What is the quotient of the complex number 4-3i divided by its conjugate ?

Answers

Answer 1

Answer:

Quotient is[tex]\frac{7-24i}{25}[/tex]

Step-by-step explanation:

Given is a complex number as 4-3i

We have to find the quotient when divided by its conjugate

Its conjugate is

[tex]4+3i[/tex]

When divided we have

[tex]\frac{4-3i}{4+3i} =\frac{4-3i}{4+3i} \frac{4-3i}{4-3i}[/tex]

(to simplify the above)

=[tex]\frac{(4-3i)^2}{4^2+3^2} \\=\frac{7-24i}{25}[/tex]

Quotient is [tex]\frac{7-24i}{25}[/tex]

Answer 2

Answer:

7/25 - 24/25i

Step-by-step explanation:


Related Questions

What role do plants have in the carbon-oxygen cycle?

a) They release oxygen into the air as a waste product of photosynthesis.
b) They release carbon dioxide into the air as a waste product of photosynthesis.
c) They absorb oxygen from the air to use during photosynthesis.
d) They do not have a role in the carbon-oxygen cycle.

Answers

A. Plants release oxygen to the air for us to breathe.
A.They release oxygen into the air as a waste product of photosynthesis.
Hope This Helps you!

solve for q.
k=4pq^2

Answers

k=4pq^2
k/4p=q^2
q=(k/4p)^2
Solve for q:
k = 4 p q^2

k = 4 p q^2 is equivalent to 4 p q^2 = k:
4 p q^2 = k

Divide both sides by 4 p:
q^2 = k/(4 p)

Take the square root of both sides:
Answer: q = sqrt(k/p)/2 or q = -sqrt(k/p)/2

a) You want to buy a new sweatshirt. They normally cost 28.80, but you found one that's on sale for 40% off its normal price. How much will you pay, not including tax?


1) $16.18


2) $17.28


3) $18.38


4) $19.48

b) If you get 17 out of 20 questions correct on this test, what percentage will you get correct?

1) 100%

2) 95%

3) 90%

4) 85%

Answers

For question A, the answer is 2.  Since the sale sweatshirt if 40% LESS, this means that 60% of the original price still remains. 28.80 x .60 = 17.28

For question B, the answer if 4.  You can divide 17 by 20 getting .85

In recent years, 23.8% of all registered doctors were female. If there were 57,800 female registered doctors that year, what was the total number of registered doctors?

Answers

57,800 is 23.8% of the total number of registered doctors.

To find out the number of registered doctors, we divide the number of female doctors by 23.8% as a decimal (which is just 0.238):

57,800 ÷ 0.238 = 242,857
-------------------------------------------------------------------------------------------------------------
Answer:

So there are 242,857 registered doctors.

Final answer:

To determine the total number of registered doctors, one can use the percentage of female doctors and the number of female doctors to calculate the overall total. By dividing 57,800 by 0.238, you find there were approximately 242,857 registered doctors.

Explanation:

The question asks for the total number of registered doctors, given that 23.8% are female and there are 57,800 female registered doctors. To find this, we use the formula:

Percentage (%) = (Part/Total) × 100

First, we express the percentage as a decimal by dividing it by 100, so 23.8% becomes 0.238. Next, we will rearrange the formula to solve for the Total:

Total = Part / Decimal Percentage

So we have:

Total = 57,800 / 0.238

Doing the calculation:

Total = 242,857 (approx.)

Therefore, the total number of registered doctors is approximately 242,857.

Ms. Johnson asked her class to write an equivalent
expression to
14d - 9 + 21k - 7dk + 2.
riley wrote the expression
7dk(2 - 3 - 1) _ 7

ahmad write the expression
7(2d + 3k - dk) - 7

Ariana wrote the expression
7k(2d - 3 - d) - 7

who is correct? explain how you know

Answers

Ahmad wrote the correct expression.
To prove that 7(2d + 3k - dk) - 7 is equal to 14d - 9 + 21k - 7dk + 2
Please check this solution:
7(2d + 3k - dk) - 7 = 14d - 9 + 21k - 7dk + 2
7(2d + 3k - dk) - 7 = 14d + 21k - 7dk -9 + 2
7(2d + 3k - dk) - 7 = 14d + 21k - 7dk -7

