Answers
Answer:
○ [tex]\displaystyle \frac{7 + 4i}{10}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{2 + 3i}{4 + 2i} → \frac{2 + 3i[4 - 2i]}{4 + 2i[4 - 2i]} = \frac{14 + 8i}{20} = \boxed{\frac{7}{10} + \frac{2}{5}i}[/tex]
When dividing complex numbers, multiply the denominatour and numeratour by the conjugate of the denominatour. Then simply towards the end.
* Here is something you should know:
[tex]\displaystyle \sqrt{-1} = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\: [every\:multiple\:of\:four][/tex]
I am joyous to assist you at any time.
Related Questions
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
Answers
Answer:
The first choice.
Step-by-step explanation:
It pass through the x axis at x = 3, so a factor must be (x - 3).
Answer:
The first option is correct :)
~Hope this helps
How would I simplify this expression
Answers
Answer:
-3 - 16b
Step-by-step explanation:
by simply doing the multiplication and then add combinable terms.
9 - 4(3 + 4b) = 9 - 12 - 16b = -3 - 16b
Explanation:
Let's simplify step-by-step:
9-4(3 + 4b)
Distribute:
= 9 + (-4)(3) + (-4)(4b)
= 9 + (-12) + (-16b)
Combine Like Terms:
= 9 + (-12) + (-16b)
= (-16b) +(9 + (–12) )
= -16b + (-3)
Answer:
-16b + (-3)
A school store buys pencils in bulk and sells them to students for a small profit. The school pays $2.00 for 100 pencils and sells them for 10 cents each. How many pencils would they have to sell to make a $100 profit?
Answers
Answer:
1,000 pencils
Step-by-step explanation:
First, there are 10,000 cents in $100.
So divide 10,000 by 10.
1,000.
I hope this helps!
pls ❤ and mark brainliest pls
A woman stands on a mountain at 8,000 feet above sea level. A man stands in a valley at 400 feet below sea level. What equation shows the difference in their elevations?
8,000 + (-400) =
8,000 - 400 =
8,000 - (-400) =
-8,000 - 400 =
Answers
Answer:
8,000 - (-400)
Step-by-step explanation:
Answer: 8,000 - (-400) =
Step-by-step explanation:
which expression are equivalent to the given expression
y^-8 y^3 x^0 x^-2
Answers
Answer:
y^-24, x^-2 y^-5, 1/ y^24, x^2/y^11, x^2y^-11 and 1/ x^2y^5
ok i tried searching up the problem and how to solve it but didn`t come up with much.
i don`t know if this changes anything, but I noticed that some of these answers are opposites
ex (from the sequence you gave me in the comments below) : y^-24, x^-2, y^-5, y^24, x^2, y^5
maybe thats what it meant by matching the expressions?
again, sorry if this wasnt much help i have a small brain DD::
B
8
С
Find the length of "c" to the
nearest tenth using the
Pythagorean Theorem.
Enter
Answers
Answer:
10.6
Step-by-step explanation:
Pythagorean theorem: a² + b² = c²
Where a and b = the legs and c = hypotenuse
We are given two legs and need to find the hypotenuse
Given:
Short leg (a) = 7
Long leg (b) = 8
Hypotenuse = c
Now to find the value of c we simply plug in the values of the variables into the Pythagorean theorem and solve for c
Pythagorean theorem: a² + b² = c²
a = 7, b = 8, c = c
Plug in values
7² + 8² = c²
Now solve for c
Simplify exponents
49 + 64 = c²
Add
113 = c²
Taking the square root of both sides
c = 10.6 ( rounded to the nearest tenth )
Answer:
c = 10.6
Step-by-step explanation:
[tex]h {}^{2} = p {}^{2} + b {}^{2} \\ c {}^{2} = (8) {}^{2} + (7) {}^{2} \\ c = \sqrt{64 + 49} \\ c = \sqrt{113} \\c = 10.6[/tex]
Write the equation of the circle centered at (4, - 9) with diameter 16.
HELP A GIRL OUT
Answers
Answer:
16= (x-4)^2 +(y+9)^2
Step-by-step explanation:
hey! The formula for the equation of a circle is r^2= (x-h)^2 + (y-k)^2
r= the radius (in your case you have the diameter so you do not need to square it)
(h,k)= is the center coordinates, so your center coordinate would be (4, -9). You now have your h (h=4) and your k (k=-9) so you can plug it in the formula! :)
a nice rating would help out
A rectangle has perimeter 66 cm and length 27 cm. What is its width?
(help pls it’s my hw)
Answers
Answer:
Step-by-step explanation:
A rectangle has the perimeter of 66cm, and since a rectangle has 2 lengths and 2 widths, we can tell that 2 widths = 66-27*2 = 12
so 1 width is half of 12 which is 6
. Point C is on line segment AB
so the ratio of AC to CB is 1 to
3. What are the coordinates of
Point ?
