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

The lines shown below are perpendicular. If the green line has a slope of
2/5 , what is the slope of the red line?

Answers

Answer:

-5/2

Step-by-step explanation:

for perpendicularity;

[tex]m1 = \frac{ - 1}{m2} [/tex]

where m1 is first slope

and m2 is second slope

so here, let m1 be green line slope

and m2 be red line slope

thus,

[tex]m2 = \frac{ - 1}{m1} [/tex]

[tex]m2 = \frac{ - 1}{ \frac{2}{5} } = - 1 \div \frac{2}{5} [/tex]

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

The function g is defined by g(x)= 3x2 - 3.
Find g(3z).

Answers

=3(3z)2-3
=3(9z2)-3
=27z^2-3
=3(9z^2-1)
=3(3z+1)(3z-1)

y = x3 + x2 − 4x − 16

Answers

Answer:

use photo math

Step-by-step explanation:

Answer:

Step-by-step explanation:

 

 DIFFERENTIATE W.R.T. X

3x 2  +2x−4

 

EVALUATE

x  3  +x  2  −4x−16

 

 

 

 

 

 

EVALUATE

x  

3

+x  

2

−4x−16

The ratio of students with brown eyes in Michelle’s class to all of the students in her class is 20:25. What is another way to write this ratio?

Answers

Answer:

3/4, 5/6, 8/10 this is in fraction form though. just change it to 3:4

Suppose the true proportion of high school students who walk to school in New York City is 0.82. If many random samples of 400 high school students are taken, by how much would their sample proportions typically vary from the true proportion?
a. 0
b. 0.001
c. 0.019
d. 0.148
e. 7.684

Answers

Answer:

i think it will be C

Step-by-step explanation:

with the variability formula = squareroot p(1-p)/n which gives you 0.0192

The captain of the cheerleading team, Alicia, counted that they washed 58 cars. Determine if this is a reasonable number of cars that could've been washed.

Answers

Answer:

yes but no

Step-by-step explanation:

um well that is a lot by not if there is a bunch of people doing it.

4.1 graphing linear equations worksheet

Answers

The answer of this worksheet is 32

Mr. Gonzalez is designing a planter box shaped like a rectangular prism. The width of the box is 6 feet, and the length is 4 feet. Find the height of the box if the volume is 150 cubic feet.

Answers

Answer: 6.25

Step-by-step explanation:

6•4•(6.25)= 150

The best equation to graph from is the point slope form of a line. True or false?

Answers

Answer:

i say yes

Step-by-step explanation:

this is because it will give you the point to start with and the slope so you will already have all the information to graph

Please help! Giving brainliest to best answer! 20 points

Answers

Answer:

The answers are 15,25,35 and 45

Step-by-step explanation:

The graph is only something to waste your time,use the equation to find the answers for each part

TOTAL AMOUNT (t) can be calculated by subtracting 10 from the ORIGINAL PRICE (p).

That is the equation t=p-10

Select the expression equivalent to (8.4x + 2.9) + (–3.7x + 5).

Answers

Answer:

4.7x + 7.9

Step-by-step explanation:

trust

please help solve 2d + 7 =9

Answers

Answer:

D=1 or just 1, i dont get  what the question is

Step-by-step explanation:

Answer:

d=1

Step-by-step explanation:

Move 7 to the other side by subtracting 7 on both sides:

2d+7-7=9-7

The equation now looks like this:

2d=2

Divide 2 on both sides:

2d/2=2/2

The equation now looks like this:

d=1 which is the answer

The Lowest common multiple of 2 numbers is 126
what are the 2 numbers

Answers

Answer:

Step-by-step explanation:

The least common multiple of 126 and 131 is

16,506

Which of the following ordered pairs
make this equation true?
y = 3x + 2
B. (8,2)
A. (2, 2)
C, (3, 11)
D. (5, 1)

Answers

8=3(2)+2
8=6+2
8=8
B) (8,2)

Answer:

c

Step-by-step explanation:

plug in

y=3x+2

11 = 3(3) + 2

11=11

Assume that three fifths of the population has long hair and and one tenth of the poulation has blue eyes. What is the probability that a person does not have long but does have blue eyes?

Answers

Answer:

1/25

Step-by-step explanation:

If 3/5 have long hair, then 2/5 do not have long hair

So, the probability of no long hair, has blue eyes = 2/5(1/10) = 1/25

What is the anwser to: h + 5.7 = −5.7

Answers

answer:
-11.4

explanation:
h + 5.7 = -5.7
subtract 5.7 from both sides

h = -11.4

Answer:

h=-11.4

Step-by-step explanation:

because, 5.7+-5.7=-11.4

Heather drove at a constant rate. She traveled 162 miles in 3 hours. How far did Heather travel in 1 hour?

Answers

Answer:

54 miles

Step-by-step explanation:

I think it's right I did 162÷3=54 I hope it helps :D

How much must be added to each of the three number 1, 11, and 23 so that together they form a geometric progression?

Answers

Answer:

49

Step-by-step explanation:

Let the three numbers be a1, a2, a3

Let the number to be added to form a geometric progression = x

a1 = 1 + x ; a2 = 11 + x ; a3 = 23 + x

For a geometric progression :

a2 = a1 * r

a2 = (1+x)r

11+x = (1+x)r - - (1)

r = (11+x) / (1+x) ---(1)

a3 = a2 * r

a3 = (11+x)r

23+x = (11+x)r - - -

r = (23+x) / (11+x) - - (2)

Equate (1) and (2)

(11+x) / (1+x) = (23+x) / (11+x)

(11+x) * (11+x) = (23+x) * (1+x)

121 + 22x + x² = 23 + 24x + x²

121 + 22x + x² - x² - 24x - 23 = 0

98 - 2x = 0

-2x = - 98

x = 98 / 2

x = 49

18) Which of the following situations can be represented by a
proportional relationship?
A. David has $100 in his savings account and adds $5
per week.
B. The initial fee for a website is $60 and $44 per month
to maintain the website.
C. The cost to rent a beach house is a $200 deposit and
$400 per night.
D. Linda earned $8.00 per hour at her summer job.

Answers

D. Linda earned $8.00 per hour at her summer job.

Let us factorise the following alg
x4/16-y4/81

Answers

Step-by-step explanation:

this way we get value of x and y

hope it helps ☺️☺️

if u like give thanks

Factorise the following:
a) x + 3x - 4
b) x - 2x - 3
c) x + 2x - 8

Answers

Are they supposed to be quadratic equations? Is it x^2 +3x -4 etc?

Select the car that gets the best gas mileage per
gallon of gas.

A. Car A can travel 19 miles using 0.7 gallons of gas.

B. Car B can travel 21 miles using 0.6 gallons of gas.

C. Car C can travel 15 miles using 0.4 gallons of gas.

D. Car D can travel 35 miles using 1 gallon of gas.

Answers

The answer is c because it’s talking less gas
The answer is C it travels 3.75 miles per 0.1 gallons

Please help!! 10-15 much appreciated! :)

Answers

Answer:

Step-by-step explanation:  sin β = [tex]\frac{oposite }{hypotenuse}[/tex] ; cos β = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

10) sin [tex]32^{0}[/tex] = [tex]\frac{x}{18}[/tex]

18 sin [tex]32^{0}[/tex] = x

18 (0.53) = x

x= 9.5 units

cos [tex]32^{0}[/tex] = [tex]\frac{y}{18}[/tex]

18 cos [tex]32^{0}[/tex] = y

y = 18 (0.85)

y = 15.3 units

You use the same strategy for the rest of the questions. Feel free to reach out if you have more questions.

Which of the following sets of measures
cannot be the lengths of the sides of a right
triangle?
A
5 cm, 12 cm, and 13 cm
B
9 cm, 12 cm, and 17 cm
C
1 cm, 2.4 cm, and 2.6 cm
D
2.5 cm, 6 cm, and 6.5 cm​

Answers

you can use the formula of pythagoras theorem to know what of them is wrong

in the first case

-5^2 + 12^2 =169

 13^2=169         ( it's a right equation so it can be lengths of right angle tri )

in the second case

_9^2 + 12^2 =225

  17^2 not equal 225

so these are the lengths that can't be a right angle triangle

If two supplementary angles are 3 x space plus space 7 and 2 x minus 1, what is the value for x?
Write your answer as a decimal.

Answers

Answer:

3x + 7 + 2x -1

Step-by-step explanation:

(3x+2x)+(7-1)

5x + 6

6 / 5

x=1.2 or 2/10

Here is a system of equations.
y=3x-1
y=-x-5
Graph the system. Then write its solution. Note that you can also answer "No sol
B
G H

Answers

let me know if you want to know the algebraic way to solve without the graph!! i’d be more than happy to help!

Micaela spent $32 on writing utensils pens cost four dollars and pencils cost two dollars if she bought a total of 10 and how many of each kind did she buy

Answers

Answer:

6 pens and 4 pencils

Step-by-step explanation:

6 x 4 = 24

4 x 2 = 8

24 + 8 = 32

8.35 < 3x +18.75
Pls help

Answers

Step-by-step explanation:

8.35 < 3x + 18.75

3x + 18.75 > 8.35

3x > 8.35 - 18.75

3x > -10.4

x > -3.47

Find the slope of the line that passes through the given points.(2, 1) and (7,10)

Answers

Answer:

1.8

Step-by-step explanation:

Slope: 1.8

Equation of the line: y=1.8x-2.6

9 + 15 using the distributive property to factor out the greatest common factor

Answers

Answer:

    24

Step-by-step explanation:

9 can be broken down to 3 because 3 x 3 = 9

15 can be broken down to 3 also because 3 x 5 = 15

> 9 + 15

= 3 ( 3 ) + 3 ( 5 )

= 3 ( 3 + 5 )

= 3 ( 8 )

= 24

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