What is the length of a segment in the complex plane with endpoints at 4 + 2i and 7 – 2i?

Answers

Answer 1

just subrtact and add then you will get 5i

Answer 2

Answer:

Step-by-step explanation:

A little trick: the imaginary part ([tex]i[/tex]) in the coordinates of complex numbers act same as the y-coordinate in a rectangular plane.

So we want the distance between the coordinate points (4,2) and (7,-2).

How do we get the distance between 2 points? We use the distance formula.

Distance Formula = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Where [tex](x_1,y_1)=(4,2)[/tex] and [tex](x_2,y_2)=(7,-2)[/tex]

Let's solve for distance:

[tex]\sqrt{(-2-2)^2+(7-4)^2}\\ =\sqrt{(-4)^2+(3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5[/tex]

Hence, the length of the segment in the complex plane with endpoints at 4 + 2i and 7 – 2i is 5.

Related Questions

-2(x+8)=4x+10 what is the solution set of the equation

Answers

Short answer : x = -13/3

But let's solve your equation step-by-step.

-2(x+8)=4x+10

Step 1: Simplify both sides of the equation.

(Distribute)

Step 2: Subtract 4x from both sides

Step 3: Add 16 to both sides.

Step 4: Divide both sides by -6.

Answer:

x = -13/3

Which formula contains a rational number

Answers

b and c
cuz b is has 1/2, which is a fraction that can be placed as 1:2 ratio
cuz c is 4 and can be used as 4/1, which then can be placed as 4:1 ratio

Answer:

Step-by-step explanation:

most likely b and d

Dawn is an avid reader and reads 30 pages every 8 days. Part A How many pages per day does Dawn read? Part B At this rate, Dawn takes 28 days to read her favorite novel. How many pages does the novel have?

Answers

Final answer:

Dawn reads 3.75 pages per day. At this rate, a favorite novel that she completes in 28 days contains 105 pages.

Explanation:

This is a problem of rates and proportions.

Part A: To find out how many pages Dawn reads in a day, we divide the total pages she reads in 8 days by the number of days. Going by the data, if she reads 30 pages in 8 days, then, using the proportion, Dawn reads 30/8 = 3.75 pages per day.

Part B: To find out how many pages Dawn's favorite novel has, we multiply the rate (pages/day) by the number of days. So, if she takes 28 days to read the novel at a rate of 3.75 pages per day, then by using the multiplication principle, the novel has 3.75 pages/day * 28 days = 105 pages.

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Jacki plans to pay for the down payment of a new car with her credit card. The annual interest rate for her credit card is 17%. The following expression represents the balance of the credit card, in dollars, after t years. 2,250(1.17)^t
Write an exponential expression in the form (b)c that reveals the monthly interest rate of Jacki's credit card. Round any decimals to the nearest thousandth.

Answers

Given that the annual interest rate of Jacki's credit card is 17%, then the exponential expression that reveals the monthly interest rate of Jacki's credit card is given by:

[tex]2,250\left(1+\frac{0.17}{12}\right)^{12t}=2,250(1+0.014)^{12t} \\ \\ =\bold{2,250(1.014)^{12t}}[/tex]

Answer:

[tex]A=2250(1.014)^{12t}[/tex] is the exponential expression.

Step-by-step explanation:

The expression which represents the balance of credit card, in dollars, after t years is

[tex]A=2250(1+\frac{0.17}{12})^{12t}[/tex]

Where rate of interest is 17% and amount spent is $2250.

Since 17% interest is the annual interest and we have done the expression in the form of monthly compounding.

So the expression will be

[tex]A=A_{0}[1+.014]^{12t}[/tex]

[tex]A=A_{0}(1.014)^{12t}[/tex]

[tex]A=2250(1.014)^{12t}[/tex]

José correctly answered 80% of the questions on a language arts quiz. If he answered 16 questions correctly, how many questions were on the language arts quiz?

Answers

there were 20 questions on the quiz

Jose had 20 questions on his test

Solve for x.
a(5 - x) = bx - 8

Answers

Consider the given equation:

[tex]a(5-x)=bx-8[/tex]

We have to solve the given equation for the value of 'x', we get

We will use distributive property which states [tex]a(b+c) = ab+ ac[/tex]

[tex](a \times 5)+(a \times -x) = bx-8[/tex]

[tex]5a-ax = bx -8[/tex]

Equating the like terms and the constants, we get

[tex]5a+8= ax+bx[/tex]

Taking 'x' common from the RHS of the equation.

