What is the modulus of 5 - 3i

Answers

Answer 1

Hello!

The above expression exemplifies a “complex number.” A complex number takes the following form:

a + bi

In this case, A is equal to (5) while B is equal to (-3). To find the modulus of a complex number, we will need to use the following formula (let “x” represent the modulus):

x = √(a² + b²)

Insert any known values into the formula above:

x = √((5)² + (-3)²)

Simplify the right side of the equation:

x = √(25 + 9)
x = √34

We have now proven that the modulus is equal to √34.

I hope this helps!

Answer 2

Final answer:

The modulus of the complex number 5 - 3i is found using the Pythagorean theorem and comes out to be square root of 34.

Explanation:

The modulus of a complex number, such as 5 - 3i, is the distance from the origin to the point representing the complex number in the complex plane. We calculate it by using the Pythagorean theorem. The modulus of the complex number 5-3i is given by √((Re z)² + (Im z)²) = √((5)² + (-3)²) = √(25 + 9) = √34, where Re z represents the real part of the complex number, and Im z represents the imaginary part. So, the modulus of the complex number 5 - 3i is √34.

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Related Questions

the mean temperature during the winter in the arctic tundra is -34°c. you can convert degrees celsius to degrees fahrenheit by using the formula f=9/5c+32. what is the mean temperature in degrees fahrenheit?

Answers

9/5 * -34 + 32 = -29 degrees fahrenheit ( to nearest degree)

an equation of the horizontal line that passes through the point (-2,5)

Answers

y=5 it's a horizontal lines so b in y=mx+b would have to be 5 and since it's horizonal, it doesn't have a slope so it's just y=5

y = 5 is the equation of the horizontal line that passes through the point (-2,5).

Mathematically, an equation is a statement that two expressions are equal. The expressions on either hand of the equals sign are termed the left-hand side and the right-hand side of the equation. The equals sign is perused as" is equal to" or" equals".

An equation comprises variables, numbers and comparison sign.

As the ordinate of the given point is 5 then y = 5 is the horizontal line that passes through (-2,5).

Thus, the equation that passes through the point (-2,5) and is the horizontal line is y = 5.

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HELP PLEASE AND ANSWER WITH STEPS thank you so much

Answers

30) D; week 5
REASON: because 95 is greater than 75
31) h + 2c
32) the answer is 8
REASON: because the x values are 1 more than the y values
33) the answer is C
it'll make sense when you plug the x and y values in

Lisa has 1 set of 12 cars and she gives her sister 3cars. What fraction of Lisa's set did she give her sister

Answers

She gave her sister 1/4 of her set.

3/12=1/4

Hope this helps!!

She gave her 1/4 of her cars because 12/3 is 4.

determine the value of x

Answers

The sum of the interior angles of all triangles is 180 degrees. This means you can set all the angles' expressions equal to 180 and solve algebraically for x.

180 = 3x + 2x + x
180 = 6x
30 = x

Answer:
30°

Help as soon as possible!!!!

Answers

2 = 1.313 is the right answer
3 = 24 is the right answer
4 = 27 is the right answer

What they said^^^^^^^^^^^^^

the slope of the containing the point (-2,3) and (-3,1) is

Answers

The two given points are
(x1,y1) = (-2,3) and (x2,y2) = (-3,1)

Which further breaks down into these four pieces of info:
x1=-2
y1=3
x2=-3
y2=1

Plug those four values into the slope formula
m = (y2 - y1)/(x2 - x1)
m = (1 - 3)/(-3 - (-2))
m = (1 - 3)/(-3 + 2)
m = (-2)/(-1)
m = 2

------------------------------------------------------

Answer: 2

You would use the slope formula for this:
[tex] \frac{ y_{2} - y_{1}}{ x_{2} - x_{1}} [/tex]

You can put your points in and get the equation:
[tex] \frac{ 1 -3}{-3+2} [/tex]
[tex] \frac{-2}{-1} [/tex]

Or just 2 as the slope

Jenny has $25 and she earns $10 for each lawn that she mows. Jenny wants to buy a concert ticket that costs $65.
Enter the minimum number of lawns Jenny needs to mow to be able to buy the concert ticket.

Answers

Ok so subtract 25 from 65 which gives u 40 and then 40 divide by 10 equals 4

at least four times.

a number cube is rolled 24 times.how many times will a number be less than tree be expected to be rolled?

