simplify the expression (sqrt3+i)(sqrt3-i) and write the result in the form a+bi

Answers

Answer 1

Answer:

4

Step-by-step explanation:

This expression is a difference of squares.

(√3 + i)(√3 - i) = (√3)²-(i)², which is

3 - (-1)

= 3 + 1

= 4


Related Questions

HELP PLEASE 30 POINTS!!​

Answers

Answer:

p - w = $25 OR w + $25 = p

Step-by-step explanation:

pencil = p

pen = w

p - w = $25 OR w + $25 = p

Select all of the true statements.
A. 4.8 + (-8.9) = -13.7
B. 12+(-3) = -9
C. -9.-0.1 = 90
D. -4+ 4 =

Answers

Answer:

D

Step-by-step explanation:

-4+4=0 which is correct

4.8-8.9=-4.1 wrong

12-3=-9 wrong

-9-0.1=90 wrong

What number is grater than 1 but less than 7

Answers

Answer:

5

ok

THIS IS SIMPLE

MARK AS BRAINLIST

The vertex of this parabola is at (-3,-1). When the yvalue is 0, the x-value is 4. What is the coefficient of the squared term in the parabola's equation?
A. -7
B. -3
C. 3
D. 7​

Answers

Answer:

d

Step-by-step explanation:

If 9 garden hoses cost $196.83 and the price of each hose is the same how much does each hose cost?

Answers

Answer:21.87

Step-by-step explanation:

196.83 divided by 9

Answer:

They each cost $21.87

Step-by-step explanation:

If each hose costs the same you can just divide the total (196.83) by the number of hoses (9) to get 21.87.

How did the Medieval Church control people's lives?

Answers

Answer:

The Church regulated and defined an individual's life, literally, from birth to death and was thought to continue its hold over the person's soul in the afterlife

Pls mark Brainliest

Step-by-step explanation:

1. How would you solve the equation
3a + 7 = – 2 by graphing?

Answers

Answer:

You draw it on the graph right

PLEASE HURRY!! What is the slope of the line that passes through the points (-1, 2) and (-4, 3)?

Answers

Answer:

the slope = -⅓          

                     

                     

                                                                                                                                                                     

The slope of the line (-1,2) and (-4,3) should be m= -1/3

Please help!!!!!!! Tysm!!

Answers

Answer:

it's the first answer

Step-by-step explanation:

its 2/9 because 1/3 × 2/3 = 2/9

Answer:

It's C

Step-by-step explanation:

1/3 x 2/3 = 2/9, which simplifies back to 1/3

and 1/3=2/6

What is the circumference of a circle with a radius of 86 inches? use 3.14 for PI​

Answers

Step-by-step explanation:

[tex]circumference = 2\pi\: r \: \\ = 2 \times 3.14 \times 86 \\ = 540.08[/tex]

Answer:

540.08

Step-by-step explanation:

Given a 17-sided polygon, what is the sum of the measures of the exterior angles?

Answers

Answer:

360 degree

Step-by-step explanation:

A seventeen sided polygon or a 17 sided polygon the rule is same that the sum of the measures of the exterior angles is 360.

Help lol I dunno what to do

Answers

Answer:

same

Step-by-step explanation:

Answer:

The answer is 9.2

Step-by-step explanation:

2x + 5y = -24
3x - 5y = 14
Solve by elimination
y and x

Answers

Answer:

x = -2

y = -4

Step-by-step explanation:

The way systems of equations  work is that you have to substitute to solve for a variable *(only one of the 2 ways to figure this out)*

so, we will use addition property of equality in a form to add the two equations together, since +5y and -5y added together will cancel out.

that would leave

5x = -10

divide both sides by 5

x = -2

Now that we know x = -2, we can plug in -2 into one of the equations to find y.

2 ( -2)  + 5y = -24

-4 + 5y = -24

-4 + 4 + 5y = -24 + 4

5y = -20

y = -4

x = -2

y = -4

You buy 4 balloons and 2 banners for $8. Your friend buys 6 balloons and 1 banner for $8.


Each balloon costs ?$

and each banner costs ?$

Answers

Answer:

Each balloon costs $1

Each banner costs $2

Step-by-step explanation:

First of all, let's write down the equation from this problem.

Let "y" be the cost of the ballon, and let "x" be the cost of a banner. Then the following is true from the question...

