Answers
Answer:
B
Step-by-step explanation:
We are given the complex number:
[tex]\displaystyle z = 6(\cos 120^\circ + i\sin 120^\circ)[/tex]
And we want to find z³.
Recall that:
[tex]\displaystyle z^n = r^n(\cos(n\theta) + i\sin (n\theta))[/tex]
In this case, n = 3. Hence:
[tex]\displaystyle z ^3 = (6)^3 (\cos (3(120^\circ)) + i\sin (3(120^\circ))[/tex]
Simplify:
[tex]\displaystyle z^3 = 216(\cos 360^\circ + i\sin 360^\circ)[/tex]
Evaluate:
[tex]\displaysyle z^3 = 216( 1 + i(0)) = 216[/tex]
In conclusion, our answer is B.
Related Questions
Kakuro is like a crossword puzzle with numbers.
Answers
9514 1404 393
Answer:
[[. . 3 6 .][1 3 4 9 .][9 2 . 7 1][. 1 2 8 3][. 4 9 . . ]]
Step-by-step explanation:
It is helpful to remember that the first four digits {1, 2, 3, 4} total 10, and the last four digits {6, 7, 8, 9} total 30. It is also worthwhile to note that the smallest sum of two digits is 3 = 1+2, and the largest sum of 2 digits is 17 = 8+9. Some sums can only be made one way: 4 = 1+3, 16 = 7+9.
Here, we will refer to rows 1-5 from the top down, and columns 1-5 from the left to right.
__
Based on the above, column 5 can only be made one way: 1+3. Column 4 can only be made one way: 9+8+7+6. Then the choices for row 3B will be 1+7 or 5+3. We know it can't be 5+3 because 5 is not part of column 4. This makes our first fill-in (row, column) be (3,4)=7, (3,5)=1, (4,5)=3.
The sum of the remaining cells in row 4 must be 14-3 = 11, and cell (4,4) must be 6, 8, or 9. It cannot be 9, because that would require the remaining two cells to have a sum of 2, which they cannot. So, cell (4,4) is 6 or 8.
Cell (1,4) cannot be 9, either, because we cannot use 0 in cell (1,3). Then the only place for 9 in column 4 is in cell (2,4)=9.
With cell (1,4) being restricted to 6 or 8 (the two remaining numbers in column 4, cell (1,3) must be 3 or 1, and cell (2,3) must be 4 or 6. It cannot be 6 because that would require a sum of 2 in the first two cells of row 2, so (2,3)=4, (1,3)=3, and (1,4)=6. This makes (4,4)=8 and the remaining two cells of row 4 must be 1 and 2. 1 cannot go in (4,3), so we must have (4,3)=2 and (5,3)=9, (5,2)=4, (4,2)=1. That leaves 2 and 3 for rows 2 and 3 of column 2. The first two cells of row 2 must total 4, so must be 1 and 3. Cell (2,2) cannot be 1, so must be 3, leaving (2,1)=1, (3,1)=9, (3,2)=2 and that completes it.
The fill-ins are ...
[. . 3 6 .]
[1 3 4 9 .]
[9 2 . 7 1]
[. 1 2 8 3]
[. 4 9 . . ]
List the domain and range of the relation {(7. - 8), (5,5), (0.-8), (5,1) (7.8)}
Answers
Lets call the above set of points [tex]L[/tex].
The domain is between minimum and maximum of the x-coords points specified,
[tex]\mathrm{min}(L;x)=0[/tex]
[tex]\mathrm{max}(L;x)=7[/tex]
So domain is [tex]D_L=[\mathrm{min}(L;x),\mathrm{max}(L;x)]=[0,7][/tex].
The range is the same story but you look at y values,
[tex]\mathrm{min}(L;y)=-8[/tex]
[tex]\mathrm{max}(L;y)=8[/tex]
So range is [tex]R_L=[\mathrm{min}(L;y),\mathrm{max}(L;y)]=[-8,8][/tex].
Hope this helps :)
Is 736157 odd or even?
Answers
it is an odd number containing 7 on unit place.
Answer:
its odd.
Step-by-step explanation:
if the unit place is divisible by two or it is zero then the number is even otherwise it is odd.
One of the legs of a right triangle measures 1 cm and the other leg measures 17 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answers
Answer:
using phythagoras formula of right angles we can calculate the hypotenuse
1^2=x^2+17^2
x^2=17^2-1^2(transpose)
×^2=288 (introduce a square root)
x=15.01(round of to the nearest tenth)
Step-by-step explanation:
x=10
The measure of the hypotenuse is 17.029
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have Pythagoras theorem:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Given;
The legs of a right triangle measures 1 cm
The other leg measures 17 cm
Now,
|AC|^2 = |AB|^2 + |BC|^2
|AC|^2 = |1|^2 + |17|^2
|AC|^2 = 1 + 289
AC=17.029
Therefore, by pythagoras theorem answer will be 17.029.
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The sum of a rational number and an irrational number is irrational.
ALWAYS
NEVER
SOMETIMES
Answers
Proof:
Let
A = some rational numberB = some irrational numberC = some rational number (that isn't necessarily equal to A)We'll show that a contradiction happens if we tried to say A+B = C.
In other words, we'll show a contradiction happens for the form rational+irrational = rational.
Because A and C are rational, we can say
A = p/q
C = r/s
where p,q,r,s are integers. The q and s in the denominators cannot be zero.
So,
A+B = C
B = C - A
B = (r/s) - (p/q)
B = (qr/qs) - (ps/qs)
B = (qr-ps)/(qs)
B = (some integer)/(some other integer)
B = some rational number
But wait, we stated that B was irrational. The term "irrational" literally means "not rational". Irrational numbers cannot be written into fraction form of two integers. This is a contradiction and shows that A+B = C is never possible if A,C are rational while B is irrational.
This must lead to the conclusion that A+B must always be irrational if A is rational and B is irrational.
The template is this
rational + irrational = irrational
rational + rational = rational
HAVE A GOOD DAY
What is the next term in the geometric sequence? 1,4,-16,64
Answers
Answer:
256
Step-by-step explanation:
1,4,16,64,256
As 4 is being multiplied in each case.
Can anyone please explain this question to me?
(2√5+3√6)²
Answers
[tex]\displaystyle \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex] \displaystyle\large \bf( 2 \sqrt { 5 } + 3 \sqrt { 6 } ) ^ { 2 }[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \large \sf( 2 \sqrt { 5 } + 3 \sqrt { 6 } ) ^ { 2 }[/tex]
Use the algebraic identify [tex]\sf\left(a+b\right)^{2}=a^{2}+2ab+b^{2} [/tex]to expand [tex]\sf\left(2\sqrt{5}+3\sqrt{6}\right)^{2}[/tex].[tex] \large \sf \: 4\left(\sqrt{5}\right)^{2}+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
The square of [tex]\sf\sqrt{5}[/tex] is 5.[tex] \large \sf4\times 5+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
Multiply 4 and 5 to get 20.[tex] \large \sf20+12\sqrt{5}\sqrt{6}+9\left(\sqrt{6}\right)^{2} [/tex]
To multiply [tex]\sf\sqrt{5}[/tex] and [tex]\sf\sqrt{6}[/tex], multiply the numbers under the square root.[tex] \large \sf20+12\sqrt{30}+9\left(\sqrt{6}\right)^{2} [/tex]
The square of [tex]\sf\sqrt{6}[/tex] is 6.[tex] \large \sf20+12\sqrt{30}+9\times 6 [/tex]
Multiply 9 and 6 to get 54.[tex] \large \sf20+12\sqrt{30}+54 [/tex]
Add 20 and 54 to get 74.[tex] \large \boxed{\bf12 \sqrt{30} + 74 = 139.72..}[/tex]
I’m stuck on this question if someone could help me I would highly appreciate:)
Answers
Answer:
18
Step-by-step explanation:
They want u to find MR, and I can do that by taking CR - CM
But first we need to know what is x
Now u know CM + MR =CR
Therefore
(3x - 2) + (x+8) = 46
3x - 2 + x + 8 = 46
4x + 6 = 46
4x = 40
x = 10
Now we know x is 10, let's just make it easier first
CM = 3x-2
= 3 (10) - 2
= 28
MR = x + 8
= 10 + 8
= 18
Now we got all our values
They want MR?
MR = x + 8
= 10 + 8
= 18
HERE U GO
Answer:
18
Step-by-step explanation:
cm=3x -2
mr=x +8
cr=46
cm+mr=cr
3x-2+x+8=46
4x+6=46
4x=46-6
x=40/4
x=10
hence, mr=x+8
=10+8
=18
Sophia is furniture shopping for her new apartment. She has picked out a bed that costs $1,867, a sofa that is priced at
$3,215, and a dining room table for $1,471. All items include tax. If she wants to get the best estimate for the amount of
money she will need to save to purchase these items, to what place value should she round each item's price?
Answers
Answer:
To the thousandth place
-6 * -6 + 7 * -6 + 8
Answers
Answer:
0
Step-by-step explanation:
The * means multiplication where the ^ means exponents, so you multiply in this case.
-6 * -6 = 36
Two negatives equals a positive.
PEMDAS shows that multiplication and division occurs first so...
7 * -6 = -42
36 + -42 + 8
-8 + 8
= 0
You can search it up to see what PEMDAS is.
3 times the difference of a number and 1 is nine more than the same number. Find the number.
Answers
Answer: 6
Step-by-step explanation:
3 (x-1) = x + 9
3x - 3 = X + 9
3x - x = 9 + 3
2x = 12
x = 12/2
x = 6
The correct answer will be "n = 6". A complete solution is provided below.
Let,
The number be "n".
According to the question, the expression will be:
→ [tex]3(n-1)=9+n[/tex]
→ [tex]3n-3=9+n[/tex]
By adding "3" both sides, we get
→ [tex]3n-3+3=9+n+3[/tex]
→ [tex]3n=12+n[/tex]
By subtracting "n" from both sides, we get
→ [tex]3n-n=12+n-n[/tex]
→ [tex]2n=12[/tex]
→ [tex]n=\frac{12}{2}[/tex]
→ [tex]n = 6[/tex]
Thus the above is the appropriate answer.
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please help me, if you help then thanks!
Answers
Answer:
[tex] \frac{ - 8 {x}^{3} }{ {y}^{4} } [/tex] (first option)
Step-by-step explanation:
[tex] \frac{ - 32 {x}^{5} {y}^{3} }{4 {x}^{2} {y}^{7} } [/tex]
[tex] \frac{ - 8 {x}^{5} {y}^{3} }{ {x}^{2} {y}^{7} } = \frac{ - 8 {x}^{3} {y}^{ 3} }{ {y}^{7} } [/tex]
[tex] = \frac{ - 8 {x}^{3} }{ {y}^{4} } [/tex]
please view the image to get a better understanding ..im stressing :((
*please include the work to show what Danielle did wrong
What is the sum of x³ + 5x² – 7 and
5x³ – 3x² + 2x – 1?
Answers
Answer:
Daniella didn't do distributive property before she started.
Step-by-step explanation:
([tex]x^{3}[/tex]+5[tex]x^{2}[/tex]-7) + (5[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x-1)
5[tex]x^{6}[/tex]-3[tex]x^{5}[/tex]+2[tex]x^{4}[/tex]-1[tex]x^{3}[/tex]+25[tex]x^{5}[/tex]-15[tex]x^{4}[/tex]+10[tex]x^{3}[/tex]-5[tex]x^{2}[/tex]-35[tex]x^{3}[/tex]+21[tex]x^{2}[/tex]-14x+7
5[tex]x^{6}[/tex]+22[tex]x^{5}[/tex]-13[tex]x^{4}[/tex]-26[tex]x^{3}[/tex]+16x[tex]x^{2}[/tex]-14x+7
Use the numbers 0 - 9 in the blanks to make the equations true
Answers
Answer:
what blanks
Step-by-step explanation:
The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
Answers
Answer:
1 is your answer. I HOPE IT WILL HELP YOU A LOT.
Question 5
In the solution of the system in the solution of equations, what is the value of x?
2x - 4y = 14
X + 2y = 7
A -7
B 7
C 0
D no solution
Answers
Answer:
D) no solution
Step-by-step explanation:
2x - 4y = 14
X + 2y = 7
2x - 4y + x + 2y = 14 + 7
2x - 4y + x + 2y = 21
3x - 2y = 21
no solution
Answer:
x=2y+7
step by step explanation:
2x-4y=14
2(x-2y)=14
x-2y=14/2
x-2y=7
x=2y+7
Someone help please I don’t know how to answer this
Answers
Answer:
12e + 6
Step-by-step explanation:
to simplify, just add the like terms which are the values with the same variable
Answer:
12e+6
Step-by-step explanation:
collecting like terms means out all the matching letters together, so 4e + 8e=123.
an u please help me out
Answers
Rewrite the root be,
[tex]\sqrt{39}=\sqrt{3\cdot13}=\sqrt{3}\sqrt{13}[/tex]
We know that [tex]\sqrt{3}\approx1.7,\sqrt{13}\approx3.6[/tex]
Write decimals as fractions and multiply them,
[tex]\frac{17}{10}\cdot\frac{36}{10}=\frac{612}{100}=6.12[/tex]
So it should be on somewhere around the next tick from 6.
Hope this helps :)
help on bothering please !!!!!reaangie nas perimeter
en
is in bana is with 25.
the value of m
En 182
Hn 224
Gn - 12.2
) -
The area of a rectangle is 134 + 2 square
units. The width is 9. The length is 6.
What is the length?
A 6.5
C 15.5
B 13
D 19
Answers
Answer:
6) F
7) B
Step-by-step explanation:
6)
[tex]\boxed{perimeter \: of \: rectangle = 2(length + breadth)}[/tex]
60= 2[½(n -6) +2n +5]
Expand:
60= 2(½)(n -6) +2(2n) +2(5)
60= n -6 +4n +10
Simplify:
60= 5n +4
Minus 4 on both sides:
5n= 60 -4
5n= 56
Divide both sides by 5:
n= 56 ÷5
n= 11.2
Thus, option F is correct.
7)
[tex]\boxed{area \: of \: rectangle = length \: \times breadth}[/tex]
13q +2= 9(q +6)
Expand:
13q +2= 9q +54
Bring q terms to one side, constant to the other:
13q -9q= 54 -2
Simplify:
4q= 52
Divide both sides by 4:
q= 52 ÷4
q= 13
Thus, option B is correct.
Evaluate m^2 -4m+2 for m =-2
Answers
Answer:
answer is 6
Step-by-step explanation:
m^2 - 4m + 2
-2(2) - 4(-2) + 2
-4 + 8 + 2
-4 + 10
6
You take random sample of 200 people from Salinas and find that their average income is $48,000 per year
with a standard deviation of $9000. Also assume that population incomes are normally distributed.
Approximately how many people make between $39,000 and $57,000?
X
Answer format: Enter a positive integer
Answers
We have that The Total Number of People is
[tex]X\approx 137[/tex]
From the question we are told that
sample of 200
income is $48,000 per year
standard deviation of $9000
Generally the equation for the Ratio of people is mathematically given as
[tex]Y=P(\frac{39000-48000}{9000}<z<\frac{57000-48000}{9000})\\\\\Y=P(z<1))-(1-p(z-1))\\\\Y=0.8413-0.1582\\\\\Y=0.6826[/tex]
Therefore
The Total Number of People is
[tex]X=0.6826*200\\\\X\approx 137[/tex]
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5-(n-4)=3(n+2)
Please help I’ll give brainliest
Answers
If your salving by factoring it is 3/4
Mark all of the statements that are true.
O A. The domain for this function is the set {-5).
I B. The domain for this function is all real numbers.
C. This graph is not a function because the value of y is the same for
every value of x.
D. The range for this function is the set (-5).
I E. All real numbers are in the range of this function.
Answers
Any real value can be entered into the function but the answer will always be -5
We have the graph of a function (say f(x)).
We have to determine which of the given statements are correct w.r.t this graph of f(x).
What do you mean by domain and range of a function?The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
According to the question, we have the equation of this line as -
y = -5.
The value of y is constant for every value of x. Therefore, the range of the function is Set → {- 5}.
The function has same value → y= -5 for all values of x, ranging from →
- ∞ to + ∞, Therefore, its domain is the set of all Real numbers.
A function can have same value of y for different values of x.
Hence, Option B and D are correct.
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2. Describe a situation that could be modeled with the ratio 4: 1.
Answers
Answer:
u can do something like u have 8 pencils and 2 pens
Step-by-step explanation:
cause two divided by two is four and u only have to divide it once so that how u get that answer
(14 − 7)11 [(4 + 3)2]4 Simply
Answers
A box filled with books weighs 1112 kilograms.
Assume 1 kilogram = 2.20 pounds.
What is the best estimate of the weight of the box in pounds?
20 pounds
25 pounds
30 pounds
I don't know.
Answers
Answer:
24.464~20 pounds
Step-by-step explanation:
11.12*2.20
=24.464
24.46=20
Hope this helps :)
The best estimate of the weight of the box in pounds is 2,446.4 pounds.
Given that, a box filled with books weighs 1112 kilograms.
We need to find what is the best estimate of the weight of the box in pounds.
How to convert kilograms to pounds?To convert kilograms to pounds, multiply your kilogram measurement by 2.2.
Given, 1 kilogram = 2.20 pounds
Now, 1112×2.2=2,446.4 pounds
≈2,446
Therefore, the best estimate of the weight of the box in pounds is 2,446 pounds.
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28 plus 27 multiplied by 36
Answers
Answer:
1980
Step-by-step explanation:
Solve for b
-3(6b + 4) = 2(-5b+10)
b=
Answers
Answer:
b = -4
Step-by-step explanation:
-3(6b + 4) = 2(-5b + 10)
-18b - 12 = -10b + 20
(-18b + 10b) - 12 = (-10b + 10b) + 20
-8b - 12 = 20
-8b (- 12 + 12) = 20 + 12
-8b = 32
-8b/-8 = 32/-8
b = -4
Answer:
x
Step-by-step explanation:
What could I say for this question anybody who answers this gets brainlist
Answer ASAP!
Answers
please help me, if you help then thanks!
Answers
Answer:
The last one is the answer.
Step-by-step explanation:
Inverses are like opposites so [tex]\sqrt{x}[/tex] would be the inverse of [tex]x^{2}[/tex]. However don't be fooled by the second option because that is not the same although it seems like it. The true inverses are [tex]\sqrt[3]{27}[/tex] and [tex]3^{3}[/tex]. 3 cubed is 27 and the cube root of 27 is 3.