Answers

24÷6=4
it should be 4 out of 24 times

The number of the times cube is rolled for getting less than three is 8.

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability of getting less than three = 2 / 6 = 1 / 3

The number of the times cube rolled is,

Pn = ( 1 / 3 ) x 24 = 8

Therefore, the number of the times cube is rolled for getting less than three is 8.

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Question 2 Unsaved Cat is 5 less than twice Dog's age. Cat is 11 years old. Find Dog's age.

Answers

The dog is 8 years old because If you take 8 and multiply it by 2 you get 16 and then you subtract 5 and you get 11 years old or the cats age

Let the dog's age be called x.

From the given statement, the following equation can be framed

Cat's age = 2*x -5

We are given to know that Cat's age is 11 years

So, we have:

11 = 2x -5

2x = 16

x = 16/2

x = 8

Dog's age = 8 years

What is the domain of the function y= 100-x^2?

Answers

Answer:

The domain for this function is all real numbers

Step-by-step explanation:

There is no restriction for the function y=100-x^2 since it is defined as a quadratic equation, it can managed any number

If (tan^3 theta -1) / (tan theta - 1) - sec^2 theta +1 = 0, find cot theta.
a. -1 b.0 c. 1 d. sec theta

Answers

Hey there !

Check the attachment.
Hope it helps you :)

Answer:

Option A. [tex]cot\theta = -1[/tex]

Step-by-step explanation:

[tex]\frac{tan^{3}\theta -1}{tan\theta -1}-sec^{2}\theta +1=0[/tex]

we have to the value of [tex]cot\theta[/tex]

We further solve the equation

[tex]\frac{(tan\theta -1)(tan^{2}\theta +1+tan\theta )}{(tan\theta -1)}-sec^{2}\theta+1=0[/tex] [a³- b³= (a-b)(a² + b²+ ab)]

[tex]sec^{2}\theta +tan\theta -sec^{2}\theta +1=tan\theta +1=0[/tex]

[tex]\frac{1}{cot\theta }=-1[/tex]

[tex]cot\theta = -1[/tex]

Therefore Option A. [tex]cot\theta = -1[/tex] is the answer.

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
1 A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5 9 degree Celsius.
11 A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
111 A temperature increase of 5 9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I only B) II only C) III only D) I and II only

Answers

y=mx+b

where in this case

59(F−32)

59F−59(32)

You can see the slope of the graph is

59, which means that for an increase of 1 degree Fahrenheit, the increase is 59 of 1 degree Celsius.

59(F)

59(1)=59

Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of

95 degrees Fahrenheit.

59(F)

(F)=

Since

95 = 1.8, statement II is true.

The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of

59 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:

59(F)

59(59)

2581(whichis≠1)

An increase of

59 degree Fahrenheit leads to an increase of 2581, not 1 degree, Celsius, and so Statement III is not true.

The final answer is D.

Write an Inequality for the following situation

No more than 8 books are in your bag

Answers

No more means less or equal.
if number of books is x,
then
x≤8.

It says "No more than 8 books are in your bag". Here "Not more than" a specific number would be a set of all values that are "less than or equal" to given number.

So let's consider 'n' represents the number of books in the bag and we know this number can not be a negative value i.e. n is "greater than or equal" to 0.

Also n is "less than or equal" to 8 as given in the question.

Hence, the inequality would be 0 ≤ n ≤ 8.

a circle has an area of 81 3.14 units . what is the diameter in terms of 3.14a circle has an area of 81 Pi square units what is the diameter of the circle

Answers

You have posted 2 separate questions here. Please, next time, separate them with a blank line:

A circle has an area of 81 3.14 units . what is the diameter in terms of 3.14?

I'd prefer you write this as
"A circle has an area of 81 pi units . what is the diameter in terms of pi?

Area of a circle = A = pi*r^2. Note that r= diameter / 2. Here, the area is 81 pi square units, or 9^2 * pi square units, which means that the radius is 9 units. The diameter is then 2(9 units) = 18 units.

Your second question, separated from the first, is:

"a circle has an area of 81 Pi square units what is the diameter of the circle?"

Use the following formula or formulas: d = 2*r; A = pi*r^2; A = pi*(d/2)^2. Find r first, and then find d.

