Write a complex number that lies above the real axis and to the right of the imaginary axis. Then write a complex number that lies below the real axis and to the left of the imaginary axis.

Answers

Answer 1

Answer:

Z = 5 + 3i and Z = -8 - 2i

Step-by-step explanation:

* Lets study the drawing of the complex numbers

- The x-axis is the real axis

- The y-axis is the imaginary axis

* Look to the attached figure

- Any point in the first quadrant is above the real axis and right

 to the imaginary axis (Z4)

# Z = x + yi

- Any point in the second quadrant is above the real axis and left

 to the imaginary axis (Z2)

# Z = -x + yi

- Any point in the third quadrant is below the real axis and left

 to the imaginary axis (Z3)

# Z = -x - yi

- Any point in the fourth quadrant is below the real axis and right

 to the imaginary axis (Z1)

# Z = x - yi

* Now lets solve the problem

- The point above the real axis and right to the imaginary axis lies

 in the first quadrant

∴ The real part is positive and the imaginary part is positive

∴ Z = 5 + 3i

- The point below the real axis and left to the imaginary axis lies

 in the third quadrant

∴ The real part is negative and the imaginary part is negative

∴ Z = -8 - 2i

Write A Complex Number That Lies Above The Real Axis And To The Right Of The Imaginary Axis. Then Write
Answer 2
Final answer:

A complex number that lies above the real axis and to the right of the imaginary axis could be '2 + 3i', while a complex number that lies below the real axis and to the left of the imaginary axis could be '-2 - 3i'. The direction in the coordinate system (upward or rightward is positive, downward or leftward is negative) determines the signs of real and imaginary components.

Explanation:

In the complex plane, a complex number is considered to lie above the real axis if its imaginary part is positive, and to the right of the imaginary axis if its real part is positive. Hence, an example of a complex number that lies above the real axis and to the right of the imaginary axis is 2 + 3i, where 2 is the real part and 3i is the imaginary part.

Conversely, a complex number lies below the real axis if its imaginary part is negative, and to the left of the imaginary axis if its real part is negative. So, an example of such a number could be -2 - 3i, where -2 is the real part and -3i is the imaginary part.

Remember, in the coordinate system used to plot complex numbers, motion upward or to the right is usually considered positive, while motion downward or to the left is considered negative.

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Related Questions

find the percent 133% of 140

Answers

The answer would be 186.2.

Answer:

The correct answer is  133% of 140  = 186.2

Step-by-step explanation:

Points to remember

X % of Y is given by

(X/100)*Y

To find 133 % of 140

We have to find 133 % of 140,

According to the formula we can write,

133% of 140 = (133/100) * 140

 = 1.33 * 140

 = 186.2

133% of 140 = 186.2

Therefore the correct answer is  133% of 140  = 186.2

Can someone please help me

Answers

Answer:

L.A. = 384 cm²S.A. = 640 cm²

Step-by-step explanation:

Lateral Area:

We have four congruent triangles with base b = 16cm and height h = 12cm.

The formula of an area of a traingle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_\triangle=\dfrac{(16)(12)}{2}=(8)(12)=96\ cm^2[/tex]

[tex]L.A.=4A_\triangle=4(96)=384\ cm^2[/tex]

Surface Area:

[tex]S.A.=B+L.A.[/tex]

In the base we have the square with side s = 16cm. The formula of an area of a square:

[tex]A_\square=s^2[/tex]

Substitute:

[tex]B=16^2=256\ cm^2[/tex]

[tex]S.A.=256\ cm^2+384\ cm^2=640\ cm^2[/tex]

How do you write the mixed number 3 2/4 shown as a fraction greater than one

Answers

Answer: 14/4

Step-by-step explanation:

since 4/4 is one three would be 12/4. Adding 2/4 to 12/4 is 14/4. So the answer is 14/4

3 2/4 as a mixed number is 14/4

3 multiplied by 4 is 12 and you just add 2 to that and it'll be 14/4

You travel between these two mile markers and then find your average speed in miles per hour. Select the three equations that represent this situation.

2.5 hours = 150/speed

speed=150/2.5 hours

150 miles=2.5 hours times speed

speed/150 miles = 2.5 hours

Answers

Answer:

The second one

Step-by-step explanation:

Subtract 190 minus 40 to find the miles traveled: 190-40=150

Now divide the miles by the time: 150/2.5

what is the answer to the equation Nora ran 5 miles last week. She ran 7 miles this week.
During the same two weeks, Beth ran three times as many miles as Nora.

Answers

Answer:

Week 1:  15

Week 2: 21

Step-by-step explanation:

5 x 3 = 15

7 x 3= 21

What is the median?