[tex]5a+8 = x(a+b)[/tex]

[tex]x = \frac{5a+8}{a+b}[/tex]

Therefore, the value of 'x' is [tex]x = \frac{5a+8}{a+b}[/tex].

The value of 'x' in equation a(5 - x) = bx - 8 is x=5a+8/(b+a).

Consider the given equation

a(5-1)=bx-8

We have to solve the given equation for the value of 'x', we get

We will use distributive property which states

What is the statement of the distributive property?

a(b+c)=ab+ac

5a-ax=bx-8

Equating the like terms and the constants, we get

5a+8=bx+ax

Taking 'x' common from the RHS of the equation.

5a+8=x(b+a)

x=5a+8/(b+a)

Therefore, the value of 'x' is x=5a+8/(b+a).

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David's bowling score is 5 less than 3 times Aaron score the sum of the score is 215 find the score of each student

Answers

David's score is 160
Aaron's score is 55

Aarons score = x

Davids score = 3x-5

3x-5 +x = 215

4x-5 = 215

4x = 220

x = 220/4 = 55

Aarons score was 55

Davids score was 160

What is 8 ÷ 9 equal I don't get it when my couculator says 0.99999888888888888???!!!

Answers

"8 ÷ 9 = 8/9" ; (as a fraction).

Using a calculator: "8÷9 = "0.88888888888...." ; or; there may be a value such as:
__________________________________

"0.8888888888888889" ; There may be a "9" at the end; that is; the calculator may round the value at the end.
_______________________________________
I suggest recalculating the value on your calcutator.

Please sure to "clear" your calculator. Usually this can be done by pressing the [AC] button ; & then. the [C] or [CE] button.

Then, try: "8 ÷ 9" again. You should get value similar to the correct answer; such as:
______________________
"0.88888888888" ;

or: "0.8888888888888889" .
______________________
Otherwise, there is a possibility that the calculator itself is damaged or broken (e.g. got "stepped on" or "heavy objects" were placed; and the "calculator buttons"/other internal parts of the calculator were damaged and are now malfunctioning).
______________________
Hope this helps!
______________________

3. Which ordered pair is a solution of the equation y = x – 3?
(–2, 5)
(–5, 2)
(2, 5)
(5, 2)

Answers

The answer is (5,2)

5,2 is the ordered pair

Macy is making a border out of strips of wall boarder placed end to end along the 12-foot wall in her room. Each strip is foot long.

How many strips of wall border will Macy need?

Answers

3 for each wall so the totally is 12

Annette is surveying people in the city about their interest in a new shopping mall. She found that 180 people, or 37.5% of those surveyed do not want a new mall. How many people did Annette survey?

Answers

Answer:

480 people

Step-by-step explanation:

First you would divide 180 by 37.5,

180 divided by 37.5 = 4.8

Then you multiply 4.8 with 100

4.8 times 100 =480

Therefore, Annette surveyed 480 people

We want to find the total number of people that Annette surveyed given that we know a percentage and the number that the percentage represents.

We will find that the number of people that Annette survey is 480.

To get the solution:

Let's assume that she surveyed a total of X people.

Then we can write the equivalence:

100% = X

We know that the 37.5% is equivalent to 180 people, then we can write:

37.5% = 180

The two equations are:

100% = X

37.5% = 180

Now we can take the quotient between these two equations to get:

(100%/37.5%) = X/180

Solving for X we get:

(100%/37.5%)*180 = X = 480

So the total number of people surveyed is 480.

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For the perfect cup of hot cocoa, Eva uses 3 scoops of hot cocoa mix, 10 miniature marshmallows, and 8 ounces of water. What is the ratio of scoops of hot cocoa to miniature marshmallows?

Answers

3 scoops of cocoa, 10 marshmallows, 8 oz water

ratio of hot cocoa to marshmallows..
how much cocoa does she use......3 scoops
how much marshmallows does she use....10 marshmallows
so the ratio of cocoa to marshmallows is : 3/10 or 3:10 or 3 to 10 <=

The ratio of 3 scoops of hot cocoa mix to 10 miniature marshmallows and 8 ounces of water. is 3:10

What is Ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

Given :-

amount of cocoa scoops = 3

amount of miniature marshmallows used = 10

We have to find out the Ratio of scoops of hot cocoa to miniature marshmallows:

First we will simplify the term if there is any

Scoops of hot cocoa / miniature marshmallows = 3/10

Since, the simplification is already been done

Thus, the ratio will be:
3 : 10

Hence, The ratio of scoops of hot cocoa to miniature marshmallows is 3:10

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Select from the drop-down menu to correctly complete the statement about the given figures.
Triangles PQR and MNO are ( here it has a drop down menu I'll include those options below)
Similar or not similar?

