Answer:
Correct answer: a) -8
Step-by-step explanation:
Complex Numbers
A complex number z in polar form is expressed as
[tex]z=r(\cos\theta+\mathbf{i}\sin\theta)[/tex]
The nth power of a complex number in polar form is:
[tex]z^n=r^n(\cos(n\theta)+\mathbf{i}\sin(n\theta))[/tex]
If the complex number is given in rectangular form
[tex]z=x+\mathbf{i}y[/tex]
then the values of r and θ are given by:
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]\displaystyle \theta=\arctan\left(\frac{y}{x}\right)[/tex]
The given complex number is:
[tex]z=1-\mathbf{i}\sqrt{3}[/tex]
The value of r is:
[tex]r=\sqrt{1^2+(-\sqrt{3})^2}[/tex]
[tex]r=\sqrt{1+3}=2[/tex]
r=2
Calculating the angle:
[tex]\displaystyle \theta=\arctan\left(\frac{-\sqrt{3}}{1}\right)[/tex]
[tex]\displaystyle \theta=\arctan(-\sqrt{3})[/tex]
Since the number is in the quadrant IV, the angle is:
[tex]\theta=-60^\circ[/tex]
Thus, z is expressed in polar form as:
[tex]z=2(\cos(-60^\circ)+\mathbf{i}\sin(-60^\circ))[/tex]
Calculating:
[tex]z^3=2^3(\cos(-180^\circ)+\mathbf{i}\sin(-180^\circ))[/tex]
Given cos 180°=-1 and sin(-180°)=0
[tex]z^3=8(-1+0)[/tex]
[tex]z^3=-8[/tex]
Correct answer: a) -8
Answer:
A
Step-by-step explanation:
just finished test
Subtract 0.6 - 0.23.
The following graphs show the performance of two stocks over the first five months of the year. A graph titled Stock A B C has month on the x-axis, from 0 to 6, and price on the y-axis, from 0 to 40 in increments of 13.33. A line has points (1, 20), (2, 24), (3, 25), (4, 29), (5, 30). A graph titled Stock X Y Z has month on the x-axis, from 0 to 6, and price on the y-axis, from 20 to 32 in increments of 4. A line has points (1, 20), (2, 24), (3, 25), (4, 29), (5, 30). Which graph appears to show the best performance? Which scale makes the graph appear to be rising more slowly? a. Stock XYZ shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly. b. Stock ABC shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly. c. Stock XYZ shows the best performance. The scale of Stock XYZ makes the graph appear to be rising more slowly. d. Stock ABC shows the best performance. The scale of Stock XYZ makes the graph appear to be rising more slowly.
Answer:
C) Stock XYZ shows the best performance. The scale of Stock XYZ makes the graph appear to be rising more slowly.
Step-by-step explanation:
i did this question on my test, from reading the graph, i am almost certain this is the answer. correct me if i am wrong!
Answer:
B)
Step-by-step explanation:
B because the Stock XYZ shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly.
please help!! <3 and plsexplain how u got it *15 points*
Kiyo bought a pizza for $12.75 and four medium drinks at Pauli's Pizza. Define a variable and write an expression to represent the total amount of money he spent. Then find the total cost if one drink costs $3.
Answer:
4×3=12 total cost for the drinks
12.75 + 12= $24.75 total cost for the pizza and drinks combined
In the figure below, m
show work i’ll make you brainliest plz help
please help anyone
Answer:
p = 30
Step-by-step explanation:
EFGH is a cyclic quadrilateral ( all vertices lie on a circle )
The opposite angles of a cyclic quadrilateral are supplementary, thus
p + 5p = 180
6p = 180 ( divide both sides by 6 )
p = 30
What is the scale factor of this dilation?
1/2
3/5
1 2/3
2
Helpppppp plz I’ll give brainliest if it’s right.
What is the greatest common factor of 10 and 16? Then, use the greatest common factor to write an equivalent expression of 10 + 16.
Answer:
GCF is 2
Step-by-step explanation:
10+2+16
Jenna is making 9 costumes for the dance recital. Each costume uses 12 feet of fabric. How much fabric does Jenna need altogether? Use distributive property to solve.