4y + 2x = 8

6y + x = 8

Now since both of them are equal to 8 both of them are equal to each other, and so we can get the following equation...

4y + 2x = 6y + x

2x - x = 6y - 4y

x = 2y

Now if we substitute 2y instead of x in one of the previous equations we will obtain...

6y + x = 8

6y + 2y = 8

8y = 8

y = 1

From the equation x = 2y we know that...

x = 2y

x = 2(1)

x = 2

Please help! Tysmm :))

Answers

118
..........................

Can someone pleaseee help me solve this

Answers

The answer is 23 your welcome

Help meee 50 points explain ALL OF IT if you really do it ill give you 200 points pls

Answers

Answer:

Explain what there is no picture

Step-by-step explanation:

Hai!

1. He is Considering 3 Themes: Space, Safari, and Comics.

2. He is Considering 2 Places: Skating rink and the Park.

3. He is Considering 3 Days of the week: Friday, Saturday, and Sunday.

4. EXAMPLE 1 One possibility is that Noah is considering is a party with a Safari Theme at the park on Friday EXAMPLE 2 One possibility is that Noah is considering is a party with a Comics Theme at the park on Saturday

5. There is 21 Possible Outcomes

Hope I helped. Best of luck! :3

PLS HELP THE PICTURE IS DOWN BELOW

Answers

Answer:

4

Step-by-step explanation:

Normally you would have to figure out the distance of the x- and y-components and use the Pythagorean Theorem; however, because the y-coordinates of both points are the same, you only need the x-coordinates.

You have the first point back 3, and the second point forward 1.

So starting at -3, you move 4 points to get to 1.

((-3 to -2 (1), -2 to -1 (2), -1 to 0 (3), 0 to 1 (4)))

I need help answering b

Answers

The diagram should help

can someone please help me with this i need it badddd

Answers

g=61°, h=9. the opposite angles are equal, and the opposite sides are equal.

Becky is using the expression 2z + 3 to represent the number of chairs in her classroom. There are twice as many chairs as tables, and there are three extra chairs in the back. What does z represent?

The number of chairs.
The number of tables.
The number of chairs at tables.
The number of chairs and tables.

Answers

Answer:

The number of chairs

Step-by-step explanation:

The equation is 2z + 3

2 ( = multiply by)

z ( # of chairs)

+3 ( the 3 extra chairs in the back)

Answer:

The number of tables

Step-by-step explanation:

Sens there is twice as many chairs as tables, the number 2 represents the chairs. The 3 represents the 3 extra chairs in the back. so the only logical object to represent z is the number of tables.

A polygon has a perimeter of 18 units. It is dilated with a scale factor of 3/2 what is
the perimeter of its image?

Answers

Answer:

A

Step-by-step explanation:

Is the correct answer

The perimeter of the polygon after dilation = 27 unit

What is dilation factor?

The scale factor in a mathematical object's dilatation defines how much the picture will grow or shrink in relation to the original thing.

The perimeter of polygon = 18 unit,

Since, the scaling factor is 3/2,

So when the polygon is dilated, the perimeter of the polygon will also multiply with 3/2,

Perimeter of polygon = 18×3/2

                                    = 27 unit

The perimeter of the polygon after dilation = 27 unit

To know more about Dilation factor on:

https://brainly.com/question/13176891

#SPJ5

Write an expression for the description: the product of 3 and p subtracted from 6

Answers

Answer:

6 - 3p

Step-by-step explanation:

The word "product" indicates to multiply 3 and p, and "subtracted from" tells us to use subtraction.

Answer:

the sum of 6 6 66 and the product of 3 3 33 and d d dd".

Step-by-step explanation:

how to change .75 to a percentage NOW

Answers

Answer:

Move the decimal place over to the left two spaces

.75--> 7.5--> 75%

and reverse

75%--> 7.5--> .75

Step-by-step explanation:

brainliest plz

Answer:

75%  

Step-by-step explanation:

"Percent" means "per 100" or "over 100". So, to convert 0.75 to percent we rewrite 0.75 in terms of "per 100" or over 100.

Multiply 0.75 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.