Get the common variable which is 7.
7(2d + 3k - dk) - 7 = 7(2d + 3k - dk) - 7

For checking, we can simplify the equation...
from 7(2d + 3k - dk) - 7 = 14d - 9 + 21k - 7dk + 2
We simplify it to:
7(2d + 3k - dk) - 7 = 14d + 21k - 7dk -7
7 * 2d = 14d
7 * 3k = 21k
7 * - dk = -dk

Therefore, 
7(2d + 3k - dk) - 7 is equal to 14d + 21k - 7dk -7

15% of 20 is _____. a3,b30,c 300

Answers

The Answer is 3 A :3 :)              ..
Hey there!

1% of 20 = 20/100.

20/100 = 0.2

Multiply 15 and 0.2. . .

15 x 0.2 = 3 <--------------

The correct answer to your question is option "A."
15% of 20 is 3.

Hope this helps you.
Have a great day!

Kenya has 2 hours to work a 100 problem math test.At what rate must she work in order to finish in 2 hours

Answers

100/2 is fifty problems an hour. If you would like a different unit, then Kenya needs to finish 25 questions every 15 minutes.

Answer:

Kenya should solve the problems at the rate  0.83 questions per minute.

Step-by-step explanation:

Total number of hours Kenya has to work on 100 questions is 2 hours .

2 hours = 2x60=120 minutes.

Kenya has to work on 100 problems in 120 minutes .

In 1 minute Kenya can solve 100 ÷ 120= 0.83 questions per minute.

Kenya should solve the problems at the rate  0.83 questions per minute.

what is equivalent to 3 to the negative 2nd power

Answers

3 to the negative second power is written like this: [tex] 3^{-2} [/tex]. 

When simplifying an expression with a negative exponent, you take a positive version of the exponent, in this case that would be 2, and apply that to the base. 
After doing that, we have 9. 
The next step is to put one over that number.
In this case, now after doing that the answer is [tex] \frac{1}{9} [/tex]. 

Hope this helps!

write the rule for this pattern 5, 20, 80, 320

Answers

The rule is multiplying by 4

5 x 4 = 20
20 x 4 = 80
80 x 4 = 320

A kilometer is more than one half a mile true or false!

Answers

The answer is true.
1 Kilometer is 0.621371 miles
True.

1 km = about 0.62 miles

Hope this helps!

Frank’s electric bill has a cycle day of the 3rd and a due date 8 days later with a one day grace period. What happens if Frank pays his electric bill on the 12th of the month?

Answers

his payment is recieived after the due date but he will not be assessed a late fee because of the grace period

Frank’s electric bill has a cycle day of the 3rd

And the due date of the bill is 8 days later

that is 3+8 = 11th of that month is the due date

The bill is to be paid by 11th

But 1 day grace period is given

So

11+1

=12

If one pays the bill by 12th of that month , then no penalty will be imposed.


And

Frank pays his electric bill on the 12th of the month

So no penalty will be imposed.


Ms.Sherman is preparing 5 5/8 cups of rice for a family reunion, she plans to use 1/4 of a cup for each serving. How many servings of rice is Ms.Sherman preparing

Answers

Ms. Sherman is preparing 5 5/8 cups of rice. She is using a fixed amount of 1/4 cup for each serving. Since we know the total amount of rice she is using and the amount per serving, we divide these to determine the number of servings.

It might be easier to see if we used friendlier numbers. If she has 10 cups total and uses 2 cups per serving she would have 10 / 2 = 5 servings.

Now, back to the numbers we were given. We need to divide 5 5/8 by 1/4. Let's first re-write 5 5/8 as an improper fraction (multiply 8 by 5 and add 5 to get 45 then place this over the already existing denominator of 8). 5 5/8 = 45 / 8.