Answer:
108
Step-by-step explanation:
If there is 9 costumes and each of the 9 costumes is 12 feet then you multiply 9 x 12 to get the answer, which is 108. (Please give me brainliest)
Simplify the expression
(-a)^-18
Find the distance between points p (-2,6) and q (4,-8)
Answer: 2√58
the distance between points p (-2,6) and q (4,-8) is [tex]\sqrt{(4-(-2))^{2}+(-8-6)^{2} } =\sqrt{6^{2} +(-14)^{2} }=2\sqrt{58}[/tex]
Step-by-step explanation:
Given that f(x)=4x3-12x2+10 and g(x)=x3 – 2x2 + 5x
The value of f(x)- g(x)= ax'+bx?+ cx+d. What are the values of the coefficients a,b,c,d?
Answer:
The values of a,b,c and d are as follows:
a = 3, b = -12, c = -5, d = 10
Step-by-step explanation:
Given functions are:
[tex]f(x) = 4x^3-12x^2+10\\g(x) = x^3-2x^2+5x[/tex]
We have to find the value of f(x) - g(x). This means we have to subtract function g(x) from function f(x)
So,
[tex]f(x) - g(x) = (4x^3-12x^2+10)-(x^3-2x^2+5x)\\= 4x^3-12x^2+10-x^3+2x^2-5x[/tex]
Combining alike terms
[tex]= 4x^3-x^3-12x^2+2x^2-5x+10\\= 3x^3-10x^2-5x+10[/tex]
Now it was given that:
f(x)- g(x)= ax^3+bx^2+ cx+d
By comparing both we get
a = 3, b = -12, c = -5, d = 10
Hence,
The values of a,b,c and d are as follows:
a = 3, b = -12, c = -5, d = 10
Consider the equation 0.16m - 0.4 - 0.4 what is the value of m?
A. 0
B. 2.1
C. 2.9
D. 5
Answer: I think it’s 5
Step-by-step explanation:
Well if you go on calculator 16 * 5 which would represent m - 0.4 would give you the answer 0.4.
I'm lost at this point, if you can help me I'll give you 10 points..
Answer:
So all the possible solutions are:
[tex]\bold{204.4~and~217.6.}[/tex]Solution Steps:
First you need to solve the real inequality to understand how to find the rest of the possible equations.
Subtract 13.2 from both sides:
[tex]13.2-13.2=[/tex] Cancels Out[tex]217.6-13.2=204.4[/tex]So now we know the real answer, but now we must find all the possible solutions.
(Means anything greater than or equal to 217.6 when you plug it into x + 13.2 ≥ 217.6.)
Numbers that are greater than 378:
1.) [tex]204.4+13.2=217.6[/tex] ≥ [tex]217.6[/tex] (True)
2.) [tex]217.6+13.2=230.8[/tex] ≥ [tex]217.6[/tex] (True)
3.) [tex]204.3+13.2=217.5[/tex] ≥ [tex]217.6[/tex] (False)
4.) [tex]0+13.2=13.2[/tex] ≥ [tex]217.6[/tex] (False)
5.) [tex]13.2+13.2=26.4[/tex] ≥ [tex]217.6[/tex] (False)
6.) [tex]200.4+13.2=213.6[/tex] ≥ [tex]217.6[/tex] (False)
7.) [tex]-200+13.2=-186.8[/tex] ≥ [tex]217.6[/tex] (False)
8.) [tex]13.2+13.2=26.4[/tex] ≥ [tex]217.6[/tex] (False)
Now put all the numbers together to form the code.
(Could either be the numbers on the side of the table or the accumulation of all the numbers in possible solutions.)
Code:
[tex]2044,2176[/tex] or [tex]1,2[/tex]______________________________
[tex]\bold{Hope~this~helps!}\\\bold{If~you~need~help~with~anything~else,~feel~free~to~ask!}\\\\\bold{~~~~~-TotallyNotTrillex}[/tex]
please solve this question
Answer:
the answer is b
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Both of the cost for 8 hours is $30
Write the slope intercept form of the equation of the line through the given points.
through: (0, 2) and (-4, -1)
Answer:
You use the formula (y to the second power minus y to the first power minus the same formula with the two different points
Step-by-step explanation:
Can someone show me how do I do this please?