0.75      100        75

-------- x --------  = -------- which equals to 75%

1             100        100

Hope this helps

can i have brainliest plz

please help me plz im begging u

Answers

Answer:

B

Step-by-step explanation:

solve the matrix and prove that it is equal 0​

Answers

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Given}}} : [/tex]

[tex] \tt{ {A}^{T} = \begin{bmatrix} 2 & - 4 \\ 4 & 3 \\ \end{bmatrix}}[/tex]

[tex] \underline{ \underline { \text{To \: Find}}} : [/tex]

[tex] \sf{ {A}^{2} - 5A+ 22I= 0}[/tex]

[tex] \underline{ \underline{ \text{Solution}}} : [/tex]

The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by [tex] \sf{ {A}^{T}} [/tex]. Again , Interchange it's rows and columns in order to find ' A '.

[tex] \tt{A = \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix}}[/tex]

Now , LEFT HAND SIDE ( L.H.S )

[tex] \tt{ {A}^{2} - 5A+ 22I}[/tex]

Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.

⟼ [tex]\begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 & 0 \\ 0 & 1\\ \end{bmatrix}[/tex]

⟼ [tex]\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}[/tex]

⟼ [tex]\begin{bmatrix} 4 + ( - 16) & 8 + 12 \\ - 8 + ( - 12) & - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}[/tex]

⟼ [tex] \begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}[/tex]

⟼ [tex]\begin{bmatrix} - 22 & 0 \\ 0& - 22 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}[/tex]

⟼ [tex]\begin{bmatrix} - 22 + 22 & 0 + 0 \\ 0 + 0 & - 22 + 22 \\ \end{bmatrix}[/tex]

⟼ [tex]\begin{bmatrix} 0 & 0\\ 0 & 0 \\ \end{bmatrix}[/tex]

⟼ [tex] \sf{0}[/tex]

RIGHT HAND SIDE ( R.H.S ) : 0

L.H.S = R.H.S [ Hence , proved ! ]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

Step-by-step explanation:

\underline{ \underline{ \text{Given}}} :

\begin{gathered} \tt{ {A}^{T} = \begin{bmatrix} 2 & - 4 \\ 4 & 3 \\ \end{bmatrix}}\end{gathered}

\underline{ \underline { \text{To \: Find}}} :

\underline{ \underline{ \text{Solution}}} :

The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by \sf{ {A}^{T}}

. Again , Interchange it's rows and columns in order to find ' A '.

\begin{gathered} \tt{A = \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix}}\end{gathered}

Now , LEFT HAND SIDE ( L.H.S )

\tt{ {A}^{2} - 5A+ 22I}

Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.

⟼ \begin{gathered}\begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 & 0 \\ 0 & 1\\ \end{bmatrix}\end{gathered}

⟼ \begin{gathered}\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}\end{gathered}

⟼ \begin{gathered}\begin{bmatrix} 4 + ( - 16) & 8 + 12 \\ - 8 + ( - 12) & - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}\end{gathered}

⟼ \begin{gathered} \begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}\end{gathered}

⟼ \begin{gathered}\begin{bmatrix} - 22 & 0 \\ 0& - 22 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}\end{gathered}

⟼ \begin{gathered}\begin{bmatrix} - 22 + 22 & 0 + 0 \\ 0 + 0 & - 22 + 22 \\ \end{bmatrix}\end{gathered}

⟼ \begin{gathered}\begin{bmatrix} 0 & 0\\ 0 & 0 \\ \end{bmatrix}\end{gathered}

⟼ \sf{0}0

RIGHT HAND SIDE ( R.H.S ) : 0

please help it due in some time

Answers

Answer:

i think that it would be A.

Step-by-step explanation:

If the surface area of a cube is 150 cm², what is the volume of the cube?
A)
125 cm3
B)
150 cm3
C)
175 cm3
D)
225 cm3

Answers

Answer:125

Step-by-step explanation:

OMG I REALLY NEED SOME HELP! THIS IS DUE IN 3 MINUTES!

Answers

Step-by-step explanation:

8) all real numbers.

10)

[tex]y = a {b}^{x} \\ 12 \div 4 = 3 \\ b = 3 \\ a = 4 \\ y = 4 \times {3}^{x} [/tex]

You deposit $1,000 Into a bank account. The account pays 3.75% annual Interest compounded monthly. Find the balance after 6 years. Round answers to two decimal places

Answers

Is my calculations are correct the answer would be 498.125
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