z²-2i=0
Answer:
Solution given:
z⁴=-4
doing square root on both side
[tex]\sqrt{z⁴}=\sqrt{2²*-1}[/tex]
we know i²=-1
substituting i² we get
z²=[tex]\sqrt{2²*i²}[/tex]
z²=2i
z²-2i=0 is a required answer. where
z² and 2 is real number.
Answer:
z = {-1 -i, -1 +i, 1 -i, 1 +i}
Step-by-step explanation:
Using Euler's formula, we can write the equation as ...
z^4 = 4e^(i(π +2πn)) . . . . . . where n is any integer
Then the 4th root is ...
z = (√2)e^(i(π +2πn)/4 = (√2)e^(i(π/4 +nπ/2)) . . . . . for n = 0–3
z = √2(cos(π/4+nπ/2) +i·sin(π/4 +nπ/2)) . . . . . for n = 0–3
z = ±1 ±i
z = {1 +i, -1 +i, -1 -i, 1 -i}
_____
Additional comment
Values of n are only needed in the range 0–3, because the answers repeat for values other than those.
An ant can travel at a constant speed of 980 inches every 5 minutes. At this rate, how far can the ant travel in 7 minutes? *
1 point
A grocery store charges $5 for every 3 1/4 pounds of furit. Eleizibeth has 9 3/4 pounds of fruit in her grocery cart. How much will Elizabeth have to pay to purchase the fruit?
Sorry for the spelling :)
Answer:
15 dollars
Step-by-step explanation:
because f it 9 3/4 and it 5 dollars for every 3 1/4 its like multiplying 3 to 3 1/4 so 15 dollars :(:
Math riddle! Correct answer gets brainliest!
Answer with what x and y are equal to.
Answer:
[tex]\displaystyle [9, 4\frac{1}{2}][/tex]
Step-by-step explanation:
I figure these exercises out by numeric association. I see a 3, so I know right away that there might be a 9 somewhere. So, you start by plugging 3 in for [tex]\displaystyle x,[/tex] THEN plug [tex]\displaystyle 1\frac{1}{2}[/tex] in for [tex]\displaystyle y[/tex] sinse there are twise the quantity of [tex]\displaystyle y[/tex] than there are of [tex]\displaystyle x.[/tex] Now, doing so will give you [tex]\displaystyle 24 ≠ 18.[/tex] This tells you to try another pattern, so go with plugging [tex]\displaystyle 4\frac{1}{2}[/tex] in for [tex]\displaystyle y[/tex] and [tex]\displaystyle 9[/tex] in for [tex]\displaystyle x[/tex]. Doing so gives you what you are looking -- [tex]\displaystyle 36 = 36.[/tex] Therefore, the association wourked perfectly. ☑
I am joyous to assist you at any time.
That locked sign defines that both sides are equal.
The equations are
2x=4y=>x=2y--(1)3x+9=2x+4y=>x+9=4y=>x=4y-9--(2)From (1) and (2)
[tex]\\ \rm\Rrightarrow 4y-9=2y[/tex]
[tex]\\ \rm\Rrightarrow 2y=9[/tex]
[tex]\\ \rm\Rrightarrow y=9/2=4.5[/tex]
Put in eq(1)
x=2(4.5)=9Hence
(x,y)=(9,4.5)Solve the equation x^2 – 4x – 31=-2x + 25 to the nearest tenth.
Answer:
x=1+sqr57,1-sqr57
Step-by-step explanation:
Answer:
x = -6.5, x = 8.5
Step-by-step explanation:
The given equation ...
x^2 -4x -31 = -2x +25
can be rewritten to a form that facilitates completing the square:
x^2 -2x = 56 . . . . . add 2x+31
x^2 -2x +1 = 57 . . . add 1 to complete the square
(x -1)^2 = 57 . . . . . write the left side as a square
x -1 = ±√57 . . . . . take the square root
x = 1 ±√57 ≈ {-6.5, 8.5} . . . . . add 1, evaluate
Solutions are near x = -6.5 and x = 8.5.
The perimeter of a rectangular field is 336 m.
If the width of the field is 74m, what is its length?
Answer:
94 m
Step-by-step explanation:
Perimeter = 2(l + W)
336=2(74 + L)
336/2=74+L
168-74=L
L=94 m
which number s below belong to the solution set of the inequality check all that apply 4 times less than 112 pls help me
The values of "s" that belongs to the solution set must be less than 28.5
The inequality that represents the statement 4 times "s" less than 112 is expressed as;
4s < 112Divide both sides of the inequality expression by 4 as shown:
4s/4 < 114/4
s < 114/4
s < 28.5
Hence the values of "s" that belongs to the solution set must be less than 28.5
Learn more on inequalities here: https://brainly.com/question/12371526
Find the area of the shape shown below.
