Hope it helps!

What is the solution to the system of equations graphed below?

Answers

The solution for this is (6,-1)

please help i dont know how to do this​

Answers

Answer:

1. a quantity that stands alone and is not changed by other quantities. most often x variable.

2. a quantity that changes depending on another quantity, as a result of the rule. most often the y variable

Step-by-step explanation:

Answer: A quantity that stands alone and is not changed by other quantities most often X variable.

A quantity that changes depending on another quantity, as a result of the rule most often Y variable.

Solve the following equation 3x - 2(x + 3) = 4x - 7

Answers

I don’t know man I’m sorry

Answer:

3x-2x-6=4x-7

x-6. =4x-7

3x=1

X=1/3

Solve the following system of equations:

−2x + y = 1
−4x + y = −1

(3, 1)
(−1, 3)
(−1, −3)
(1, 3)

Answers

Answer:

(1,3)

Step-by-step explanation:

[tex]\sf Answer\begin{cases} \sf \rightarrowtail \: - 2x + y = 1 \dots(1) \\ \sf \rightarrowtail \: - 4x + y = - 1 \dots(2) \\ \sf 2 \times (1) \implies - 4x + 2y = 2 \\ \sf 1 \times (2) \implies - 4x + y = - 1 \\ \bf \star \: substracting \: both \\ \sf \rightarrowtail \: y = 3 \\ \sf \rightarrowtail \: -2x+(3)=1 \\ \sf \rightarrowtail \: -2x=-2 \\ \sf \rightarrowtail \: x=1\end{cases}[/tex]

PLS HELP FOR 10 POINTS PLEASE (SHOW YOUR WORK)
Question: Find the measure of the missing angle

IF YOUR A BOT AND IS JUST SAYING “PLEASE CHECK THE LINK BELOW FOR ANSWERS” I WILL REPORT

THANK YOU (-:

Answers

Answer:

The answer is 90 degrees

Step-by-step explanation:

It is a right angle and a right angle is equal to 90 degrees

The box in a triangle always represents a right angle

Answer:

The missing angle is 65 degrees

Step-by-step explanation:

Answer: 65 degrees

First, you can make the conclusion that a right angle is 90 degreesNext, you can add 90 to 25 to get 115You then subtract 115 from 180.You are left with 65, which is the measure of the missing angleRemember that a triangle equals 180 degrees! :)

A study was done to compare the effectiveness of distance learning with traditional classroom instruction. Fourteen students took a business administration course online, while 17 students took it in a classroom. The final exam scores were as follows. It is reasonable to assume that the samples come from populations that are approximately normal.

Online
65 74 84 63 87 76 73
90 71 68 76 82 61 69

Classroom
70 79 55 74 82 70 80 73 77
54 82 80 81 68 58 69 92

Required:
a. Construct a 95% confidence interval for the difference between the mean scores for the two types of instruction.
b. An educator claims that both methods of instruction are equally effective. Does the confidence interval contradict this claim?

Answers

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A:

Check conditions for a 2-sample t-interval:

Random sample? √

Is the sample size no more than 10% of the population? √

Are both samples approximately normal? √

Construct the 95% confidence interval:

On a TI-84, click on "Stat", scroll to "Tests", and select "2-SampTInt". Put your data into 2 lists and set C-Level to be 0.95 to represent a 95% confidence level. Make sure the data isn't pooled, and press "Calculate" to obtain your results. You will see that the 95% confidence interval for the difference between the mean scores for the two types of instruction is {-6.042,8.1175}

Part B:

The confidence interval does not contradict the claim because 0 is contained within the 95% confidence interval, so it is quite possible that there is no difference between the mean scores for the two types of instruction.

Elise randomly surveyed students at her school to find out their favorite music. the table shows the results if Elise’s survey. if there are 400 students at Elise’s school, how many can she predict will like pop the best?

Answers

Answer:

125 students

Step-by-step explanation:

according to this survey, she surveyed 80 people, and of the 80 people she surveyed, 25 of them said they like pop best

set up a proportion to find how many students will like pop if there are 400 students at her school:

25/80=x/400

80x=10000

x=125

125 students

The height of a cone is twice the radius of its base.
What expression represents the volume of the cone, in
cubic units?
2/3лх^3
4/3лх^3
2лх^3
4лх^3

Answers

Answer: 2/3πx³

Step-by-step explanation:

Let the radius of the cone be represented by x.

Since the height of the cone is twice the radius of its base, the height will be: = 2x

Volume of a cone = 1/3πr²h

where,

r = x

h = 2x

Volume of a cone = 1/3πr²h

= 1/3 × π × x² × 2x

= 1/3 × π × x² × 2x

= 1/3 × π × 2x³

= 2/3πx³

Therefore, the correct answer is 2/3πx³.

You hike 220 meters up a steep hill that has a 43 degree angle of elevation as shown in the diagram

Answers

Answer:

9460

Step-by-step explanation:

3. Assume all angles are right angles. What is the area of the figure? 12 m 8 m 10 m 16 m 12 m 12 m 1536 square meters b. 408 square meters C. 360 square meters d. 102 square meters​

Answers

C. 360 Square meters

........

The total area is 360 square meter.

What is Area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given:

We get Three Rectangle

First Rectangle:

length = 12 m

width = 16 m

So, Area = 12 x 16 = 192 square meter.

Second Rectangle:

length = 8 m

width = 12 m

So, Area = 8 x 12 = 96 square meter.

Third Rectangle:

length = 12 m

width = 6 m

So, Area = 12 x 6 = 72 square meter.

Thus, the total area = 192 + 96+ 72 = 360 square meter.

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Which pair represents opposite numbers?

Answers

Answer:

Choice B 2 and -2

Step-by-step explanation:

2 would be opposite of -2

Mark brainliest

6p – 9 = 9; then p=?​

Answers

Answer:

p = 3

Step-by-step explanation:

In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal.a. Which distribution should you use for this problem

Answers

Answer:

By the Central Limit Theorem, an approximately normal distribution, with mean $6425 and standard deviation $344.35.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Sample mean was $6,425 with a standard deviation of $3,156

This means that [tex]\mu = 6425, \sigma = 3156[/tex]

Sample of 84:

This means that [tex]n = 84, s = \frac{3156}{\sqrt{84}} = 344.35[/tex]

a. Which distribution should you use for this problem?

By the Central Limit Theorem, an approximately normal distribution, with mean $6425 and standard deviation $344.35.

John needs to print 36 copies of his colored poster. His HP printer can print 16 copies in 5 minutes. His Epson printer can print 4 copies in 1 minute.

9a) Enter an equation that can be used to find the number of minutes, t, John would take to make 36 copies if he used both printers. Enter your response in the first response box. (DO NOT PUT SPACE IN YOUR ANSWER. USE t AS YOUR VARIABLE. Write fractions using the correct order of operations.)Plz help

Answers

Answer:

It would probably be 36t

Step-by-step explanation:

because if you think about It.

It is mainly asking you how long it is going to take, so you need a a equation to find the answer.

-John needs 36 copies

- Hp printers out 16 in 5 minutes

- Epson printer out 4 in 1 minutes

so 36 x t or 36t

Which measurements could create more than one triangle?
A. A triangle with angles measuring 50° and 80° and an included side
measuring 6 inches
B. A triangle with sides measuring 6 inches, 10 inches, and 14 inches
C. A triangle with sides measuring 7 inches, 10 inches, and 20 inches
D. A triangle with sides measuring 18 mm and 21 mm and a
nonincluded angle measuring 55°

Answers

Answer:

B??

Step-by-step explanation:

Sorry if i'm wrong! :(

Answer:

D

Step-by-step explanation:

i just took the test:)

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