Answers
Answer:
Using the section formula, if a point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n, then
(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
3AC=CB
CB
AC
=
3
1
Since, A(1,1) and B(2,3) & m:n=1:3
Therefore, we have
C(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
(
1+3
(1)(2)+3(1)
,
1+3
(1)(3)+3(1)
)
C→(
4
5
,
2
3
).
6) find HJ
8)find IK
Answers
Answer:
HJ = 17
IK = 30
Step-by-step explanation:
to find HI :
GH : 2
HI : ?
IJ : 12
GI : 7
HI = GI - GH
HI = 7- 2
HI = 5
HI + IJ = HJ
5 + 12 = HJ
17 = HJ
To find IK
IJ = ?
JK = 12
KL = ?
IL = 49
JL = 31
To find IK we need to find KL and IJ
KL = JL - JK
KL = 31 - 12
KL = 19
IJ = IL - (JK + KL)
IJ = 49 - 31
IJ = 18
IK = IJ + JK
IK = 18 + 12
IK = 30
Evaluate each expression.(-9)4=
Answers
5. Use your answers to questions 3 and 4 to write an expression for how many times greater organism B's population is than organism A's population after 8 days. Simplify your expression, then write it as a number that is not in exponential form. Show your process. Write your answer in the space below. My answer
Answers
Population growth represents the rate at which the population changes
The expression for the number of times the population of B is greater than A is: [tex]2^6[/tex]The expression that is not in exponential form is: 64Given that:
[tex]r_1 = 2[/tex] ----- i.e. when the population doubles
[tex]r_2 = \frac{1}{2}[/tex] ----- i.e. when the population cut in halves
Population growth is represented as: [tex]A_n = ar^{n}[/tex]
Organism A
For the first 5 days (when it doubles) is:
[tex]A_5 = ar_1^{5[/tex]
Substitute [tex]r_1 = 2[/tex]
[tex]A_5 = a\times 2^{5[/tex]
For the next 3 days (when it cut in halves) is:
[tex]A = A_5 \times r_2^3[/tex]
Substitute [tex]A_5 = a\times 2^{5[/tex] and [tex]r_2 = \frac{1}{2}[/tex]
[tex]A= a \times 2^5 \times (\frac{1}{2})^3[/tex]
Apply law of indices
[tex]A = a \times 2^5 \times 2^{-3[/tex]
[tex]A = a \times 2^{5-3[/tex]
[tex]A = a \times 2^{2[/tex]
So, the growth factor of organism A is:
[tex]A = a \times 2^{2[/tex]
Organism B
For the 8 days, we have:
[tex]B=ar_1^8[/tex]
[tex]B=a\times 2^8[/tex]
The expression (n) for the number of times the population of B is greater than A is:
[tex]n = \frac BA[/tex]
This gives:
[tex]n = \frac{a \times 2^8}{a \times 2^2}[/tex]
[tex]n = \frac{2^8}{2^2}[/tex]
Apply law of indices
[tex]n = 2^{8-2}[/tex]
[tex]n = 2^{6}[/tex]
The expression that is not in exponential form is:
[tex]n = 2 \times 2\times 2\times 2 \times 2\times 2[/tex]
[tex]n = 64[/tex]
Hence:
The expression for the number of times the population of B is greater than A is: [tex]2^6[/tex]The expression that is not in exponential form is: 64Read more about population growth at:
https://brainly.com/question/17520917
What is the solution of the equation?
-6x+5= 3-5x
Answers
Answer:
I think the answer is x = 2
Answer: 2
Step-by-step explanation:
-6x+5=3-5x
+5x +5x
-x +5=3
-5 -5
-x = -2
-2 -2
X=2
what must be added to 2x^2 - 5x - 12 in order to get 7x^2 - x - 18
Answers
Answer:
5x^2 +4x -6
Step-by-step explanation:
that is the answer
yep
Answer:
5x² + 4x - 6
Step-by-step explanation:
Subtract 2x² - 5x - 12 from 7x² - x - 18 , that is the opposite operation, that is
7x² - x - 18 - (2x² - 5x - 12) ← distribute parenthesis by - 1
= 7x² - x - 18 - 2x² + 5x + 12 ← collect like terms
= 5x² + 4x - 6
What's the answer to this plz!?!
Answers
Answer:
1/5
Step-by-step explanation:
There are 5 yogurts in total.
(1 raspberry, 2 strawberry, 1 blueberry, 1 vanilla)
The chance of pulling a vanilla is 1/5.
Answer:
20%
Step-by-step explanation:
1/5 or 20% or 0.2 is the chance of finding vanilla yogurt
help its urgent please
Answers
Hi,
Answer is $0.19
Step-by-step explanation:-
We know that:-
15 dimes = $1.50
20 nickels = $1.00
8 quarters = $2.00
half dollar = $0.50
19 pennies = $0.19
Total = $5.19
Since Billy spended $5, so,
$5.19 - $5 = $0.19
Hope it helps you...
In a school library, 40% of the books are in Nepali language, 40% of the remaining books are in English and the remaining books are in regional languages. If the number of books in English language is 4800, find the total number of books in the library,
Answers
Step-by-step explanation:
Solution,
Let the total number of books be x, then
Books in English language=4800
40% of x=4800
40/100×x=4800
40x/100=4800
40x=4800×100
40x=480000
x=480000/40
x=12000
So the total number of books in the library is 12000.
common factor. 48x7y9−24x2y7−60x4y2
Answers
Avery has three times as much money as Jackie. Jackie has $6 less than Samantha. Together they have $56. How much money does each have?
HEEEEELP
Answers
The money belongs to Jackie, Avery, and Samantha is $10, $30, and $16 respectively.
Given that,
Avery has three times as Jackie.
Also, Jackie has $6 lower than Samantha.
Together they have $56.
Based on the above information
Let us assume the Jackie be x
So, Avery should be 3x
Samantha should be x + 6
So, the equation should be
x + 3x + x + 6 = $56
5x = $56 - $6
5x = $50
x = $10
So, Jackie has $10
Avery has $30
And, Samantha has $16
Therefore we can conclude that the money belongs to Jackie, Avery, and Samantha is $10, $30, and $16 respectively.
Learn more about the money here: brainly.com/question/10943652
13 x − y 13 x - y given that x = 11 x = 11 and y = 18 y = 18
Answers
Answer:
125
Brainliest, please!
Step-by-step explanation:
13x - y
x = 11, y = 18
13(11) - 18
143 - 18
125
Answer:
125
Step-by-step explanation:
13x - y
Substituting x = 11 and y = 18,
=> 13(11) - 18
=> 143 - 18
=> 125
math! help! pls! pls!
Answers
Answer:
3. MNP = OPN
Step-by-step explanation:
the second could be as well, but the sequence is the same for the third option, thus the second option is wrong
Hope my answer helped u :)
Please help me asap
Answers
Peyton needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4 hours and charged her $77 for parts. The total was $497. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
Answers
Answer:
Step-by-step explanation:
the equatoin is 4x+77=497
and x is the hours spent
so solving it you subtract 77 from 497 which is 420 and 420/4 is equal to 105
Hey! I hope you’ve had a good day:) I just need help in geometry right now. Can someone take a look at this question?
Answers
Answer:
(5,2)
Step-by-step explanation:
midpoint formula for future reference
(x1+x2/2),(y1+y2/2)
(3+7/2),(-5+9/2)
(10/2),(4/2)
(5,2)
e) If the radede circle is 7em, then find the area of circle. al- (SSS. x at Solna -
Answers
Hi
area of circle, which is call in proper math terme circumference ( latin for going around) is given by this formula :
2 times radius x pi
As math is all about knowing your formula and training, I let you have a shot. You wont progress other wise.
Ask in comment section if you are still blocked.
Find the difference between temperatures of 17 degrees celcius above zero and 12 degrees celcius below zero
Answers
Answer:
29° C
Step-by-step explanation:
-17(-12)
=29
Hope this helps
Answer:
29C
Step-by-step explanation:
Above zero temperature = +17C
Below zero temperature = -12C
Difference= 17 - (-12C)
= 17 + 12 C
=29C
( x+y)² + 2(x+y)×(x-y)+(x-y)²
Answers
Step-by-step explanation:
4x is the real answer of that question
what is 4.414*10 9 in standard form
Answers
Answer:
4,414,000,000
Step-by-step explanation:
4.414x10^9, move the decimal place 9 places to the left.
H. Pete wants a new truck. The sale price is 15% lower than the original price. The sale price is $20,000. Write and evaluate an expression for the original price. Uses for sale price and p for original price.
Answers
100-15=85%=SP
[tex]\\ \sf\longmapsto 85\%\times x=20000[/tex]
[tex]\\ \sf\longmapsto \dfrac{85}{100}x=20000[/tex]
[tex]\\ \sf\longmapsto x=20000\times \dfrac{100}{85}[/tex]
[tex]\\ \sf\longmapsto x=235.2(100)[/tex]
[tex]\\ \sf\longmapsto CP=23520[/tex]
can image 2 be the reflected figure
Answers
Answer:
Is there supposed to be a picture?
Step-by-step explanation:
Answer:
we need the image
Step-by-step explanation:
