Which expressions are equivalent to the given complex number? 45 + 2i A. (2 + 8i) + 2(9 + 6i)(1 - i) B. (9 + 4i) + 2(4 + 7i)(1 - 2i) C. (13 + 4i) + 2(7 + 2i)(2 - i) D. (2 + 8i) + (30 - 6i) E. (9 + 4i) + (36 - 2i) F. (13 + 4i) + (32 - 6i)

Answers

Answer 1

The expressions which are equivalent to the complex number 45 + 2i is E. (9 + 4i) + (36 - 2i)

D. (2 + 8i) + (30 - 6i)

To determine which expressions are equivalent to the complex number 45 + 2i, we can simplify each expression and check if it matches the given number.

Let's evaluate each option:

A. (2 + 8i) + 2(9 + 6i)(1 - i) = 2 + 8i + 2(9 + 6i - 9i - 6i^2) = 2 + 8i + 2(9 + 6i - 9i + 6) = 2 + 8i + 2(15 - 3i) = 2 + 8i + 30 - 6i = 32 + 2i

B. (9 + 4i) + 2(4 + 7i)(1 - 2i) = 9 + 4i + 2(4 + 7i - 8i - 14i^2) = 9 + 4i + 2(4 + 7i - 8i + 14) = 9 + 4i + 2(23 - i) = 9 + 4i + 46 - 2i = 55 + 2i

C. (13 + 4i) + 2(7 + 2i)(2 - i) = 13 + 4i + 2(7 + 2i - 14i - 4i^2) = 13 + 4i + 2(7 + 2i - 14i + 4) = 13 + 4i + 2(24 - 12i) = 13 + 4i + 48 - 24i = 61 - 20i

D. (2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i = 32 + 2i

E. (9 + 4i) + (36 - 2i) = 9 + 4i + 36 - 2i = 45 + 2i

F. (13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i = 45 - 2i

From the evaluations above, we can see that options E and D are equivalent to the given complex number 45 + 2i.

The correct options are:

E. (9 + 4i) + (36 - 2i)

D. (2 + 8i) + (30 - 6i)

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Answer 2

The  expressions that are equivalent to the given complex number 45 + 2i are: (9 + 4i) + (36 - 2i) and (2 + 8i) + (30 - 6i).

Thus, option (D) and (E) are correct.

Given complex number 45 + 2i.

A. (2 + 8i) + 2(9 + 6i)(1 - i)

Simplifying: (2 + 8i) + 2(9 + 6i - 9i - 6)

= (2 + 8i) + 2(3 + 3i)

= 2 + 8i + 6 + 6i

= 8 + 14i

B. (9 + 4i) + 2(4 + 7i)(1 - 2i)

Simplifying: (9 + 4i) + 2(4 + 7i - 8i - 14)

= (9 + 4i) + 2(-10 - i)

= 9 + 4i - 20 - 2i

= -11 + 2i

C. (13 + 4i) + 2(7 + 2i)(2 - i)

Simplifying: (13 + 4i) + 2(14 + 4i - 7i - 2)

= (13 + 4i) + 2(12 - 3i)

= 13 + 4i + 24 - 6i

= 37 - 2i

D. (2 + 8i) + (30 - 6i)

Simplifying: 2 + 8i + 30 - 6i

= 32 + 2i

E. (9 + 4i) + (36 - 2i)

Simplifying: 9 + 4i + 36 - 2i

= 45 + 2i

F. (13 + 4i) + (32 - 6i)

Simplifying: 13 + 4i + 32 - 6i

= 45 - 2i

Thus, option (D) and (E) are correct.

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Related Questions

Task 3

please pa answer na po ngayun (个_个)

Directions: Find the quotient.

1) 75.36 ÷ 0.24 =

2) 1.536 ÷ 0.3 =

3) 6.705 ÷ 0.45 = =

4) 1.875 ÷ 0.05 =

5) 6.048 ÷ 0.8 =

Task 4

Directions: Find the quotient.

1) 1.6 5.136 2) 2.8 7.364

4) 4.8 83.52

3) 3.6 65.52

5) 5.6 3.136​

Answers

Answer:

eue8whiwhwihdhd123456789101122334

I need help please!!!

Answers

Answer:

[tex]\frac{21}{100}[/tex]

Step-by-step explanation:

As you can see in the table, there are 21 people that have dogs but don't take walks. To find the probability, divide 21 by the total amount of people that attended the survey:

[tex]\frac{21}{100}[/tex]

This fraction can't be simplified.

The probability, represented as a fraction in simplest form, that a randomly selected person does not take walks but has a dog is [tex]\frac{21}{100}[/tex].

21/100 this cant be simplified

-9(m+3) +14=-49 please show work

Answers

Answer:

m=4

Step-by-step explanation:

−9(m+3)+14=−49

Step 1: Simplify both sides of the equation.

−9(m+3)+14=−49

(−9)(m)+(−9)(3)+14=−49(Distribute)

−9m+−27+14=−49

(−9m)+(−27+14)=−49(Combine Like Terms)

−9m+−13=−49

−9m−13=−49

Step 2: Add 13 to both sides.

−9m−13+13=−49+13

−9m=−36

Step 3: Divide both sides by -9.

−9m

−9

=

−36

−9

m=4

A teacher writes the algebraic expression 24푐+5푚+19.99 to represent the cost of supplies. She bought 24 packages of pencils, 5 packages of markers, and a beanbag chair. Identify variables, coefficients, and terms in the expression. Tell what each represents.

Answers

A teacher write the algebraic expression 24c + 5m + 19.99 to represent the cost of supplies. She bought 24 packages of pencils, 5 packages of markers, and a beanbag chair. Identify variables, coefficients, and terms in the expression. Tell what each represents.

Answer:

Step-by-step explanation:

The algebraic expression is written by the teacher as:

24c + 5m + 19.99

Purchased product are:

24 packages of pencils, 5 packages of markers, and a beanbag chair.

The variables are;

packages of pencils; packages of markers; a beanbag chair.

The coefficients are;

24, 5 and 19.99

This representation implies that;

The teacher bought:

24 "c"olored pencils;

5 packages of  "m"arkers; &

19.99 represent the cost of each beanbag chair.

Can someone please explain how to do this problem for me?

Three people eat 2 pizzas altogether. Both pizzas are the same size. One person eats 2/3 of a pizza. A second person eats 1/2 of a pizza. How much pizza does the third person eat?

Answers

Answer: The other person eats 5/6ths of a pizza

Step-by-step explanation:

put it into sixths

Answer:

5 /6

Step-by-step explanation:

may be 5/ 6 is the correct one

A skateboarder travels 90 M in 20 seconds what is her speed

Answers

Answer:

4.5

Step-by-step explanation:

Answer:

9 meters per 2 second or 4.5

Step-by-step explanation:

divide both by ten : )

nobodys probably gonna answer this ): but if you can please do with the answers its for my homework :)

Answers

                                                       Answer

12 ) $100013 ) Y-Intercept = 1000       Slope = [tex]\frac{3000-2000}{4-2}[/tex] = [tex]\frac{1000}{2}[/tex] = [tex]\frac{500}{1}[/tex]14 )  [tex]\left(x^{1\ },\ y^{1}\right)\left(x^{2},\ y^{2}\right)[/tex] → [tex]\left(2\ ,\ 2000\right)\ \left(4\ ,\ 3000\right)[/tex] → [tex]\frac{3000-2000}{4-2}[/tex] → [tex]\frac{500}{1}[/tex]15 ) The meaning of the slope is the steepness of the line, in this graph, the meaning is 500 over 1.

Hope this helps! <3

The volume of a fish tank is given by the function V (x) = (x + 7) (1-4) (2x + 3). Write a function describing a fish tank that has the same height but is
longer in length by 3 units and wider by 2 units.

Answers

Answer:

V(x)=(x+9) * (3) * (2x + 6)

Step-by-step explanation:

A fish tank is usually made in the shape of a 3-Dimensional rectangular prism. The volume of this shape can be obtained by using the following formula

V = w * h * l

in this formula w represents the width, h represents the heigh, l represents the length, and V represents the volume of the rectangular prism/fish tank. Therefore, we can use the function provided in the question and simply add 3 units to the length and 2 units to the width in order for it to work for our new fish tank.

V(x)=(x+9) * (3) * (2x + 6)

Fifteen billiard balls are numbered 1 to 15. One billiard ball is selected at random. Determine the odds for and the odds against for (6 Points) a) selecting the number 7 b) selecting a number greater than 10

Answers

Answer:

Odds for & against selecting number 7 = 1/14 & 14

Odds for & against selecting number more than 10 = 4/11 & 11/4

Step-by-step explanation:

Odds for event = Prob (event) / Prob (no event)

Odds against event = Prob (no event) / Prob (event)

Odds for selecting number 7

Prob (No. 7 chosen) = 1/15 , Prob (No. 7 not chosen) = 14/15

Odds for number 7 = (1/15) ÷ (14/15) = 1/14

Odds against number 7 = (14 / 15) ÷ (1/15) = 14

Odds for selecting number > 10

Prob (No. > 10 chosen) = 4 / 15  , Prob (No. > 10 not chosen) = 11/15

Odds for No. > 10 = (4/15) ÷ (11/15) = 4/11

Odds against No. > 10 = (11/15) ÷  (4/15) = 11/4

3 8 of your income is spent on your monthly bills, 2 5 is spent on food and clothing and 1 10 goes on entertainment. You put the remainder of your monthly income into savings.