Answer:
the awnser is c
Step-by-step explanation:
A- 100:1 would mean it is a 10000% markup
B- 1:100 lower than b so eliminate
C- 2:1 So a is double the amount of b so it's 100%
D- 1:2 B is 100% of a so it's flipped, not what question is asking for
So process of elimination shows that C is the correct awnser
This question is based on Algebra 1
solve for X
3x-4y=7
Answer:
[tex]x=\frac{4y+7}{3}[/tex]
General Formulas and Concepts:
Alg I
Equality PropertiesStep-by-step explanation:
Step 1: Define
3x - 4y = 7
Step 2: Solve for x
Add 4y to both sides: 3x = 4y + 7Divide 3 on both sides: x = (4y + 7)/3Please help me out :)
A passenger train travels 528 miles in 8 hours
Answer:
66 miles per hour
Step-by-step explanation:
528/8 = 66 miles per hour
Answer:
66 miles/hour.
Step-by-step explanation:
Its average speed is 528/8
= 66 miles/hour.
noah has d dimes and q quarters. he has no less than 17 coins altogether. write this situation as an inequality
Answer: d + q > 17
Step-by-step explanation:
Divide. Write your answer as a fraction or mixed number in simplest form.
8 • 3 3/5
Three friends grow groups of sunflowers.
Some think that Anna’s flowers are the tallest because the mean height of her flowers is the greatest.
Others think Anna’s flowers are the shortest because the median height of her flowers is the least.
The plots show the heights for each friend’s flowers.
Which is the most likely plot for Anna’s flowers?
Step-by-step explanation:
es la numero 3
Answer:
Option 3 is the most common plot for Anna’s flowers
Tyler ate x fruit snacks, and Han ate 34 less than that. Write an expression for the number of fruit snacks Han ate.
Answer:
x = -3/4
Step-by-step explanation:
Because you have the variable x and you do not know the number of fruit snacks he ate and you need to have the same variables to properly find the answer.
About me:
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Mr. Otero
Simplify the expression by combining like
terms:
2m2 - m + 4m2 + 8m
Enter the number that belongs in the green box.
[?]m2 + []m
Answer:
Step-by-step explanation:
2m^2-m+4m^2+8m combine like terms
6m^2+7m
Answer:
15m
Step-by-step explanation:
2m²-m+4m+8m
2m•2m-m+4m+8m
4m-m+4m+8m
3m+12m
15m
A little girl counts using the fingers of her left hand as follows: She starts by calling her thumb 1, the first finger 2, middle finder 3, ring finger 4, and little finger 5. Then she reverses direction, calling the ring finger 6, middle finger 7, first finger 8 and thumb 9, after which she calls her first finger 10 and so on. If she continues to count in this manner, on which finger will she stop?
a) What if the girl counts from 1 to 10?
b) What if the girl counts from 1 to 100?
c) What if the girl counts from 1 to 1000?
Answer:
(a) Index finger
(b) Ring finger
(c) Index finger
Step-by-step explanation:
Taking thumb as standard for the question.
Thumb series 1 , 9 , 17 ,25, 33......
general term for this
a(n) = 1 + (n-1)8
= 1 + 8n -8
= 8n -7
(a) For 1 to 10
8n -7 = 10
8n = 16+1 (remainder)
so the thumb is for 9 and the next is index finger.
10th = index finger.
(b) for 1 to 100
8n - 7 = 100
8n= 107
107 = 13x 8 + 3(remainder)
so the third finger from thumb is Ring finger
100th = Ring finger
(c) 8n - 7 = 1000
8n = 1007
1007= 125x8 +7 (remainder)
so the 7th finger next to thumb is Index finger
1000th = index finger
Find GJ
27
Please it’s due in one hour please please anyone
Answer:
the answer is 27 because hg is the same length as gj
It would have to be 27 because the side GH is the same as GJ.
Hope this helped!
Salma and John walk around a track. Salma walks each lap in 10 minutes. John walks each lap in 12 minutes. The two of them begin at the starting line at the
same time. They walk until they meet again at the starting line.
Answer:
If you're asking how long it will take for them to meet again, it will take 60 minutes.
Step-by-step explanation:
math 6th grade
Suppose an artist is working on a painting. On Monday, he painted 1/2 of it. On Tuesday, he completed another 1/3 of the painting. What percent of the painting has yet to be done? Round your answer to the nearest whole percent.
Answer:
17%
Step-by-step explanation:
1/2+1/3=5/6,so 1/6 left. That is 16.66666666666667 or 17%..
Hope this helps plz hit the crown :D
Which expression is not equivalent to the other three A) -9- 7 + 16n
Answer:
-16(1-n)
Step-by-step explanation:
Answer:
your answer would be -16(1-n)
Step-by-step explanation:
Please help me answer please
Answer:
x=75
Step-by-step explanation: