Write this expression as a complex number in standard form

Write This Expression As A Complex Number In Standard Form

Answers

Answer 1

Answer:

[tex]81+144i[/tex]

Step-by-step explanation:

We want to simplify:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i[/tex]

Recall that:

[tex]\displaystyle \sqrt{-a} = i\sqrt{a}[/tex]

Therefore:
[tex]\displaystyle \begin{aligned} (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i & = (-3i\sqrt{81})(-5+i\sqrt{9})+9i \\ \\ &= -(3i(9))(-5+i(3))+9i \\ \\ & = -27i(-5+3i)+9i \\ \\ & = 135i -81i^2 + 9i \\ \\ & = 144i - 81i^2 \\ \\ & = 81+144i\end{aligned}[/tex]

Note that i² = -1.

In conclusion:

[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9})+9i = 81 + 144i[/tex]

Answer 2
The answer is 81+144i

Related Questions


* Graph these numbers on a number line.
-5,3, -2,1
-5

Answers

-5,3,-2,1 on a number line

<-|----|----|----|----|----|----|----|----|->

-5 -2 0 1 3

Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be
written using function notation?
O FID = - Šv
O f(x) = - 3x + 4
Of(x) = -x +
O fly) = -34+4​

Answers

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Note that y = f(x)

Rearrange making y the subject

9x + 3y = 12 ( subtract 9x from both sides )

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4 , that is

f(x) = - 3x + 4

plz answer this asap

Answers

Answer:

50%

Step-by-step explanation:

Solve using quadratic formula.

1.)5x^2+13x=6

2.)3x^2+1=-5x

PLEASE HELP!!! WILL MARK BRAINLIEST!!!

Answers

Answer:

1. 2/5,-3 2. [tex]x=\frac{-5+-\sqrt{13} }{6}[/tex]

Step-by-step explanation:

i used the quadratic formula to find x also please note that 2 has 2 answers bc of the +- beofre the sqrt of 13  

Step-by-step explanation:

1).

5x² + 13x - 6 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

a = 5 , b = 13 c = - 6

We have

[tex]x = \frac{ - 13± \sqrt{ {13}^{2} - 4(5)( - 6) } }{2(5)} [/tex]

[tex]x = \frac{ - 13± \sqrt{169 + 120} }{10} [/tex]

[tex]x = \frac{ - 13± \sqrt{289} }{10} [/tex]

[tex]x = \frac{ - 13±17}{10} [/tex]

[tex]x = \frac{ - 13 + 17}{10} \: \: \: \: \: or \: \: \: \: x = \frac{ - 13 - 17}{10} [/tex]

x = 2/5 or x = - 3

2).

3x² + 5x + 1 = 0

a = 3 , b = 5 , c = 1

[tex]x = \frac{ -5 ± \sqrt{ {5}^{2} - 4(3)(1)} }{2(3)} [/tex]

[tex]x = \frac{ - 5± \sqrt{25 - 12} }{6} [/tex]

[tex]x = \frac{ - 5± \sqrt{13} }{6} [/tex]

[tex]x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} [/tex]

Hope this helps you

-5(-x - 1) + 4x – 1= 49
solve for x

Answers

Answer:

x=5

Step-by-step explanation:

-5(-x - 1) + 4x – 1= 49

Distribute

5x +5 +4x -1 = 49

Combine like terms

9x +4 = 49

Subtract 4 from each side

9x+4-4 = 49-4

9x = 45

Divide by 9

9x/9 =45/9

x = 5

Answer:

[tex]\huge \boxed{x=5}[/tex]

Step-by-step explanation:

[tex]{\Large -5(-x - 1) + 4x -1= 49}[/tex]

Expand brackets.

[tex]5x+5+ 4x -1= 49[/tex]

Combine like terms.

[tex]9x+4=49[/tex]

Subtract 4 from both sides.

[tex]9x+4-4=49-4[/tex]

[tex]9x=45[/tex]

Divide both sides by 9.

[tex]\displaystyle \frac{9x}{9} =\frac{45}{9}[/tex]

[tex]x=5[/tex]

A soma de dois números consecutivos é 11, qual expressão algébrica representa este contexto? * 1 ponto a) X + X + 1 = 11 b) X + X = 11 c) X + X – 1 = 11 d) X + 1 = 11

Answers

Answer:

a) X + X + 1 = 11

Step-by-step explanation:

Em matemática, a soma de consecutivos é expressa matematicamente como:

X + (X + 1) + (X + 2) + (X + 3) .............

Na pergunta acima, somos solicitados a encontrar a expressão algébrica que indica que a soma de DOIS inteiros consecutivos é igual a 11

Portanto, esta expressão algébrica é dada como:

X + (X + 1) = 11

X + X + 1 = 11

Portanto, a opção a) X + X + 1 = 11 é a opção correta

How to do this question plz answer me step by step plzz plz ​

Answers

Answer:

[tex] \boxed{\sf Perimeter \ of \ semicircle = 3 \pi \ cm} [/tex]

Given:

Radius of semicircle (r) = 3 cm

Step-by-step explanation:

[tex]\sf Perimeter \ of \ semicircle = \pi r [/tex]

[tex] \sf = 3 \pi \: cm[/tex]

If I get 20 pound a day how much do i make in a month

Answers

Answer:

£600

Step-by-step explanation:

1 months= 30 days

here,

money made in 1 day= £20

now,

money made in 30 days= 20×30

= 600

[:• In one month you earn £600]

Answer:560 pounds

Step-by-step explanation:

If 1 day is equal to 20 pounds, to find how much pounds will you have a month, first check how many days are there in a month. Then multiply the number of days in a month to the given pound in one day.

So =1 month = 28 days

=1 day = 20 pounds

So= 20 pounds × 28 = 560 pounds

If a person invests $250 at 9% annual interest, find the approximate value of the investment at the end of 15 years

Answers

Answer:

The end balance is $910.62 and the total interest $660.62. (That is without tax or inflation rate) I hope this helps.

Step-by-step explanation:

Answer:

without tax: interest total=$660.62

Step-by-step explanation:

I multiplied...

in the equation z=x^2-3y, find the value of z when x=-3 and y=4

Answers

Answer:

z=-3

Step-by-step explanation:

z=(-3)^2 - 3(4)

z=9 - 12

z=-3

How would I simplify 14.8+6.25+0.97

Answers

Answer:

22.02

Step-by-step explanation:

14.8+6.25+0.97 is 22.02

don't know what you mean by simplify

Jayde is wrapping a cube shape present that is 14 inches tall. How much wrapping paper will be needed to wrap the whole present?

Answers

Answer:

1176in^2

Step-by-step explanation:

find the surface area of the cube

(14*14)6=1176 inches cubed

14*14 is finding the area of one side and then we multiply it by six because that's how many congruent sides there are

Answer:

[tex]\large\boxed{1,176 in^{2} }[/tex]

Step-by-step explanation:

The cube is 14 inches tall

All of the sides in a cube are the same, which means:

Length = 14 inches

Width = 14 inches

Height = 14 inches

There are 6 sides in a cube. Each side has a length and a width.

We can use the following formula to find the surface area (SA) of the cube, or how much wrapping paper Jayde will use.

SA = # of Sides(Length(Width))

Plug in known values

SA = 6((14)(14))

The 14s represent the length and width while the 6 represents the number of sides in the cube.

Solve/Simplify

SA = 6(196)

SA = 1,176 inches²

Jayde will need to use 1,176 in² of wrapping paper to wrap the whole present.

Hope this helps :)

a) Simplify the expression and explain each step. (2 points)


4(3x+2) -2
= ?

Answers

Answer:

6 (2 x + 1)

Step-by-step explanation:

Simplify the following:

4 (3 x + 2) - 2

Hint: | Distribute 4 over 3 x + 2.

4 (3 x + 2) = 12 x + 8:

12 x + 8 - 2

Hint: | Group like terms in 8 + 12 x - 2.

Grouping like terms, 8 + 12 x - 2 = 12 x + (8 - 2):

12 x + (8 - 2)

Hint: | Subtract 2 from 8.

8 - 2 = 6:

12 x + 6

Hint: | Factor out the greatest common divisor of the coefficients of 12 x + 6.

Factor 6 out of 12 x + 6:

Answer: 6 (2 x + 1)

9/2 divided by 1/4= ? in simplest form

Answers

Answer: 18

Do Keep Change Flip (KCF)

Keep: 9/2

Change: ÷ into ×

Flip: 1/4 into 4/1

Your new problem should be 9/2×4/1

Multiply

9/2×4/1=36/2

36/2=18

Final Answer: 18

which of the following are remote interior angles of <6? check all that apply

Answers

Answer:

C. <3, E. <1

Step-by-step explanation:

A triangle has 3 vertices, so it has exactly 3 interior angles, one at each vertex.

A triangle has 2 exterior angles at each vertex, so a triangle has 6 exterior angles. Each exterior angle is adjacent to an interior angle. The interior angles that are not adjacent to an exterior angle are that exterior angle's remote interior angles.

<6 is an exterior angle of the triangle. <5 is the other exterior angle at that vertex. <2 is an interior angle of the triangle and is adjacent to <6, so <2 is not a remote interior angle to <6.

The other two interior angles of the triangle are <1 and <3.

<1 and <3 are interior angles that are not adjacent to <6, so they are the remote interior angles to <6.

Answer: <1, <3

factorise 9a^2-b^2??

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

3² * a² - b²

▹ Step-by-Step Explanation

9a² - b²

Break down each coefficient and variable:

9 = 3²

a² = a²

b² = b²

Combine everything together:

3² * a² - b²

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Since both terms are perfect squares, factor using the difference of squares formula,  a^2-b^2=[a+b][a-b] where a=3a and b=b

Find the 2nd term in the sequence. Will give Brainliest.

Answers

Answer:

17

Step-by-step explanation:

b(1) = 16

b(2) = b(2-1) +1

      = b(1) +1

     = 16+1

    = 17

solve for x 7(3-x) = 8(4-2x)

Answers

Answer:

  x = 11/9

Step-by-step explanation:

Eliminate parentheses, add 16x, subtract 21.

  7(3 -x) = 8(4 -2x) . . . . given

  21 -7x = 32 -16x . . . . . eliminate parentheses using the distributive property

  9x +21 = 32 . . . . . . . . add 16x

  9x = 11 . . . . . . . . . . . . subtract 21

  x = 11/9 . . . . . . . . . . . .divide by the coefficient of x

three people alice , ben , calvin, are conversing at a taxi stand since taxis are the only ride service in this town. although they havent met before ,they realize that all are going the same route to get desire destination. alice destination is 20 miles away , ben destination 30 miles away and calvins destination 40 miles away , the taxi costs 2 dollars per mile with tip included regardless of the number of passengers. how much should each person pay if the three share a cab to their respective destination

Answers

Answer:

Alice will have to pay $13.33

Ben will have to pay $23.33

Kelvin will have to pay $43.33

Step-by-step explanation:

Given that

Alice destination is 20 miles away

Ben destination is 30 miles away

Calvin destination is 40 miles away.

For a mile, taxi costs 2 dollars.

To find:

How much each person has to pay if they share the same taxi to their respective destinations?

Solution:

For the first 20 miles, the taxi will be shared by all 3 of them.

Charges for 20 miles = 20 [tex]\times[/tex] 2 = $40

This $40 will be shared among all 3.

Each will pay = [tex]\frac{40}{3} = \$13.33[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33

Charges for Calvin = $13.33

For the next 10 miles, the taxi will be shared by Ben and Calvin.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be shared between Ben and Calvin.

Each will pay = [tex]\frac{20}{2} = \$10[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33 + 10 = $23.33

Charges for Calvin = $13.33 + 10 = $23.33

For the next 10 miles, Calvin travels alone.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be paid by Calvin alone.

Charges for Alice = $13.33

Charges for Ben = $23.33

Charges for Calvin = $23.33 + 20 = $43.33

What is the y−intercept of the line that passes through the point (4,9)and is parallel to the line y=12x+2?

Answers

Answer:

y- intercept = - 39

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 12x + 2 ← is in slope- intercept form

with slope m = 12

Parallel lines have equal slopes, thus

y = mx + c ← is the partial equation

To find c substitute (4, 9) into the partial equation

9 = 48 + c ⇒ c = 9 - 48 = - 39 ← y- intercept

Answer:

y-intercept = -39

Step-by-step explanation:

if two lines are parallel it means they have the same gradient so we compare the equation given to the default equation of a line

y=mx+c

y=12x+2

comparing we have the gradient m=12 now finding the equation of the line parallel to the given line we use

y-y1=m(x-x1)

y1=9 and x1=4

y-9=12(x-4)

y-9=12x-48

y=2x-48+9

y=2x-39

comparing to the default equation of a line y=mx+c where c is the y-intercept

therefore the y-intercept is -39

Maria is buying new carpet for her bedroom .Her bedroom is in the shape of a square and the length of each side is 12 feet write and simplify an exponential express to find how much carpet she needs.