Answers

Answer:

Fraction of saving = 1/8

Step-by-step explanation:

Given:

Spent on bills = 3/8

Spend on food = 2/5

Spend on entertainment = 1/10

Find:

Fraction of saving

Computation:

Fraction of saving = 1 - Spent on bills - Spend on food - Spend on entertainment

Fraction of saving = 1 - 3/8 - 2/5 - 1/10

By taking LCM

Fraction of saving = [40 - 15 - 16 - 4]/40

Fraction of saving = [5]/40

Fraction of saving = 1/8

Evaluate 7 to the power of 2 pls help

Answers

Answer:

49

Step-by-step explanation:

Whenever you power something, you are just multiplying that number by itself amount of times you are powering

7 to the power of 2 is 7² = 49

The power (or exponent) of a number define how many times to use the number in a multiplication.

It is written as like a small number to the right and above the base number.

In this example the little "2" says to use 8 two times in a multiplication: 82 = 8 × 8 = 64.

To evaluate 7 to the power of 2.

7² = 7 × 7 = 49

Therefore, 7 to the power of 2 is 49.

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What are some other ways the answer can be determined ( other than Multiplication)

Will mark and 5 STARS, THANKS

Answers

By dividing I think

The scale of a map says that 3 inches represents 4 miles. What distance on a map represents an actual distance of 2 miles?

Answers

Answer:

1.5 inches

Step-by-step explanation:

half of four miles so half of 3 inches

It would be 1.5 miles then I’m pretty sure

What is the distance between A and B? Round your answer to the nearest tenth.

Answers

Answer:

6.4

Step-by-step explanation:

Just plug in the distance formula.

(4+1)^2+(1-5)^2

(5)^2+(-4)^

25+16

41

(square root 41) and get 6.4


Solve for the variable
10 + 25a = 75





Please help

Answers

Answer:

a = 2.6

Step-by-step explanation:

10 + 25a = 75

- 10.             - 10

25a = 65

÷25.     ÷25

a = 2.6

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer:13/5  or 2.6

Step-by-step explanation:

The diameter of a circular park is 98 m. Find the cost of fencing it at $4 per meter

Answers

Answer:

Answer. circumference = 151 m ( appr.) Ans :- The cost of fencing is Rs 604 .

Complete the square for the expression. Also, identify the resulting expression as a binomial squared.
x2 + 11x + ____

Answers

When completing the square is carried out on the quadratic [tex]x^2+11x[/tex] we get

[tex]x^2+11x+\dfrac{121}{4}[/tex]

when expressed as a binomial squared, we get

[tex]\left(x+\dfrac{11}{2}\right)^2[/tex]

To complete the square, we need to add a term to the expression

[tex]x^2+11x[/tex]

that would make it a perfect square. Generally, given the quadratic expression

[tex]x^2+bx[/tex]

to make it a perfect square, we have to add half the square of the coefficient of [tex]x[/tex]. That is, add [tex]\left(\frac{b}{2}\right)^2[/tex], or [tex]\frac{b^2}{4}[/tex] to the quadratic expression to get

[tex]x^2+bx+\dfrac{b^2}{4}[/tex]

which, when factored into a binomial squared becomes

[tex]\left(x+\dfrac{b}{2}\right)^2[/tex]

In our case, the quadratic [tex]x^2+11x[/tex] will become

[tex]x^2+11x+\dfrac{121}{4}[/tex]

and when expressed as a binomial squared, we get

[tex]\left(x+\dfrac{11}{2}\right)^2[/tex]

Learn more about completing the square here https://brainly.com/question/2055939

Answer:

[tex]x^{2}[/tex] +11x+ [tex]\frac{121}{4}[/tex]= [tex](x+\frac{11}{2} )^{2}[/tex]

Step-by-step explanation:

.

x ÷ 9 = 4
plz help fast

Answers

Answer:

36

Step-by-step explanation:

transpose

x= 4×9

x= 36

Answer:

x = 36

Step-by-step explanation:

If we were to switch around the equation to multiplication, we would have 9 x 4 or 4 x 9 which is 36.

n − 23 ≥ 19 solve the inequality.

Answers

Answer:

n ≥ 42

Step-by-step explanation:

n -23 ≥ 19      add 23

n ≥ 48

Find the slope of the line.
Help!

Answers

Answer:

if the line is the blue one the answer is y=0

Step-by-step explanation:

PLEASE HELP, MARKING BRAINLIEST!!

if 4m = 9n, then m/n=

Answers

Answer:

m/n=9/4

Step-by-step explanation:

4m = 9n

m/n=9/4

I’ll give the brainliest if you help meeeee

Answers


A) 4-1 would change to 4+(-1)
B) -8-(-3) would change to -8+3

A) 3
B) -5

Find the slope of the line that contains the following ordered pairs. Show all work.
8.
(18,-7) and ( 18, 2)
Formula:
Slope:

Answers

Answer:

see below

Step-by-step explanation:

slope = (y₂ - y₁) / (x₂ - x₁)                 <=== formula

         = (2 - (-7)) / (18 - 18)

         = 9 / 0

         = 0                                         <=== slope

I need help with this question

Answers

Answer:

a

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation:

Misty correctly determined the equation of the linear function represented by the table of values below to be y = negative 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).

Answers

Answer:

we can verify that the determined equation is the same as the equation determines by Misty, hence, we conclude that Misty had correctly determined the equation of the linear function.

Step-by-step explanation:

As Misty determined the equation of linear function:

[tex]y=-2x+9[/tex]

We need to check whether she has got the correct equation or not.

As the linear equation passes through the points  [tex](1, 7)[/tex] and [tex](2, 5)[/tex].

Finding the slope:

The slope between two points  [tex](1, 7)[/tex] and [tex](2, 5)[/tex]

[tex]\left(x_1,\:y_1\right)=\left(1,\:7\right),\:\left(x_2,\:y_2\right)=\left(2,\:5\right)[/tex]

[tex]m=\frac{5-7}{2-1}[/tex]

[tex]m=-2[/tex]

As we know the point-slope form is:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

So, the equation of the line will be:

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-5=-2\left(x-2\right)[/tex]

Add 5 to both sides

[tex]y-5+5=-2\left(x-2\right)+5[/tex]

[tex]y=-2x+9[/tex]

From the above calculation, we can verify that the determined equation is the same as the equation determines by Misty, hence, we conclude that Misty had correctly determined the equation of the linear function.


22. The cost of renting a pickup truck at Company A is $25 plus 15 cents per mile driven. The cost ol
Renting a truck at Company B is $25 plus 10 cents per mile driven. In the graph of the cost of a
Truck rental, what does the cost per mile driven represent?

A The point of intersection

B The y-intercept

C The x-intercept

D The slope

Answers

Answer:

D. The slope

Step-by-step explanation:

0.15 = 3/20

0.10 = 1/10

Given:

  company A:    y = 3/20x + 25

  company B:    y = 1/10x + 25

y = mx + b

m is slope

b is y-intercept

A basketball player made 81 out of 100 attempted free throws. What percent of free throws was​ made?

Answers

Answer:

81%

Step-by-step explanation:

81 out of 100 is 0.81, which is 81%

Hope this helps plz mark brainliest if correct :D

Answer:

0.800

Step-by-step explanation:

Hope it Helps

Part A). Emily participates in a trivia quiz show. In each round, 20 points are awarded for a correct answer and 10 points are deducted for an incorrect answer. Part B). Emily answer 4 questions correctly and 11 incorrectly in the first round what was her score in the first round? Emily answer'd 7 questions correct and 8 incorrect in the second round what was her score in the second round.

Answers

Answer

A. -30 points

B. 60 points

Step-by-step explanation:

20 points for correct answer and 10 points deducted for wrong answer

Each deduction is -10 while each correct answer gives + 20

4 questions correctly and 11 incorrectly

= 4(20) + 11(-10)

= 80-110 = -30 points

Second round

7 correct, 8 incorrect

= 7(20) - 8(10)

= 140-80 = 60 points

(11x + 2y) - (5x – y)

Answers

Answer:

the answer is [tex]6x+3y[/tex]

Step-by-step explanation:

[tex]\mathrm{Remove\:parentheses}:\\=11x+2y-\left(5x-y\right)\\\\-(5x-y): -5x+y\\=11x+2y-5x+y\\Simplify:\\11x+2y-5x+y: 6x+3y\\\\=6x+3y[/tex]

hope this helps :)

Try using Symbolab, I use it all the time it gives the correct answer and it gives good explanations.

En la regla de la potencia, durante el proceso de integración, se ________ 1 al exponente, mientras que en la derivación se ________ 1 a dicho exponente. De igual forma, el exponente pasa dividiendo mientras que en la derivación pasa ________. Al último, agregamos la letra c, que significa constante" *

Answers

Answer:

a) adiciona, b) sustrae, c) multiplicando.

Step-by-step explanation:

A continuación, presentamos la respuesta correcta al ejercicio citado:

En la regla de la potencia, durante el proceso de integración, se adiciona 1 al exponente, mientras que en la derivación se sustrae 1 a dicho exponente. De igual forma, el exponente pasa dividiendo mientras que en la derivación pasa multiplicando. Al último, agregamos la letra C, que significa constante.

Razones

Derivación de una función potencial:

[tex]\frac{d}{dx}(x^{n}) = n\cdot x^{n-1}, n\ne 0[/tex]

Integración de una función potencial:

[tex]\int {x^{n}} \, dx = \frac{x^{n+1}}{n+1}+C,x\ne -1[/tex]

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