(4 + 4i)/(5+4i) = divide

(4 + 4i)/(5+4i) = Divide

Answers

Answer 1

Answer:

B.

Step-by-step explanation:

[tex] \frac{4 + 4i}{5 + 4i} [/tex]

Multiplying both numerator and denominator by (5 - 4i) , the conjugate of the denominator, i. e, (5 + 4i).

[tex] \frac{4 + 4i}{5 + 4i} \times \frac{5 - 4i}{5-4i} [/tex]

[tex] \frac{(4 + 4i)(5 - 4i)}{(5 + 4i)(5 - 4i)} [/tex]

Multiplying (4+4i) and (5-4i) using distributive propertyUsing the identity (a+b)(a-b)= a² - b² where 5 will act as a and 4i will act as b

[tex] \frac{20-16i+20i-16i^2}{(5) {}^{2} - (4i) {}^{2} } [/tex]

i² = -1

(combining like terms)

[tex] \frac{20+(-16i+20i)-(-16)}{25-(-16)} [/tex]

[tex] \frac{(20+16)+4i}{25+16} [/tex]

[tex] \frac{36+4i}{41} [/tex]

distributing the denominator

[tex] \frac{36}{41} + \frac{4}{41}i [/tex]

That is, option B.


Related Questions

Paragraph to write to my girl?????

Answers

Answer:

You make me feel like I can do anything and I am so happy to be with you. Thank you for being the wonderful, amazing person that you are. You surprise me every day and you warm my heart every night. I am the person I am today because you've loved me and helped me, love.

11. Which point is not on the graph of 2x + 3y - Z - 12 = 0?
(6, 0, 0)
(3,3,3)
(0, 4,0)
(1, 1, 7)

Answers

show the graph? i can’t really tell what the answer is without the graph being there.

simplify 3xy + x 2 - 4xy + 2xupper2y​

Answers

The answer is X^2-xy+2x^2y sorry if I am wrong

When sales of a particular hybrid automobile reach 60,000 units, federal income tax credits begin to phase out. One year after reaching this threshold, buyers are still eligible for 25% of the original $3000 credit. What tax credit would buyers receive if they purchased the vehicle at this time.

Answers

Answer:

$750

Step-by-step explanation:

so, in short, we need to calculate 25% of $3000.

that is the amount of tax credit a buyer would get then.

direct and fast answer :

25% means 1/4 of the overall amount.

$3000 / 4 = $750

now, a little bit longer to explain % calculations in general.

let's say, we are talking 27%. now we have a problem to find a fast fraction as factor.

it always starts with the identification of 100%.

what is the full starting amount we are dealing with ? that is the 100%.

in our case $3000.

now, as a base for the calculation we determine 1%, which is 1/100 of 100%, of course.

1% = $3000 / 100 = $30

to get said 27% we have to multiply this by 27

27% = 1% × 27 = $30 × 27 = $810

or in general

x% = 100% × x / 100

that also works for more complex questions. e.g. calculate 1.5%

1.5% = $3000 × 1.5 / 100 = $30 × 1.5 = $45

and that is all there is to % calculations. all the questions are just some variations, where your are missing one of the 3 "ingredients" : 100% amount, x% amount and x itself.

and you need to transform the general equation above to get the missing piece of of the given information.

I need help please and thank you.

Answers

Answer:

option a.

[tex] + - \frac{13}{5} [/tex]

Step-by-step explanation:

[tex]25x^2\: - \:169 = 0 [/tex]

[tex]25x^2 = 169[/tex]

[tex] {x}^{2} = \frac{169}{25} [/tex]

[tex]x = + - \sqrt{ \frac{169}{25} } [/tex]

[tex]x = + - \frac{13}{5} [/tex]

HELPP
-1-3(5m+8) ≥-85
i need help :D

Answers

Answer:

- 1 - 3(5m + 8) ≥ -85

-1 - 15m - 24 ≥ -85

-15m ≥ -85 + 1 + 24

-15m ≥ 25 - 85

-15m ≥ -60

(-1)(-15)m ≤ -60(-1)

15m ≤ 60

m ≤ 4

Cell Phone Service
Cellular phone service is available for $31 per month for 666 minutes. What is the
monthly cost per minute? Round your answer to the nearest tenth of a cent.
The cost for the phone service is
cents per minute.

Answers

9514 1404 393

Answer:

  4.7¢/min

Step-by-step explanation:

To find the cost in cents per minute, divide the cost in cents by the number of minutes.

  $31.00/(666 min) = (3100¢)/(666 min) ≈ 4.7¢/min

Two cities,a and are mapped on the coordinate plane. How far apart are they from each other?

Answers

Answer:

[tex]\sqrt{97} \\ \sqrt{9^{2}+4^{2} }[/tex]

Step-by-step explanation:

) A patient drank 12 ounces of orange juice. How many milliliters did the patient drink?

Answers

Answer:

He drank 354.882 mills of orange juice

Step-by-step explanation: One ounce is equal to 29.5735 mills, so you multiply 29.5735 by 12

Answer: 355 Millileters

The original price of a set lunch was 30 dollars. It is now sold at a 20%
discount. There is an extra discount of 10% for students. How much
should a student pay to order a set lunch?

Answers

Find out the total discount percentage that students receive.

20% + 10% = 30%

30/100 x 30 = 9 dollars

30 - 9 = 21 dollars (Final answer)
20% of $30 = $6
30 - 6 = $24
10% of $24 = $2.40
24 - 2.40 = $21.60 cost of student lunch

You have to do each percent separate to get the cost.
If you just take 30% off from the original cost of $30 it will be the wrong answer.

Applying for a loan. What separates me from other applicants applying for this money?

Answers

Answer:

Step-by-step explanation:

You could have a good credit score and good credit history.

Place the steps for finding f-1(x)

Answers

9514 1404 393

Answer:

  B, C, H, D, F, A

Step-by-step explanation:

Starting with y = f(x), swap x and y to get x = f(y), then solve for y. The solution steps "undo" what is done to y, in reverse order. Y is ...

multiplied by 721 subtracted from the productthe square root of the difference

To "undo" these steps in reverse order, after swapping x and y, you must square both sides, add 21, then divide by 7.

If the left tiles are labeled A to H from top to bottom, the correct sequence of steps is ...

  B, C, H, D, F, A

What is the surface area of this rectangular prism

Answers

Answer:

3*7 = 21*2=42

13*3=39*2=78

7*13=91*2=182

42+78+182=302

So the answer is D

Hope This Helps!!!

Answer:

D. 302

Step-by-step explanation:

This is how I did it:

First multiply 7 by 3, 21

Multiply that by 2 because there are 2 of those faces. 42.

Then multiply 3 by 13, and again by 2. 78.

And 13 by 7 by 2. 182.

Add. 302.

Or do an equation and use a calculator: 7(3)(2)+3(13)(2)+13(7)(2)=302

Help please!!!!!!!!!!!!!!!!!!

Answers

I guess try A I really don’t know

Problem is in the picture below

Answers

Answer:

90 maybe is a correct answer

Answer:

Y=40°

Step-by-step explanation:

VUW~YXZ

VWU~YZX

YXZ+XYZ+YZX=180°

70°+XYX+70°=180°

140°+XYZ=180°

XYZ=180°-140°

XYZ=40°

On a 9 question multiple-choice test, where each question has 5 answers, what would be the probability of getting at least one question wrong?

Answers

Answer:

P(at least one wrong) = 1- P(all correct) =1-.25^6=1-1/4096=4095/4096. This assumes that the answers are picked at random. This kind of question is always the complement of an extreme binomial outcome.

Question 1a) Suppose you sample 100 times at random with replacement from a population in which 26% of the individuals are successes. Write a Python expression that evaluates to the chance that the sample has 20 successes.

Answers

Answer:

from math import comb

n = 100

x = 20

p = 0.26

q = 0.76

print(comb(n, x)*(p**x)*(q**(n-x)))

Step-by-step explanation:

Given that :

Number of trials, n = 100

P(success), p = 26% = 0.26

P(success)' = 1 - p = 1 - 0.26 = 0.74

Chance that sample has 20 successes = x

This problem meets the condition for a binomial probability distribution :

p(x = 20)

Recall :

P(x = x) = nCx * p^x * q^(n-x)

Using python :

comb is an built in function which calculate the combination of two arguments it takes ; and returns the combination value.

** mean raised to the power and

* is used for multiplication

The Python code as per the given question is provided below.

Program explanation:

The number of trials,

100

Probability of success,

20% or 0.26

Size of array generated,

2000

The output that shows chances of 20 success,

S

Program code:

import numpy as np

S=sum(np.random.binomial(100,0.26,2000)==20)/2000

S

Learn more about Python expression here:

https://brainly.com/question/21645017

Solve. SHOW ALL YOUR WORK
2.51 * .2

77/ 1.2

Answers

Answer:

0.502

64.1666

Step-by-step explanation:

Detained explanation of the product operation and division operation is attached below.

2.51 * 0.2 = 0.502

(after multiplying) the number of decimal places of the town values is added and counted from the right in the product to place the data Comal point appropriately.

77/1.2 ; values were multiplied by 10 in other to obtain inter values for the denominator.

The average THC content of marijuana sold on the street is 9.6%. Suppose the THC content is normally distributed with standard deviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,

a. What is the distribution of X? X ~ N(
9.6
Correct,
1
Correct)

b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 9.8.


c. Find the 67th percentile for this distribution.
%

Answers

Answer:

Im sorry but why is this a question? Like what school gives this out


Jen recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 8 miles per hour faster than on her way home. If jen
spent a total of 2 hours bicycling find the two rates.

Answers

the answer is in the picture above

Express the following composite numbers as products of prime factors 64

Answers

Answer:

64 is a composite number, and it is 8 squared. 64 = 1 x 64, 2 x 32, 4 x 16, or 8 x 8. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Prime factorization: 64 = 2 x 2 x 2 x 2 x 2 x 2, which can also be written 64 = 2⁶.

what is the sum of a 7 term geometric series if the first term is 6 the last term is -24576 and the common ratio is -4

Answers

Answer:

Sum = 19,662

Step-by-step explanation:

Given that this is a finite geometric series (meaning it stops at a specific term or in this case -24,576), we can use this formula:  

[tex]\frac{a(1-r^n)}{1-r}[/tex], where a is the first term, r is the common ratio, and n is the number of terms.

Substituting for everything and simplifying gives us:

[tex]\frac{6(1-(-4)^7)}{1-(-4)} \\\\\frac{6(16385}{5}\\ \\\frac{98310}{5}\\ \\19662[/tex]

OMG THIS IS SO HARD

Answers

Answer:

Answer to the first question is D. Answer to the second question is also D.

Step-by-step explanation:

First question:

All the sides of the square are equal meaning you just have to multiply 1 side by 4 to get the perimeter(all the sides added together.) If one side is (s+3) then you either add that to itself 4 times or multiply it by 4. It's the same thing so it's 4(s+3) and (s+3)+(s+3)+(s+3)+(s+3).

Second question:

Adding a negative number is equivalent to subtracting a positive number. In this case, 59.2-84.7 = 59.2+(-84.7)

HELP
Identify the domain of the function shown in the graph.

Answers

Answer:

D = [4, 10]

Step-by-step explanation:

Since the line starts when x = 4, the domain begins there. And since the line ends when x=10, the domain ends there.

TRUE or FALSE: The regression equation is always the best predictor of a y value for a given value of x. Defend your answer.

Answers

Answer:

FALSE

Step-by-step explanation:

The regression equation is a prediction model which is generated for a given independent, x and dependent, y variable. The regression model is usually ideal when both the dependent and independent variables are numerical. The regression equation cannot be generated if either the x or y value is non-numeric. In such situation, classification models may be better suited for such cases especially if there is no efficient method of converting the non-numeric column into a numeric variable.

Subtract the given numbers in the indicated base.
41 five
tes
24 five
-
The difference is
five

Answers

9514 1404 393

Answer:

  12

Step-by-step explanation:

In base-5 arithmetic, ...

  41 -24 = 12

_____

If we use : to separate columns with different place value, this can be looked at a couple of ways.

Subtraction by addition

  2 : 4 + 0 : 2 = 3 : 1 . . . . . make the 1s place match

  3 : 1 + 1 : 0 = 4 : 1 . . . . . . make the 5s place match

The total amount added was 0:2 +1:0 = 1:2.

Subtraction using borrowing

  4 : 1 - 2 : 4 = (4-1) : (5+1) - 2 : 4

  = (4-1-2) : (5+1)-4 = 1:2

marking brainliest for a simple math problem​

Answers

Answer:

B. 88

Step-by-step explanation:

the total data = 1+2+4+5 = 12

the median is (a6+a7) /2

a6 = 87, a7 = 89

so, the median = (87+89)/2 = 88

Answer:

B. 88

--

the median is (a6+a7) /2

a6 = 87, a7 = 89

so, the median =[tex]\frac{87+89}{2}[/tex]= 88

O EXPONENTAL AND LOGARITHMIC FUNCTIONS
Finding the initial or final amount in a word problem on...
An initial amount of money is placed in an account at an interest rate of 2% per year, compounded continuously. After two years, there is $1269.79 in the
account. Find the initial amount placed in the account. Round your answer to the nearest cent.

Answers

Answer:

$ 1220.00

Step-by-step explanation:

1269.79 = A [tex]e^{.02 * 2}[/tex]

1269.79 /A = [tex]e^{.04}[/tex]

ln(1269.79 /A) = .04 ln(e)

ln(1269.79 /A) = .04

1269.79 /A = [tex]e^{.04}[/tex]

1269.79 /A = 1.0408

A =  1269.79 / 1.0408

$ 1220.00

A bricklayer needs to order 6 300 kg of building sand.

a) Write 6 300 kg in grams, giving your answer in standard form.

One grain of this sand approximately weighs 7 x 10°g.

b) How many grains of sand are there in 6 300 kg of sand? Give your answer in standard from.

Answers

Answer:

It would be 6300000. I can't write this in standard form.

Step-by-step explanation:

Answer:

6.3 x 10^6

Step-by-step explanation:

According to the WHO report, girls who are one month old have a mean head circumference of 36.6 centimeters with a standard deviation of 1.2 centimeters. As with most body measurements, head circumference has a normal probability distribution. Medscape defines microcephaly (small head syndrome) as a head circumference that is more than two standard deviations below the mean. What is the probability that a one-month old girl will be categorized as having microcephaly

Answers

Answer:

0.0228 = 2.28% probability that a one-month old girl will be categorized as having microcephaly

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Medscape defines microcephaly (small head syndrome) as a head circumference that is more than two standard deviations below the mean. What is the probability that a one-month old girl will be categorized as having microcephaly?

Probability of a z-score of -2 or less, which is the p-value of Z = -2.

Looking at the z-table, Z = -2 has a p-value of 0.0228.

0.0228 = 2.28% probability that a one-month old girl will be categorized as having microcephaly

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