Answer:

18 units

Step-by-step explanation:

[tex]\pi r^2=81\pi[/tex]

Solve for [tex]r[/tex]:

[tex]\pi r^2=81\pi \\r^2=81\\r=9[/tex]

Knowing diameter is 2*r, we can apply the formula to find diameter

[tex]d=2*r\\d=2*9\\d=18[/tex]

Marie draws a marble out of a bag. It is either red or green. She records the color and then puts the marble back in the bag.

She repeats this process 80 times to get the following results:

Red:30

Green : 50

Because Marie knows that there are 5 marbles in the bag she knows that the probability of choosing a red marble must be either 1/5,2/5,3/5,4/5, or 5/5. Based on her data which of these models is most probable?

*THIS QUESTION IS WORTH 30 POINTS*

Answers

2/5. 30/80 is .375 , and 2/5 is .4, so 2/5 is the closest approximation to her data.

Answer:

2/5 thx for the points

Step-by-step explanation:

the sum of four times a number and 17 is 33. Find the number, please? I really need help!!

Answers

first, you need to write out the problem. the sum (which is adding) of 4 times a number ( which we will call n) and 17 is 33. you would write it like this:

(4 x n) + 17 = 33

First, find out what 33 - 17 is. (it's 16)
4 times 4 is 16
(4 x 4) + 17 = 33
16 + 17 = 33

Jake has a teepee that is cone shaped it has a height of 9 feet and a diameter of 8 feet find the volume of the teepee in terms of Pi.

Answers

The formula is:
V = π(r^2)h/3
Since this problem gives you the diameter and not the radius, I would take half of the diameter because a radius is half of a diameter.
The half of 8 is 4, so the radius is 4
V = π(4^2)(9/3)
V = π(4^2)(3)
V = π(16)(3)
V is about 150.8

A cylinder shaped drum is used to store used motor oil. The drum has a height of 3 ft and a radius of 1.5 ft

Answers

V = 21.21
[tex]V = \pi r^{2} h[/tex]
V = volume
r = radius
h = height

The base of a triangular prism is an isosceles right triangle with a hypotenuse of
√50 centimeters. The height of the prism is 8 centimeters. Find the surface area of the triangular prism. Round your answer to the nearest tenth.

Answers

Are sure that is right

SA= Lateral Area + Area (of base)

Lateral area = perimeter of base x height

An isosceles triangle has two congruent base segments. The hypotenuse of an isosceles right triangle is (length of base segment) x (the square root of 2). I did the math for you (shown above) to get 5 as a base.

So 5 + 5 + square root of 50 is your perimeter

Multiply the perimeter times your height (8) and you get the lateral area.

Add your lateral area to the base area (triangle = 1/2 bh)

LA = 136.568...
Area of Triangle base = 12.5

Surface area = 149.068... square cm

albert makes $10/Hr. at his job this week he also recieves a small cash bonus of $40 due to a company incentive program. let X represent the number of hours albert worked

Answers

If he makes 10 hours, then x will represent hours, and there is a $40 bonus:
10x + 40

50 PIONTS AND BRANLIEST
Which of the following statements is not true?

|-5.5| > |5.4|
0.9 > -7.2
-9.4 < -6.4
|-2.3| < 0

Answers

The answer to this question is |-2.3| < 0. This is because |-2.3| = 2.3, and 2.3 is not less than 0.

The last as the absolute value of -2.3 is 2.3 which is greater than 0

Samantha measured two of the angles in PQR and found that they had measures of 65° and 70°. Then, she measured two of the angles in XYZ and found that they had measures of 65° and 45°. What statement best describes the two triangles?

Answers

The two triangles are similar.

The angles of a triangle sum to 180°. Using the known angles in the first triangle, we find the missing angle measure:
180-(65+70) = 180-135 = 45

We do the same for the second triangle:
180-(65+45) = 180 - 110 = 70

Any two triangles that have all 3 angles congruent is similar by AAA.

Answer:

D: The two triangles may be congruent, but additional information is needed about the sides of each triangle.

