When dividing complex numbers, why do
you need to multiply the numerator and
denominator by the complex conjugate of the
denominator?
Answers
Answer:
Hope this helps..
Step-by-step explanation:
So when you need to divide one complex number by another, you multiply the numerator and denominator of the problem by the conjugate of the denominator. This step creates a real number in the denominator of the answer, which allows you to write the answer in the standard form of a complex number.
Answer:
You have to multiply by the complex conjugate because the denominator has to be a real number. By multiplying the complex conjugate you can transform the denominator in to a real number.
Step-by-step explanation:
Related Questions
Find the distance between the pair of points given on the graph.
Answers
Answer:
ITS 4 CM
Step-by-step explanation:
Answer:
5 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 2, - 4) and (x₂, y₂ ) = (1, 0) ← 2 points on the line
d = [tex]\sqrt{(1+2)^2+(0+4)^2}[/tex]
= [tex]\sqrt{3^2+4^2}[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
St lunch, 6 friends share 4 pizzas equally. What fraction of a pizza does each friend get?
Answers
Answer:
2/3
Step-by-step explanation:
6 friends share 4 pizzas, each get 4/6 = 2/3 pizza
The person is 64 in. tall and casts a 48 in. Shadow. The tree casts 81 in. Shadow. How tall is the tree?
Answers
Answer:
65 in. shadow.
Step-by-step explanation:
if someone is 64 in. and they cast a 48 in. shadow than their shadow is 16 in. smaller than they are. 81 in. - 16 in. = 65 in.
97 in. is the height of the tree
An endangered whale species has a population of 6000. Biologists estimate that the stock is decreasing at 3% per year. At this rate, approximately how many years will it be before only 60% of the species remains?
A 9.0 years
B 9.6 years
© 10.0 years
D 16.8 years
Answers
9514 1404 393
Answer:
D. 16.8 years
Step-by-step explanation:
The multiplier each year is 1-3% = 0.97, so the multiplier after x years is 0.97^x. You want to know the value of x when that multiplier is 60%, or 0.60.
0.97^x = 0.60
x·log(0.97) = log(0.60) . . . . . . take logarithms
x = log(0.60)/log(0.97) ≈ 16.8
At the given rate, it will be 16.8 years before 60% of the species remains.
The radius of a circle with an area of 9/4pi is increased by a scale factor of x. The resulting circle has an area of 81pi . What is the value of x?
Answers
Answer:
x = 36.
Step-by-step explanation:
I have attached the work to your problem.
Please see the attachment below.
I hope this helps!
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answers
Answer:
26
Step-by-step explanation:
lol
Answer:
AC = 26
Step-by-step explanation:
AB + BC = AC
18+ 8 = AC
26
11. Rocco and Biff are two koalas sitting at the
top of two eucalyptus trees, which are
located 10 m apart, as shown. Rocco's tree
is exactly half as tall as Biff's tree. From
Rocco's point of view, the angle separating
Biff and the base of his tree is 70°. How high off the ground is each koala?
Answers
Answer:
Biff's tree is 14 m off the ground and Rocco's tree is 7 m off the ground.
Step-by-step explanation:
Let the height of Biff's tree be represented by x, so that the height of Rocco's tree is [tex]\frac{x}{2}[/tex].
Draw a straight line from Rocco's point of view to a point t to the middle of Biff's tree. This line divides x into two equal parts, and the angle is divided into [tex]35^{0}[/tex] each.
By alternate angle property,
Tan [tex]35^{0}[/tex] = [tex]\frac{\frac{x}{2} }{10}[/tex]
[tex]\frac{x}{2}[/tex] = Tan [tex]35^{0}[/tex] × 10
= 7.00021
⇒ x = 2 × 7.0021
= 14. 0042
x = 14
Therefore, Biff's tree is 14 m off the ground and Rocco's tree is 7 m off the ground.
Answer:
Biff height = 9.48m
Rocco's height= 4.74m
Step-by-step explanation:
As Rocco's tree is half as tall as Biff's tree, draw a horizontal line from Rocco on Rocco's tree which intersects the Biff's tree at he middle.
The angle 70 degrees is divided by 2 because of the horizontal line.
An upper right angle triangle is form by Rocco (point A), Midpoint of Biff's tree(point B), and Biff (point C).
As
[tex]tan\theta = \frac{perpendicular}{base\\}[/tex]
where θ=35 and base= 10m
[tex]tan35=\frac{perpendical}{10}[/tex]
[tex](tan35)(10)=perpendicular\\perpendicular=4.74[/tex]
As the perpendicular found is that of a triangle formed from midpoint of Biff's, to find the total height, multiply the found perpendicular with 2.
Biff height = 4.74*2 = 9.48m
Rocco's height is half of biff height
Rocco's height= 9.48/2 = 4.74m
Of 60 corn seeds that were planted, 18 of them did not sprout. What percent of the corn seeds
did not sprout? Show how you arrived at your answer.Of 60 corn seeds that were planted, 18 of them did not sprout. What percent of the corn seeds
did not sprout? Show how you arrived at your answer.
Answers
Answer:
30%
Step-by-step explanation:
18 / 60 = .3 * 100 = 30%
Answer:
The percent of the the corn seeds is 30%.
Step-by-step explanation:
Because when you calculate 60% and 18% will get a percent 30%.
Solution for 18 is what percent of 60:
18:60*100 =
( 18*100):60 =
1800:60 = 30
Now we have: 18 is what percent of 60 = 30
Question: 18 is what percent of 60?
Percentage solution with steps:
Step 1: We make the assumption that 60 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$.
Step 3: From step 1, it follows that $100\%=60$.
Step 4: In the same vein, $x\%=18$.
Step 5: This gives us a pair of simple equations:
$100\%=60(1)$.
$x\%=18(2)$.
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
$\frac{100\%}{x\%}=\frac{60}{18}$
Step 7: Taking the inverse (or reciprocal) of both sides yields
$\frac{x\%}{100\%}=\frac{18}{60}$
$\Rightarrow x=30\%$
Therefore, $18$ is $30\%$ of $60$.
Hope this helps :D and can i get brainlest plz
PLZ HELP ASAP!! WHAT IS 7- x-3 DIVIDED BY 4 + 2 ( WILL MARK BRAINLIEST)
Answers
Round 189.939360828 to 4 decimal places.
Answers
Answer:
189.9394
Step-by-Step Explanation:
Round to the nearest 0.0001 or
the Ten Thousandths Place.
if the blue radius below is 4.5 unit lrpendicto the green chord and the segment ab is 4.5 units long, what is the length of the length of the chord?
Answers
Answer:
b) 9 units
Step-by-step explanation:
segment ab is the same length as segment bc
Need Answer Fast). The solution to a problem is an irrational number. which statement is true about the solution? Will Mark Brainliest.
Answers
Step-by-step explanation:
There is no option to choose from, but the knowledge of what irrational numbers are, would help cover this cost.
A rational number is a number that can be written as a simple fraction, a/b. Examples are 1/2, 5/6,...
If a number cannot be written as a simple fraction, then it is called irrational.
Example of irrational numbers: √2, π
Answer:
Here are the statements!!!
High school football team had the best game of the season they scored eight touchdowns (seven points each) and three field goals (3 points each). How many points did they score in all
Answers
Answer:
65 points in all
Step-by-step explanation:
3 x 3 = 9
7 x 8 = 56
56 + 9 = 65
:))
Calculate the circumference of the circle in terms of π. the diameter is 6 C=πd
Answers
Answer:
18.85
Step-by-step explanation:
Answer:
18.84
Step-by-step explanation:
C = [tex]\pi d[/tex]
C = [tex]\pi 6[/tex]
C = 3.14 * 6
C = 18.84
What is the value for x?
Enter your answer in the box.
Answers
Answer:
8
Step-by-step explanation:
because we know its an isosceles triangle angle A and C will both be the same and since we know A = 69 C will also be 69. we also know that angles in a triangle add to 180 so take away the two 69s from the 180 to get 42
then we work backwards if its 5x + 2 then we need to do 5x - 2 to get 40 then divide it by 5 to get your answer 8!
(sorry if the explanation doesnt make sense )
Decimal expansion of 5/8
Answers
Answer:
0.625
Step-by-step explanation:
5/8 is the same as dividing so divide them both and it will equal 0.625
Answer:
0.625
Step-by-step explanation:
1/8 = 0.125
0.125 times 55 = 0.625
Which choice is equivalent to the product below?
√8 × √3
Answers
The right answer is 2√6
look at the attached picture
Hope it will help you
Good luck on your assignment
Find the value of x.
with work plz
Answers
Answer: x = 117 degrees.
Step-by-step explanation: The sum of the interior angles of a pentagon should equal 540 degrees. The value of x has to make the total of the angles equal to 540. 140 + 138 + 59 +86 is 423. Now we need to subtract 423 from 540 to know the value of x since it has to all add up to 540. 540-423 is 117.
Answer:
117°
Step-by-step explanation:
sum of angles of a polygon=(n-2)*180
where n is the number of sides.
it has 5 sides.
x+86+140+138+59=(5-2)*180
x+423=3*180
x=540-423
x=117°
PLEASE HELP, BEST ANSWER GETS BRAINLIEST:
Copy and complete.