Two right triangles, PQR and MNO. For triangle PQR, angle Q is thirty degrees. For triangle MNO, angle N is forty-five degrees.

Answers

Given that the two trianglea are right angles, this means that one of the angles is 90 degrees.

If one on the angles of triangle PQR is 30 degrees, then the third angle will be 60 degres.

Thus, the three angles of triangle PQR are: 90, 30, 60

If one on the angles of triangle MNO is 45 degrees, then the third angle will be 45 degres.

Thus, the three angles of triangle MNO are: 90, 45, 45

For two triangles to be similar, their angles has to equal.

Therefore, triangles PQR and MNO are not similar.

The triangles are not similar. For triangle PQR to be similar to triangle MNO, each angle would have to be congruent. The two triangles only have a 90 degree angle in common. Triangle PQR has 90, 30, and 60 degree angles while triangle MNO has 90, 45, and 45 degree angles.

A red string of holiday lights blinks once every 3 seconds,while a string of blue lights blinks every 4 seconds.how many times will both sets of light blink at the same Time in 1 minute?

Answers

The answer would be five times.

A common factor of 3 and 4 is 12.

Since there are 60 seconds in a minute, you would divide 60 by 12.

60/12=5.

Thus, your answer is 5 times.

the red light string will blink 20 times and the blue 15 60 divided by 4 is 15 & 60 divided by 3 is 20

Solve for variable c in this equation.

a(b - c) = d

A. c = ab - d / b

B. c = ab + d / a

C. c = d - ab / a

D. c = ab - d / a

Answers

Let's solve for c. Step by step.a(b−c)=dStep 1: Add -ab to both sides.ab−ac+−ab=d+−ab−ac=−ab+dStep 2: Divide both sides by -a.−ac−a=−ab+d−ac=ab−daAnswer:c=ab−d/a

(02.02 LC) Choose the equation that could be used to find three consecutive integers whose sum is 36. (5 points) n + (n + 2) + (n + 4) = 36 n + (n + 1) + (n + 3) = 36 n + (n + 1) + (n + 2) = 36 n + (n − 1) + (n − 3) = 36

Answers

n + (n + 1) + (n + 2) = 36 Let's first create the equation ourselves and then see if it fits any of the available options. We want 3 consecutive integers that add up to 36. Let's use the value "n" to represent the first number in the sequence. n Now the next number will be n+1 and the third will be n+2. And since we want the sum, we get n + n + 1 + n + 2 = ? And finally, we want the sum to be 36, so our final equation is n + n + 1 + n + 2 = 36 With this equation in mind, let's look at the available choices. n + (n + 2) + (n + 4) = 36 Well, it has the 36 OK, but it has +2 and +4 where we have +1 and +2. So it won't fit and it's wrong. n + (n + 1) + (n + 3) = 36 Closer. Got the 36 and the +1. But it has +3 instead of +2, so not a fit either. n + (n + 1) + (n + 2) = 36 This looks good. Has a couple of extra parenthesis, but they don't affect the final answer and it has the +1, +2 and the 36. This one is correct. n + (n â’ 1) + (n â’ 3) = 36 Hmm. The n - 1 has a possibility. Perhaps they want n to be the middle of the 3 numbers to add. If that's the case, then the other number should be n+1 which it isn't. Maybe they want the n to be the last number. If that's the case, then the third number should be n-2. But that doesn't work either. So this equation won't work. So of the 4 choices, the only answer that works is "n + (n + 1) + (n + 2) = 36"

Ana runs 3/4 miles in 6 minutes or 1/10 hour what is her stoped in miles per hour

Answers

3/4 divide 1/10
15/2=7.5m/hr

I would like to know how to solve 7 1/9 = 2 4/5 + m

Answers

It would be m=194/45

The answer would be 2

12 more than the quotient of a number t and 7 is v

Answers

12+(t÷7)=V is the answer

In a video game, a character needs to shine a light through two spinning wheels that have holes in them.The first wheel makes a complete rotation in 7 seconds.The second wheel makes a complete rotation in 9 seconds.The hole are lined up at 0 seconds.How many seconds will pass before they are lined up again?

Answers

63 seconds

they would have to rotate until they became equal so one would rotate 7 times and one would rotate 9 times.

What number has 2 more tens than 11?

Answers

Well I'd say it's any number before or after 11. Since it says 2 more tens it could be 31 by adding. You can also use algebra to help you.

111111111111111111111111111111111111

Answers

The red and green trails.

2.75 + 1.2 = 3.95

3.95 < 4

2.75 + 1.2 = 3.95

this is less than 4 so Red and Green

List the numbers from 50 to 60 that would make this number sentence true

Answers

85 + 54 = 139

We need to get something greater than 139, and we can solve this by doing

139 - 85 = 54

By doing that, we know everything from 55-60 is greater than 139, so your list would be 55, 56, 57, 58, 59, and 60!

85+54=139 If you do a number less than 54 that will help you. For example, 85+52=137 which is less than 139! Hope this helps! :)

Isabelle bought 12 bottles of water at $2 each

Answers

Isabelle bought 4 bottles of water.

Here's how to solve for the number of bottles of water Isabelle bought:

Let x be the number of bottles of water Isabelle bought.

The total cost of the water bottles is 2x dollars (2 dollars per bottle * x bottles).

We know the total cost was $21, so we can set up an equation:

Total cost = Cost of water bottles + Cost of pizza

21 = 2x + 13

Now, solve for x:

Subtract 13 from both sides: 21 - 13 = 2x + 13 - 13

Simplify: 8 = 2x

Divide both sides by 2: 8 / 2 = 2x / 2

Get the final answer: x = 4

Therefore, Isabelle bought 4 bottles of water.

Complete question:

Isabelle buys bottles of water at $2 each and a large pizza at $13. The total cost was $21. How many bottles of water did Isabelle buy?

find two consecutive integers whose sum is 45

Answers

22+23 are the two consecutive integers

The two consecutive integers are: 22, and 23 .
____________________________________________________
x + (x + 1) = 45 ;

in which:
"x" is the first integer (of the 2 consecutive integers) ;
"(x + 1)" is the second integer (of the 2 consecutive integers);
_______________________________________________________
We want to solve for "x";
which is the first integer (of the 2 consecutive integers);
then we can solve for the second integer (of the 2 consecutive integers);
as well;
_______________________________________________________
We have:
_______________________________________________________
x + (x + 1) = 45 ;

Rewrite as:

x + x + 1 = 45 ;

↔ 1x + 1x + 1 = 45 ;

→ 2x + 1 = 45 ;

Subtract "1" from each side of the equation;

2x + 1 −1 = 45 − 1 ;

to get:
2x = 44 ;

Divide EACH SIDE of the equation by "2" ; to isolate "x" on one side of the equation; and to solve for "x" ;
______________________________________________
2x / 2 = 44 / 2 ;

to get: x = 22 ;
______________________________________________
Our two consecutive integers:

x = 22 ;

(x + 1) = 22 + 1 = 23 .
______________________________________________
The two consecutive integers are: "22" and "23" .
______________________________________________
Let us check our answer:

Are "22" and "23" consecutive integers? Yes!

Do "22" and "23" add up to "45" ? ;

→ 22 + 23 = ? 45 ? ; Yes!
_________________________________________

Multiply. (−2/3)(5/4)

Answers

(-2/3)(5/4) = -10/12

-10/12 = -5/6 (if you want to simplify)

hope this helps

The answer is -5/6 or 10/12 not simplified

What a number that never gets 1 when you divide 2 when Evan and 3x -1 when odd

Answers

any answer choices??

Help please solving this multiplication not sure.

Answers

4 x 5 = 20 , 1 x 5 = 5.
20 chew bones and 5 dog toys.

Chew bones
if he gives 4 per month then in 5 months you would solve 4 x 5 =

Dog toy
if he gives 1 per month then in 5 months you would solve 1 x 5 =

let me know what you got for the answer

Q: A: The lowest elevation in the world is in the Dead Sea at 413 feet below sea level. The highest elevation in the world is Mount Everest at 29,035 feet above sea level. Which integer BEST represents the elevation of the Dead Sea

Answers

the answer is 413. Because it says below sea level
hope this helped!

Corys roses grow 1 inch each month. When he planted them they were 6 inches tall. What is the initial value for the scenario described?

Answers

Some equation that shows the inch growth every month after 6 inches.

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