The division we need to undertake is [tex] \frac{45}{8} / \frac{1}{4} [/tex]
To divide by a fraction we multiply by the reciprocal (what you get when you flip the fraction over) so our problem becomes [tex]( \frac{45}{8} )( \frac{4}{1} )[/tex]

We multiply across to get [tex]( \frac{45}{8} )( \frac{4}{1} ) = \frac{(45)(4)}{(8)(1)}= \frac{180}{8}=22.5 [/tex]

That is, she is making 22.5 servings. As a fraction this is 22 1/2

What is .58 as a fraction in simplest form

Answers

This fraction is 58/100 currently in its decimal.
It is not currently in simplest form, and to do so divide each part by 2. 
Then you have 29/50, which is the fraction in simplest form. 
Hope this helps!

I need help on question #84 !

Answers

Area of whole thing is 900
900=l*w
Since it is a square they are the same length so the answer to this part is 30
30-6 gives you the remainder which is 24
You have a sidewalk on both sides so you divide by 2
24/2=12
12 should be the width

X+23=-23 solve for x pls help !!!!

Answers

x + 23 = -23
x = -23 - 23
x = -46
the answer =-46 because if you graph it it will go from 23down to - 23

What is the area of a square rug that measures 6 feet on a side? 3 square feet 24 square feet 12 square feet 36 square feet

Answers

Well we know the area of a square is l*w, or s^2. So we can use s^2 where s=6 in your case. Now 6^2 is 6*6, which is 36.

So the area of a square rug that measures 6 feet is 36 feet

Answer= 36 feet
36ft is the area of a square rug that measures 6ft on a side.

Instructions: Select the correct answer.

If the radius of a flying disc is 7.6 centimeters, what is the approximate area of the disc?

A. 23.864 square centimeters

B. 90.6832 square centimeters

C. 181.3664 square centimeters

D. 238.64 square centimeters

Answers

The formula for the area of a circle (in this case, the disc) is
[tex]\pi {r}^{2} [/tex]
So, we apply the given radius to the formula to give us our answer:
[tex]\pi \times {7.6}^{2} = 181.4583917[/tex]
So, your approximate answer is C.

Answer:

the answer would be C

Step-by-step explanation:

For the data set summarized in the boxplot, identify the interquartile range (IQR).
A) 22.0
B) 37.5
C) 57.0
D) 59.0

Answers

The interquartile range of the data set summarized in the boxplot is 22.

What is the interquartile range?

The interquartile range is the difference between the third quartile and the first quartile. On a boxplot, the third quartile is the third line on the box and the first quartile is the first number on the box.

Interquartile range = 70 - 48 = 22

To learn more about box plots, please check: https://brainly.com/question/27215146

which number dose 5 represent a value 10 times the value represented by 5 in 35,187

Answers

The thousands is the answer and you spelled does wrong

In 35,187, the digit 5 represents 50,000. Ten times this value is 500,000. Therefore, in the new number, the digit 5 represents 500,000.

To find the value represented by the digit 5 in the number 35,187, we need to consider its place value. In the given number, 5 is in the ten-thousands place, which means it represents 5 * 10,000 or 50,000.

Now, we're asked to find a number where 5 represents a value ten times that of its representation in 35,187. So, we need to multiply 50,000 (the value represented by 5 in 35,187) by 10.

50,000× 10 = 500,000.

Therefore, in the new number, the digit 5 represents 500,000.

To summarize, the number where 5 represents a value ten times its representation in 35,187 is 500,000.

complete question=

Which number represents a value 10 times the value represented by 5 in 35,187?

I'll give brainliest if you show your work.
Jeremy surveyed students in his class about their spending habits in the school cafeteria. He used the data to create a scatterplot.

How Students Spend Money in the Cafeteria
Which is the equation of his trend line?
y= 2.75x
y= 3.05x- 0.6
y= 3.25x- 1
y= 9.75x- 14

Answers

Answer:

[tex]y=3.25x-1[/tex]

Step-by-step explanation:

step 1

Find the slope

we have the points

(2,5.5) and (5,15.25)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{15.25-5.5}{5-2}[/tex]

[tex]m=\frac{9.75}{3}=3.25[/tex]

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

[tex]m=3.25\\point\ (2,5.5)[/tex]

substitute

[tex]5.5=3.25(2)+b[/tex]

solve for b

[tex]b=-6.5+5.5=-1[/tex]

therefore

[tex]y=3.25x-1[/tex]

Answer: c

Step-by-step explanation:

What are the roots of the polynomial equation? x² + 7x + 12 = 0 Enter your answers in the boxes. x1= x2=

Answers

The equation factors as
.. (x +3)(x +4) = 0
By the zero-product rule, the roots are
.. x1 = -4
.. x2 = -3
Find the roots by solving for x.
x= -3, -4

using the image below find the y value for the point that divides the line segment cd into ratio 4:1

Answers

i cant help you if there is no picture

Answer:

A) 2

Step-by-step explanation:

What is the slope of the line of best-fit in the scatterplot below?
9/27
3/7
7/3
27/9

Answers

slope = (19-12)/(6-3) = 7/3

answer
7/3

Answer:

Option C is correct

7/3

Step-by-step explanation:

Formula for slope is given by':

[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex]              ....[1]

As per the statement:

The graph shows the best fit line scatter-plot.

Consider two points i.e

(3,12) and (6, 19)

Substitute these points in [1] we have;

[tex]\text{Slope} = \frac{19-12}{6-3}[/tex]

⇒[tex]\text{Slope} = \frac{7}{3}[/tex]

Therefore, the slope of the line of best-fit in the scatter plot is, 7/3

Can someone help me with A), B), and C)

Answers

A) The transformation is
.. y = 3f(x) -10
.. y = 3x -10 . . . . . . f(x) = x, here and in the rest of the problem.

B) The transformation is
.. y = (1/2)f(x) +4
.. y = (1/2)x +4

C) The transformation is
.. y = f(x) -1
.. y = x -1

besides the 90 degree angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13

Answers

Use sine cosine and tangent to find the answer. Sine=opposite/hypotenuse
Cosine= adjacent/hypotenuse tangent= opposite/adjacent. This should help you find your answers.

Answer:

b.) 23° and 67°

Step-by-step explanation:

Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.  

a.) 18° and 39°

b.) 23° and 67°

c.) 43° and 47°

d.) 65° and 25°

If the function graphed is f(x), find f(1).

A.) -4

B.) - 1/4

C.) 0

D.) 4


***
Is it C.) 0 ???

Answers

Locate 1 on the x axis. This is the horizontal number line. 

Draw a vertical line through 1 on the x axis. Extend this vertical line as far up and down as you can.

Notice how the vertical line crosses the blue curve. Mark this point. Then draw a horizontal line from this point to the y axis. The horizontal line will touch -4 on the y axis. So that means the point (1,-4) is on the curve.

If the input it is x = 1, then the output is y = -4

So that's why the answer is choice A

Now reverse your process to describe the pattern represented by the rule y = −2x + 13. Be as detailed as you can. HEEELLLLLLLLLPPPPP PLEAAASEEE

Answers

the y intercept is 0,13

In 2010, Josh purchased a house for $110,000. In 2014, the house was valued at $105,000. What is the rate of change for the value per year?

Answers

Final answer:

To find the rate of change for the value of Josh's house per year, subtract the initial purchase price from the current value, then divide by the number of years that have passed. The result shows the house's value decreased by $1,250 per year.

Explanation:

To calculate the annual rate of change for the value of Josh's house, you would subtract the final value of the house from the initial value and then divide by the number of years that have elapsed. This calculation gives you the change in value per year. In this case, the initial value of the house in 2010 is $110,000 and the final value in 2014 is $105,000. There are 4 years between 2010 and 2014.

Rate of change per year = (Final Value - Initial Value) / Number of Years

Rate of change per year = ($105,000 - $110,000) / 4

Rate of change per year = (-$5,000) / 4

Rate of change per year = -$1,250

Therefore, the value of Josh's house decreased by $1,250 per year from 2010 to 2014.

in a art class,40% of the students used watercolors for painting.Ten students in art class used watercolors.How many students were there in the class

Answers

There are 25 students Work

A student reports three trials to measure the density of an unknown metal. The percent error in these trials is given in the table. Trial Count Percent Error Trial 1 0.05 Trial 2 0.02 Trial 3 0.01 Indicate the most accurate valu

Answers

I think that the most accurate one is trial 3 since it is the least incorrect and closest percent-wise to the actual correct density of the metal. 
Hope this helps!
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