637743

Answers

Answer:

5

Step-by-step explanation:

Put the numbers in order then find the middle number. 334677

Here there are two middle numbers, 4, and 6. Add 4 and 6 together, 10 then divide by 2, 5. So the median is 5! Hope this was helpful have a Great day!!!

Which is the endpoint of a Ray?

Answers

A geometric ray has one endpoint and extends from the endpoint to infinity in one direction on a line. Rays are written with a right-facing arrow over two capital letters. The first letter represents the endpoint, and the second letter represents another point on the ray.

hope this helps :)

Answer:

Step-by-step explanation:

Point r

8x + 2(x − 7) = 7x + 3x − 14

Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)

Part B: Name one property you used to solve this equation. (4 points)

Answers

hope it helps you!!!!!!!!!!!!!!

Start with

[tex]8x+2(x-7)=7x+3x-14[/tex]

Apply the distributive property to expand the left hand side:

[tex]8x+2x-14=7x+3x-14[/tex]

Sum like terms:

[tex]10x-14=10x-14[/tex]

Apply the additive property of equality to add 14 to both sides:

[tex]10x=10x[/tex]

Apply the additive property of equality to subtract 10x to both sides:

[tex]0=0[/tex]

This means that the equation was actually an identity, i.e. the left and right hand sides were actually the same expression.

Since they are the same expression, it doesn't matter which values you plug into x, it will always be a solution of this equation.

Solution: infinite. All numbers are solutions of this equation.

Property used: Listed while solving the equation.

I NEED HELP ASAPPPPPPPPPPPP

Answers

Answer:

c.

Step-by-step explanation:

The answer to your question is C

The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between x(height) and y(arm span) is shown in the scatterplot below. The equation of the line of best fit modeling this relationship is given.
Y=4.5x + 0.977x

Mike is 175cm tall and George is 170cm tall.
Using the model, how many centimeters longer would we expect Mike's arm span to be than George's?

____Cm

Answers

Final answer:

Given the line of best fit equation Y = 4.5X + 0.977, we would expect Mike's arm span to be approximately 23 cm longer than George's, assuming their respective heights are 175cm and 170cm.

Explanation:

The given equation appears to have a typo, as it seems to contain two x terms, which is unusual for a line of best fit in this context. I believe it should be Y = aX + b, where 'a' represents the slope and 'b' the y-intercept.

Assuming the correct equation is Y = 4.5X + 0.977, we can calculate Mike's and George's arm spans by plugging in their respective heights (in cm) for X:

Mike's arm span = 4.5*175 + 0.977= 788.977 cmGeorge's arm span = 4.5*170 + 0.977 = 765.977 cm

So, we would expect Mike's arm span to be longer than George's by about:

788.977 cm - 765.977 cm = 23 cm

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Which table represents a function

Answers

Answer:

The third one, also I see you with boogie wit da hoodie, Hoodie SZN is a really good album.

Step-by-step explanation:

A number divided by three less two is at most two

Answers

Answer:

Negative infinity,12

Hope this helps you out!

Yes is going to be negative

The probability of winning a game is 75%. How many times should you expect to win if you play 60 times?

Answers

Answer:

[tex]45\ games[/tex]

Step-by-step explanation:

we know that

If the probability of winning a game is 75%

that means-----> of every 100 games wins 75

Using proportion

[tex]\frac{100}{75}=\frac{60}{x} \\ \\ x=75*60/100\\ \\x=45\ games[/tex]

Evaluate 1 + (-2/3) - (-m) where m = 9/2

Answers

Answer:

4 5/6

Step-by-step explanation:

m = 9/2

1 + ( - 2/3) - (- m)

= 1 + (-2/3) - ( - 9/2)

= 1 - 2/3 + 9/2

= 1/3 + 9/2

= 29/6

= 4 5/6

Answer:

4 5/6

Step-by-step explanation:

Which of the following is a reasonable estimate for the weight capacity of an elevator that can carry up to 15 people?
A.
3 × 103 lb
B.
3 × 102 lb
C.
3 × 10-3 lb
D.
3 × 10-2 lb

Answers

A is the most common

are they supposed to look like 1x10^-20 lb?? that would make it easier for you to determine the answer

i hope this helps

Which expression is equivalent to...? Screenshots attached. Please help! Thank you.

Answers

Answer:

[tex]4x^{3} y^{2} (\sqrt[3]{4 x y})[/tex]

Step-by-step explanation:

Another complex expression, let's simplify it step by step...

We'll start by re-writing 256 as 4^4

[tex]\sqrt[3]{256 x^{10} y^{7} } = \sqrt[3]{4^{4} x^{10} y^{7} }[/tex]

Then we'll extract the 4 from the cubic root.  We will then subtract 3 from the exponent (4) to get to a simple 4 inside, and a 4 outside.

[tex]\sqrt[3]{4^{4} x^{10} y^{7} } = 4 \sqrt[3]{4 x^{10} y^{7} }[/tex]

Now, we have x^10, so if we divide the exponent by the root factor, we get 10/3 = 3 1/3, which means we will extract x^9 that will become x^3 outside and x will remain inside.

[tex]4 \sqrt[3]{4 x^{10} y^{7} } = 4x^{3} \sqrt[3]{4 x y^{7} }[/tex]

For the y's we have y^7 inside the cubic root, that means the true exponent is y^(7/3)... so we can extract y^2 and 1 y will remain inside.

[tex]4x^{3} \sqrt[3]{4 x y^{7} } = 4x^{3} y^{2} \sqrt[3]{4 x y}[/tex]

The answer is then:

[tex]4x^{3} y^{2} \sqrt[3]{4 x y} = 4x^{3} y^{2} (\sqrt[3]{4 x y})[/tex]

Need help with algebra 2!

Answers

Answer:

[tex]x=38.56[/tex]

Step-by-step explanation:

First, we'll solve for the missing angle.

The interior angles of a triangle add up to 180, so let's make an equation.

[tex]35+90+x=180 \\ \\ 125+x=180 \\ \\ x=55[/tex]

Now we can use the law of sines.

[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]

Where the lowercases are the side lengths and the uppercases are the angle measures.

Plug in the values we know.

[tex]\frac{27}{sin(35)}=\frac{x}{sin(55)}[/tex]

Solve using a calculator.

[tex]x=38.55999618 \\ \\ x=38.56[/tex]

A variable is four less than six times another variable. Express it as a function rule

Answers

Answer:    6x-4

Step-by-step explanation:  The number 6 is multiplied by another variable so it would be written as 6x and then 4 is less than whatever 6x is so it would be 6x-4.

Help on #9 I don't get it!

Answers

Your trying to rearrange the equation with v were the r was.

2( v - h ) / k = r

2( v - h ) k / k = rk

2( v - h ) = rk

2( v - h ) / 2 = rk / 2

v - h = rk / 2

v - h + h = rk / 2 + h

v = rk / 2 + h

marias lemonade recipe calls for 2 cups of lemon juice and 8 cups of water however she would like to make lemonade with a stronger lemon flavor which change to the recipe would produce the strongest lemon flavor?​

Answers

Answer:

maybe 2 and a half cups of lemon juice and 7 cups of water

Step-by-step explanation:

hopes this helps :) oof

PLEASE ANSWER THIS IS URGENT!!!!!!

Answers

Answer:

80 pages

Step-by-step explanation:

First, work out how many minutes are in two hours.

2 hours = 120 minutes.

Multiply 2/3 by 120

2/3 × 120 = 240/3

Simplify the the fraction

240/3 = 80/1 = 80.

Answer:

Step-by-step explanation:

page read in 1 minute =2/3 40 pgs

page read in 2 hours=(1 hrs = 60 min) 2hrs =120 min

2/3 *120 = 80 pgs

What are the amounts of a and b

Answers

ANSWER

a=1

b=-12

EXPLANATION

The function has a hole at

x=3

The function also have a vertical asymptote at

x=-4.

This implies that, the denominator of the function is

[tex](x - 3)(x + 4) [/tex]

[tex] {x}^{2} + 4x - 3x - 12[/tex]

[tex]{x}^{2} + x - 12[/tex]

Comparing this to the function in the denominator,

[tex] {x}^{2} + ax + b[/tex]

we have

a=1 and b=-12

give two equivalent fractions for 6/8​

Answers

Step-by-step explanation:

[tex]\dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}\\\\\dfrac{6}{8}=\dfrac{6\cdot2}{8\cdot2}=\dfrac{12}{16}\\\\\dfrac{6}{8}=\dfrac{6\cdot3}{8\cdot3}=\dfrac{18}{24}\\\\\dfrac{6}{8}=\dfrac{6\cdot4}{8\cdot4}=\dfrac{24}{32}\\\\\dfrac{6}{8}=\dfrac{6\cdot5}{8\cdot5}=\dfrac{30}{40}\\\vdots[/tex]

A rectangular prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3 unit

Answers

Answer:

The volume of each cube  = (side)^3  = (1/3)^3  = 1/27 cubic units

The number of cubes  that will fill the prism  =

Vol of prism            4

__________  =    _____  =    4 * 27   =   108 cubes

Vol of cube            (1/27)

Step-by-step explanation:

Final answer:

Approximately 108 cubes, each with side lengths of 1/3 unit, can fit into a rectangular prism that has a volume of 4 cubic units.