Answers
2nd circle to 3rd circle: 10%
So, 1st circle to 3rd circle is 20%
Answer:
19%
Step-by-step explanation:
1. Decrease by 10% = 0.9 times
2. Repeat decrease by 10% = 0.9*0.9= 0.81 times
0.81 times decrease equals to 100%-81%= 19% decrease
Consider function fbelow.
f(t) = 4* - 6
Determine function g which is created by shifting the graph of function fup 5 units.
O A.g(x) = 98 - 6
OB.g(x) = 4(x+5)-6
O C.g(x) = 44.1
OD.g(x) = 4x + 5
Answers
Answer:
Step-by-step explanation:
For this case we have a function of the form:
f (x) = 4 ^ x-6
We want to move the graph five units up.
Therefore, the new function is given by:
g (x) = f (x) +5
Substituting we have:
g (x) = 4 ^ x-6 + 5
Rewriting the function:
g (x) = 4 ^ x-1
Answer:
The new function is given by:
g (x) = 4 ^ x-1
option C
Click to let other
The function g which is created by shifting the graph of function f up 5 units is given by [tex]g(x) = 4^x - 1.[/tex]
Option C is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To shift the graph of function f up 5 units, we need to add 5 to the output (y-value) of the function.
Therefore, the function g(x) will be:
g(x) = f(x) + 5
Substituting the expression for f(x), we get:
[tex]g(x) = 4^x - 6 + 5\\g(x) = 4^x - 1[/tex]
Therefore,
The function g which is created by shifting the graph of function f up 5 units is given by [tex]g(x) = 4^x - 1.[/tex]
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
Select the correct answer. What is the simplified form of this expression? (-x2 + x) + (4x2 − x − 1)
Answers
Answer:
[tex]3x^2-1[/tex]
Step-by-step explanation:
[tex](-x^2+x)+(4x^2-x-1)= \\\\-x^2+4x^2+x-x-1= \\\\3x^2-1[/tex]
Hope this helps!
Sarah graphed the solution to the inequality StartAbsoluteValue f + 3 EndAbsoluteValue less-than 9 on the number line.
A number line going from negative 14 to positive 10. Open circles are at negative 12 and positive 6. Everything between the points is shaded.
Which inequality statement can be used to help determine if the graph is correct?
When f = 0, StartAbsoluteValue 0 + 3 EndAbsoluteValue less-than 9, which is true because 3 is less than 9.
When f = negative 12, StartAbsoluteValue negative 12 + 3 EndAbsoluteValue less-than 9, which is true because 9 is equal to 9.
When f = 10, StartAbsoluteValue 10 + 3 EndAbsoluteValue less-than 9, which is true because 9 is greater than 13.
When f = negative 14, StartAbsoluteValue negative 14 + 3 EndAbsoluteValue less-than 9, which is true because 9 is greater than –11.
Answers
Answer:
Correct option: first one.
Step-by-step explanation:
Let's analyse each option:
1)
When f = 0, |0 + 3| < 9, which is true because 3 is less than 9.
This statement is true, and the value f = 0 in inside the solution graphed by Sarah.
2)
When f = -12, |-12 + 3| < 9, which is true because 9 is equal to 9.
This statement is false, because the inequality uses a "less-than" symbol and not a "equal" symbol, so 9 < 9 is false
3)
When f = 10, |10 + 3| < 9, which is true because 9 is greater than 13.
This statement is false, because 9 is not greater than 13.
4)
When f = -14, |-14 + 3| < 9, which is true because 9 is greater than –11.
This statement is false, because the value of |-14 + 3| is 11 and not -11.
So the correct option is the first one.
Answer:
Answer is A,
Step-by-step explanation:
edge2020
Which situations can be represented by the equation 3+15=288? Select all that apply.
Nate buys a phone that costs $288. He is able to put $15 down and then pay the remaining balance in 3 equal payments. What is x, the amount of one payment?
Nate upgrades his phone. He makes 3 equal payments of $288 each and pays an additional $15 in taxes. What is x, the total cost of the phone?
Nate bought his 3 children identical phones and chargers. He spent a total of $288. If each charger was $15, what is x, the cost of one phone?
Nate bought his 3 children identical phones and chargers. He spent a total of $288. If each charger was $5, what is x, the cost of one phone?
Nate bought his 3 children identical phones totaling $288. Nate used a coupon for “$15 off total purchase.” What is x, the discounted price of one phone?
Answers
Answer:
the first and last option.
Step-by-step explanation:
the equation will be equal to 288.
x is the amount of one payment that he makes 3 times, hence the 3x.
15 is his initial payment so that is added to the 3x to equal 288.
the second equation still equals to 288.
the 15 is still there because added to the phone price it is equal to 288.
the x represents the price of the phones and 3 is how many he's getting, hence the 3x.
Answer:
the equation will be equal to 288.
x is the amount of one payment that he makes 3 times, hence the 3x.
15 is his initial payment so that is added to the 3x to equal 288.
the second equation still equals to 288.
the 15 is still there because added to the phone price it is equal to 288.
the x represents the price of the phones and 3 is how many he's getting, hence the 3x.
Step-by-step explanation:
Mark me brainiest please
Travis is temporarily not working while his office is being remodeled. He
expects to be back at work in 2 months, but won't be able to afford his
mortgage payment until then. Which of the following is the best option for
him?
A. Forbearance agreement
B. Foreclosure
C. Moving to another state
D. Bankruptcy
Answers
Because he can not afford to to pay them at the moment but he will be able to pay them when they are done and he gets to go back to work
Answer:
Correct answer is Forbearence agreement
Step-by-step explanation:
he was incorrect
There are xboys playing in the park. The number of girls playing in the park is equal to the square root of the number of boys. If the total
number of boys and girls playing in the park is 42, find the number of boys.
A. 49
B.6
C. 36
D. 7
Answers
Answer:
x = 36 and √x = 6; total 42 children
Step-by-step explanation:
Number of boys: x
Number of girls: √x
Total number of kids: x + √x = 42.
Find x.
Rewrite x + √x = 42 as √x = 42 - x. Then square both sides:
x = 1764 - 84x + x^2, or
x^2 - 85x + 1764 = 0
Check out Answer C: x = 36. Is the above equation true for x = 36? YES
Check out Answer A: x = 49. Is the above equation true for x = 49? YES
Assume that x = 36. This would be the number of boys. The number of girls would be √36, or 6. Does the sum of 36 and 6 equal 42? YES. So the number of boys is 36 and the number of girls is 6.
Assume that x = 49. This would be the number of boys. The number of girls would be √49, or 8. Does the sum of 49 and 7 equal 42? NO. So we reject x = 49 as the number of boys and accept x = 36 as being correct.
Please Help ASAP, ehehdhhdheh
Answers
Answer:
I believe x is the angle shown. I hope this helps
I need help answering these. What does the arrows going both ways mean?
Answers
Answer:
I'm pretty sure it means it is any number
Answer:
It means there is no beginng point or end point.
Find the volume of the rectangular prism.
length = 5 1/4 inches
width = 4 1/2 inches
height = 3 inches
Answers
Answer:
70.825 square inches
Step-by-step explanation:
Answer:
[tex]= 70 \frac{7}{8} {in}^{3} \\ [/tex]
Step-by-step explanation:
[tex]v = whl \\ = 4\frac{1}{2} \times 3 \times 5 \frac{1}{4} \\ = \frac{9}{2} \times 3 \times \frac{21}{4} \\ = \frac{567}{8} \\ = 70 \frac{7}{8} {in}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Which describes the transformation? Select three options.
Triangle ABC was translated to form A'B'C'.
A'
It is rigid.
:::
It is nonrigid.
А
x
It is isometric.
B
The size is preserved.
C
The angles are not preserved.
В
Save and Exit
Next
Submit
Mark this and retum
Answers
Answer:
It is rigid
It is isometric
The size is preserved
Step-by-step explanation:
Given that Triangle ABC was translated to form A'B'C', then both triangles are congruent triangles.
A translation only moves the figure, preserving the size.
Because the size is preserved, it is a rigid transformation or isometric transformation.
Answer:
acd
Step-by-step explanation:
If y = 3x+b intersects y= mx +3 at (2, 3), find the value of b and m.
Answers
Answer:
The value of b is -3 and m is 0.
Step-by-step explanation:
You have to substitute the coordinates into both equation in order to find m and b value :
Find m,
[tex]y = mx + 3[/tex]
At (2,3),
[tex]3 = m(2) + 3[/tex]
[tex]3 - 3 = 2m[/tex]
[tex]2m = 0[/tex]
[tex]m = 0[/tex]
Find b,
[tex]y = 3x + b[/tex]
At (2,3),
[tex]3 = 3(2) + b[/tex]
[tex]b + 6 = 3[/tex]
[tex]b = 3 - 6[/tex]
[tex]b = - 3[/tex]
Answer:
b = -3
m = 0
Step-by-step explanation:
y=mx+b
3 is the constant