Step-by-step explanation:

Got in right on Edge

factorise 36n(squared) divide by 25 minus 1

Answers

Answer:

[tex]( \frac{36n^{2} }{25} - 1) [/tex] factors to become [tex]( \frac{6}{5}n - 1)( \frac{6}{5}n + 1) [/tex]

Explanation:
The binomial [tex]( \frac{36n^{2} }{25} - 1) [/tex] is what is called a difference of two squares which can be identified by the equation being in the form (a² - b²) where both terms can be square-rooted.

Because the equation is a difference of two squares, its factors will be in the form: (a - b)(a + b).

With a² = [tex]\frac{36n^2}{25}[/tex] and b² = 1, we can find the square root of both and plug them into the above factor form.

√(36n² / 25) = 6n/5
√1 = 1

So the factors are [tex](\frac{6}{5}n -1)(\frac{6}{5}n +1)[/tex]

if f(x)=8x+6, what is f(-1)

Answers

If I remember correctly this is how you solve it.

f(x)=8x+6
f(-1)=8(-1)+6
f(-1)=-8+6
f(-1)= -2

f(x) = 8x + 6

To find f(-1), substitute x = -1 :

f(-1) = 8(-1) + 6 = -8 + 6 = -2

Answer: f(-1) = -2

Given: a = 640, A = 70°, B = 52° in triangle ABC ; find b. Round answers to the nearest whole number

Answers

Answer: 537

Step-by-step explanation:

Given: a = 640 A =70° B =52°

Whenever two angles and one side of a triangle is given, we can always use the sine formular to find the other side

Using the sine formula;

sin A / a = sin B /b

sin70° / 640 = sin 52° / b

cross multiply

bsin70° = 640sin52°

To get b, we divide bothside by

sin 70°

b = 640sin52° / sin 70°

b = 504. 327 / sin70°

b = 536. 693

b = 537 to the nearest whole number

PLEASE HELP! @) POINTS
Describe the relationship between the probability of an event and its complement. If the probability of an event is 0.3, what is the probability of its complement?

Answers

= 1 - 0.3
= 0.7

Ratio is 0.3 to 0.7 or 3 to 7

1. The probability P of an event and its complement P' are mutually exclusive and add up to 1

2. If the probability of an event is 0.3, then the probability of its complement is 0.7. (1 - 0.3 = 0.7)

To estimate the percentage of all their customers that would buy a new flavor, an ice cream shop surveys the first five customers that place an order. Will this likely give an accurate estimate of this percentage? Select from the drop-down menus to correctly complete the statement:
This method is (blank) to give an accurate estimate of the percentage since it (blank) from a large enough randomly selected sample of customers.

The options for the first blank are:
A. Likely
B. Not likely

The options for the second blank are:
A. Used data
B. Did not use data

PLZ HELP!!!!!

Answers

1 blank) Not likely.

2 blank) Not used data.

Good luck!

- Jazz

1st blank : Not likely.

2nd blank : Did not use data.

Hope I'm correct :)

Give me 5 stars if so!

Hector has a $5 off coupon at Brenda's Bagels. Bagels cost $8.99 per dozen. Write an equation that models the total amount of money (y) Hector owes if he buys (x) dozen bagels.

Answers

The equation is y = 8.99x - 5

PLEASE HELP..... I WILL GIVE BRAINLIEST!!

Answers

For the first part:

Every shirt she grabs, will cost her dollars, so if she grabs 3 shirts, then the cost of the shirts is:

[tex]12+12+12=3(12)[/tex]

With the same rationale, if she grabs 2 pairs of jeans, the cost of the jeans is:

[tex]19+19=2(19)[/tex]

So, her total is:

[tex]3(12)+2(19)[/tex]

If you subtract 3 from the total, then the expression is:

[tex]3(12)+2(19)-3=36+38-3=71[/tex]

For the second part:

If she's paying 3 less for each shirt, then the cost of 3 shirts will become:

[tex](12-3)+(12-3)+(12-3)=3(12-3)[/tex]

In the same fashion, for the two jeans:

[tex](19-3)+(19-3)=2(19-3)[/tex]

So the expression for the total cost is:

[tex]3(12-3)+2(19-3)=36-9+38-6=59[/tex]

For number three:

The amounts are different because the cost of the total purchase is different than the cost of each element that makes up the total purchase.

For number four:

If you're the owner, you want to give the smallest amount of discount (the one in part 1/a).

So you could clarify by saying there's 3 dollars of the TOTAL purchase's cost.

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