Answer:
A = 15u²
Step-by-step explanation:
Area of a Trapezoid Formula:
[tex]\frac{h}{2}*(b_1+b_2)[/tex]
Plug in our values (h = 3, b1 = 7, b2 = 3)
[tex]\frac{3}{2}*(7+3)[/tex]
Now we evaluate
[tex]\frac{3}{2}*(10)[/tex]
[tex]\frac{30}{2} = 15[/tex]
What is the median of this set of data: 593, 588, 540, 434, 420, 398, 390, 375
A.564
B.420
C.427
D.394
Hello:) how to do question 6? :) I’m not sure which property to use :/
Answer:
which grade are you in so that i can tell you according to that
i, vì AD//BC nên góc A +góc B =180°
ii, góc A=góc B nên góc C=góc D -> ABCD là hình bình hành
And AB=BC=> ABCD là hình thoi
don't ask why im asking for help ;-;
2.744
merry christler
2⎜x - 7/2⎟ + 3 > 4
Pls
Answer: x<3 or x>4
Step-by-step explanation: 2|x-7/2|+3+-3>4+-3 2|x-7/2|/2>1/2 x+|−7/2|+7/2>1/2+7/2 x>4 or x+|−7/2|+7/2<−1/2+7/2 x<3
can someone help me with this
Studying a group of children from first grade through high school to see the effect of pre-schooling on educational success would be which
type of study?
a
longitudinal
cross-sectional
Ос
natural observation
Od
experimental
Answer:
Longitudinal study
Step-by-step explanation:
Information is collected over extended periods of time in a longitudinal study, but in cross-sectional, natural observation, and experimental studies, information is collected over short periods of time or in one time only. Based on the choices given, this type of study would be a longitudinal study.
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.62 and a standard deviation of 0.4. Using the empirical rule, what percentage of the students have grade point averages that are no more than 1.82? Please do not round your answer.
Answer:
The percentage of the students who have grade point averages that are no more than 1.82 is 2.5%
Step-by-step explanation:
The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviations from the mean and 99.7% are within three standard deviations from the mean.
Given that:
Mean (μ) = 2.62, Standard deviation (σ) = 0.4
68% are within one standard deviation = μ ± σ = 2.62 ± 0.4 = (2.22, 3.02)
95% are within two standard deviations = μ ± 2σ = 2.62 ± 2(0.4) = (1.82, 3.42)
The percentage of the students have grade point averages that are no more than 1.82 is 100% - [95% + (100% - 95%)/2] = 100% - 97.5% = 2.5%
solve for c. 3c+2=-10 and thank you
Answer:
c= -4
Step-by-step explanation:
Given that:.3c+2 = -10
⇛ 3c = -10 - 2
⇛3c = -12
⇛c = -12:3 = -12/3
.°. c = -4 Ans .
Catrina wants to purchase a new bag she found on sale for $68. The bag is originally priced at $80. What is the percent of change in the price of the bag?
Answer: The percent change of the bag is 15%.
After Gwen, Tristan, and Keith finish exercising, they go to the fair. At the fair, they each pay the entry fee and also buy tickets they can use for food or rides. Gwen pays the entry fee and buys 10 tickets. It costs her a total of $30. Tristan pays the entry fee and buys 15 tickets. It costs him a total of $40. Keith pays the entry fee and buys 10 tickets. It costs him a total of $30. In this task, you will create a system of equations and find the cost of each ticket. Let x represent the entry fee and y represent the cost of each ticket in dollars.
Answer:
Part A:
Gwen equation
x + 10y = 30
Part C:
Keith equation:
x + 10y = 30
Part B:
Tristan equation:
x + 15y = 40
Part D:
You would use Keith's and Tristan's equation, because Gwen and Keith have the same exact equation so you can just use Keith's equation.
Part E:
Multiply the second equation by -1, then add the equations together.
(x+10y=30)
-1(x+15y=40)
Becomes:
x + 10y = 30
-x - 15y = - 40
Add these equations to eliminate x:
-5y = -10
-5y/5 = -10/5
so y = 2
Now lets find x, so lets plug it in x + 10y = 30.
x + 10(2) = 30
x + 20 = 30 ( do 30-20)
x = 10
We used elimination to solve this problem.
The entree fee is $10 and each ticket costs $2.
Part F:
For this part search graph tool and go on the app, then put Keith's and Tristan's equation in Graph Tool. Once you do that just screenshot it and paste it to Part F, then your answer should be Yes, you get the same solution when it is solved algrebraically.
Step-by-step explanation:
I really hope this helps you!!!! :D Mark brainliest if it does!!!!
Answer: Part A:
Gwen equation
x + 10y = 30
Part C:
Keith equation:
x + 10y = 30
Part B:
Tristan equation:
x + 15y = 40
Part D:
You would use Keith's and Tristan's equation, because Gwen and Keith have the same exact equation so you can just use Keith's equation.
Part E:
Multiply the second equation by -1, then add the equations together.
(x+10y=30)
-1(x+15y=40)
Becomes:
x + 10y = 30
-x - 15y = - 40
Add these equations to eliminate x:
-5y = -10
-5y/5 = -10/5
so y = 2
Now lets find x, so lets plug it in x + 10y = 30.
x + 10(2) = 30
x + 20 = 30 ( do 30-20)
x = 10
We used elimination to solve this problem.
The entree fee is $10 and each ticket costs $2.
Part F:
For this part search graph tool and go on the app, then put Keith's and Tristan's equation in Graph Tool. Once you do that just screenshot it and paste it to Part F, then your answer should be Yes, you get the same solution when it is solved algrebraically.
Step-by-step explanation:
I really hope this helps you!!!! :D Mark brainliest if it does!!!!
Step-by-step explanation:
Trent purchases 44 euros worth is souvenirs while on vacation in France. If $1 U.S. = 0.678 euros, find the cost of souvenirs in United States dollars.
A 16-ounce can of mixed nuts includes 6 ounces of cashews and 10 ounces of almonds. What is the ratio of almonds to mixed nuts in this can of nuts?
Step-by-step explanation:
Total=16 ounces
Ratio of almonds to mixed nuts
almonds:mixed nuts
10 : 16
5 : 8
i need help with this!!
Answer:
[tex]x<-4[/tex]
Step-by-step explanation:
[tex]8x-4<-36\\\Add\:}4\mathrm{\:to\:both\:sides}\\8x-4+4<-36+4\\\mathrm{Simplify}\\8x<-32\\\mathrm{Divide\:both\:sides\:by\:}8\\\frac{8x}{8}<\frac{-32}{8}\\Simplify\\\frac{8x}{8}<\frac{-32}{8}\\Simplify\\\frac{8x}{x}:x\\\mathrm{Divide\:the\:numbers:}\:\frac{8}{8}=1\\=x\\Simplify\\\frac{-32}{8} \\[/tex]
Apply the fraction rule
[tex]=-\frac{32}{8}\\Divide\\ \frac{32}{8} = x=-4\\x<-4[/tex]
Find the surface area of a box of length 6 cm, width 5 cm, and height 4 cm.
Answer:
It would i feel like its 132
Step-by-step explanation:
Your favorite team jersey is on sale for $32 this is a 36% discount what was the original price of the jersey.
I had gotten 52.48
thats what I used to figure out the answer
-2.8f+0.9f-13-8 please simplify this
Answer: -1.9f - 21
Step-by-step explanation:
Combined the like terms.
Correct me if I am incorrect.
PLEASE HELP ME WITH THIS
Answer:
35/132
Step-by-step explanation:
The probability of selecting a boy for president is 7/12, the ratio of the number of boys to the number of candidates. Then the probability of selecting a girl for vice president is 5/11, the ratio of the number of girls to the remaining number of candidates. The joint probability is ...
(7/12)(5/11) = 35/132 . . . P(b=P&g=VP)
__
We can also look at this another way.
The number of ways two candidates can be selected from 12 is 12P2 = 132. The number of ways that the first can be a boy and the second can be a girl is (7)(5) = 35. Then the probability of a (BG) pair from the 12 candidates is 35/132.
_____
Additional comment
These numbers assume that selection is random and all possibilities are equally-likely. That is unlikely to be the case in an election.
Graph y=2x+5 on the plane
Answer:
Incorrect
Step-by-step explanation:
for your slope go down two to the right one
Please help me Please help me Please help me Please help
Answer:
:(((((((
Step-by-step explanation: sorry i dont know
I really need help pls!!!
Answer:
Option 1
Step-by-step explanation:
To find the slope divide Mass (y) by Volume (x)
i have two Questions.
1. Find the unit rate of 90 miles/2 hours, in feet per second.
2.Find the unit rate of 120 miles in 8 hours, in feet per second.
(extra credit: Extra Credit: How many unique handshakes can be made between 5 people?)
Step-by-step explanation:
ww have that 90 miles /2 hours is given and we are asked to find it in feet per second.
[tex] \frac{90 \: mi}{2 \: hrs} \times \frac{5280 \: ft}{1 \: mi} \times \frac{1 \: hr}{60 \: min} \times \frac{1 \: min}{60 \: sec} = 66[/tex]
So we get
66 fps.
2.
[tex] \frac{120 \: miles}{8 \: hours} \times \frac{5280}{1 \: mile} \times \frac{1 \: hour}{60 \: min} \times \frac{1 \: min}{60 \: seconds} = 22[/tex]
So we get 22 fps.
Extra credit There is 5 people and 2 hands so we use the combinations formula.
n!/r!(n-r)!. where n is the number of objects (the number of people) and r is the things taken at the time( the hands)
Subsitue
[tex] \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 3 \times 2 \times 1} [/tex]
[tex] \frac{20}{2} = 10[/tex]
what's 9 plus 10 and not 21
Answer:
19
Step-by-step explanation:
What is the solution to this quadratic equation