Answers

Answer:

well just do area, and since it's the same in each side 12×4= 144

how many quarts make 5 gallons

Answers

Answer:

4 quarts

Hope it helps!

Step-by-step explanation:

Answer: 5 gallons= 20 quarts

              1 gallon = 4 quarts

help me plz plz....​

Answers

Answer:

4775.9 [tex]cm^3[/tex]

Step-by-step explanation:

To find the volume of a cone use the expression [tex]\pi r^2\frac{h}{3}[/tex]

r = radius

h = height

Now substitute h for 27 and r for 13, [tex]\pi 13^2\frac{27}{3}[/tex]

First do 13 x 13 (because of the exponent), then divide 27 and 3, which is 9

169 x 9 = 1521

Lastly multiply by pi or use 3.14

1521 x 3.14 = 4775.94

Since it asks to round to the tenth it is just 4775.9

Answer:

4778.4 cm^3

Step-by-step explanation:

The formula for the volume of a cone is [tex]V=\pi r^2\frac{h}{3} \\[/tex].

In this case, the height is 27 and the radius is 13, so we plug in the values and get [tex]V = \pi (13)^2 \frac{27}{3}\\[/tex].

We solve and get the volume of the cone as [tex]1521\pi[/tex] or 4778.4 cm^3.

Solve for x. 5x-4 > 12 OR 12x+5 <-4

Answers

Answer:

x > 16/5 or x < -3/4

Step-by-step explanation:

Equation 1: 5x - 4 > 12

Equation 2: 12x + 5 < -4

Equation 1: 5x - 4 > 12

add 4 to both sides

5x > 16

divide by 5 on both sides

x > 16/5

Equation 2: 12x + 5 < -4

subtract 5 on both sides

12x < -9

divide by 12 on both sides

x < -9/12

simplify

x < -3/4

If =x/y=5/8
then x/5=

Answers

[tex]\dfrac{x}{y}=\dfrac{5}{8}\Big|\cdot\dfrac{y}{5}\\\\\dfrac{x}{5}=\dfrac{y}{8}[/tex]

Answer:

x/5 = y/8

Step-by-step explanation:

x          5

----- = -------

y          8

Using cross products

8x = 5y

Divide each side by 8

x = 5/8 y

Divide each side by 5

x/5 = y/8

the 8th term of an arithmetic progression is 5 times the 3rd term while the 7th is greater than the 4th term . write the first five term of the arithmetic progression​.

Answers

Answer:

the terms of any of the 2 terms should have been given

A combination lock uses three numbers between 1 and 46 with​ repetition, and they must be selected in the correct sequence. Is the name of​ "combination lock"​ appropriate? Why or why​ not? Choose the correct answer below. A. ​No, because the multiplication counting rule would be used to determine the total number of combinations. B. ​Yes, because the combinations rule would be used to determine the total number of combinations. C. ​No, because factorials would be used to determine the total number of combinations. D. ​No, because the permutations rule would be used to determine the total number of combinations.

Answers

The correct answer is D. ​No because the permutations rule would be used to determine the total number of combinations.

Explanation:

The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.

Melissa put her $500 In a savings account that earns 4% interest compounded annually. How much will be in the account after 3 years? Round your answer to the nearest hundredth

Answers

Answer: $562.43

Work Shown:

A = P*(1+r/n)^(nt)

A = 500*(1+0.04/1)^(1*3)

A = 562.432

A = 562.43

Answer: $562.43

Step-by-step explanation:

The initial start up amount is 500  and we want to expressed this as an exponential function. So since we know the initial value we need to find the rate of change. So if you earn 4% interest you are earning 4% percent more on top the actual 100%.

So 100%  + 4 % = 104% = 1.04  

The common difference is 1.04.

so  500 * 1.04^n= A where n is the number of years and A is the total amount.

A = 500 * [tex]1.04^{3}[/tex]  

A= 562.43

- 3 1/2 ( - 12 1/4 )

Answers

The answer is 343/8 or 42 7/8
343/8, or 42 and 7/8


what is the perimeter of rhombus ABCD ?

Answers

Answer:

20

Step-by-step explanation:

Since you can use the Pythagorean theorem to calculate the length of the hypotenuse, each side can be found to be 5. There are four equal sides, so it is 20.

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