Explanation:

The subject of this question covers volume and dimension within 3D Geometry, particularly recognizing cubic units as a measure of volume. Given a rectangular prism with a volume of 4 cubic units, which is filled with cubes, each with side lengths of 1/3 unit, the idea is to understand how many smaller cubes would fit into the larger prism.

When calculating, we first need to figure out the volume of one small cube: (1/3)^3 = 1/27 cubic units. Then, you would divide the total volume of the rectangular prism by the volume of one of the small cubes: 4 divided by 1/27. This gives approximately 108, meaning around 108 cubes with a side length of 1/3 can fit into a rectangular prism with a volume of 4 cubic units.

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he variable y is directly proportional to the variable x . If y = 10 when x = 6, what is the value of y when x = 15?
A) 20.5
B) 25
C) 30
D) 35
i need help asap

Answers

Answer:

B. 25

Step-by-step explanation:

10+6=16

if it is proportional, then it would be 25 to get 15.

Answer:

25

Step-by-step explanation:

y = kx

10 = 6k

5

3

= k

y =

5

3

(15)

y = 25

Jeff made $243.75 last week. If he worked 25 hours, how much is he paid for one hour of work?

Answers

12.50 is what he got paid each hour

Answer:

$9.75 per hour

Step-by-step explanation:

243.75/25= 9.75

Solve 9(8 - x) = 3x.

Answers

Hello - let's do this step by step. Show your work.

You're asking: 9(8−x)=3x.

Now, simplify both sides of the equation.

9(8−x)=3x

(9)(8)+(9)(−x)=3x (To do that, distribute)

72+−9x=3x

−9x+72=3x

Now,  subtract 3x from both sides.

−9x+72−3x=3x−3x

Simplify,

−12x+72=0

After, subtract 72 from both sides.

−12x+72−72=0−72

−12x=−72

Last thing, divide both sides by -12.

-12x/12 = -72/-12

Divide.

Therefore, you have x = 6 as your final answer.

Hello there!

9(8-x)=3x

Use the Distributive Property to distribute 9:

72-9x=3x

Move all the variables to the left side. Be sure to use the opposite operation!

-9x-3x=-72

-12x=-72

Divide both sides by 12 in order to isolate x:

         x=6

Hope this helps you!

~Just a joyful teen

[tex]SilentNature[/tex]

`Judith is 5 years younger than Trina and 5 years older than Gretchen. The average of their ages is 23. How old is each Woman?

Answers

Answer:

Gretchen: 18

Judith: 23

Trina: 28

Step-by-step explanation:

Do reverse math. to find the average you would normally add up each age and divide your answer by the amount of ages provided. but in this case we don't have enough information so you do it opposite.

23x3=69.

Trina is clearly the oldest and Gretchen is the youngest, leaving Judith in the middle.

Gretchen: 18

Judith: 23

Trina: 28

it takes some experimenting with numbers but this is correct because all three numbers add up to 69 and they are each 5 years apart.

                                                            :)

Line L and M are parallel find m<4

Answers

m<4 means the measure of angle 4, in degrees.

since the two lines are parallel, angles that are diagonal from each other are equal (like 2 and 4). One of the angles that are diagonal from angle 4 is 38°, so angle 4 is also 38°.

Answer: 38°

Answer:

your answer should be 38 degrees.

margie as 5 times as many nickels as quarters. she has a total of $2.00 how many does she have of each coin? ​

Answers

Answer:

4 quarters and 20 nickels

Step-by-step explanation:

4 quarters= 1.00

4x5=20 nickels =1

1+1=2.00

Final answer:

Margie has 4 quarters and 20 nickels, which amounts to $2.00. The solution was found by setting up and solving a system of equations.

Explanation:

The question involves solving a system of equations to find out how many nickels and quarters Margie has if she has 5 times as many nickels as quarters and the total value is $2.00. Let's define two variables: n for the number of nickels and q for the number of quarters. Now, we have two equations based on the information provided:

5n = q (Margie has 5 times as many nickels as quarters)0.05n + 0.25q = 2.00 (The total value of nickels and quarters is $2)

Substitute the first equation into the second: 0.05(5q) + 0.25q = 2.00, which simplifies to 0.25q + 0.25q = 2.00, meaning that 0.50q = 2.00. Divide both sides by 0.50 to find that q = 4. Since q = 4, we substitute it back into the first equation to find that 5n = q gives us n = 4/5, which results in n = 20. Therefore, Margie has 4 quarters and 20 nickels.

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