Which of the following are exterior angles? Check all that apply.

2 Answers:

z = 1 + i   and   z = -1 - i

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Explanation:

We want z to be a complex number in the form z = a+bi, where a,b are real numbers and [tex]i = \sqrt{-1}[/tex] is imaginary.

Let's plug that into the equation your teacher gave you

[tex]z^2 = 2i\\\\(a+bi)^2 = 2i\\\\(a+bi)(a+bi) = 2i\\\\a(a+bi)+bi(a+bi) = 2i\\\\a^2+abi+abi+b^2*i^2 = 2i\\\\a^2+2abi+b^2*(-1) = 2i\\\\a^2+2abi-b^2 = 2i\\\\(a^2-b^2)+2abi = 0+2i\\\\[/tex]

You could use the FOIL rule to take a shortcut. I'm deciding to be a bit more wordy to show a further breakdown how everything is multiplying out.

Notice that the real part a^2-b^2 must be 0 so that it matches the real part on the right hand side.

a^2-b^2 = 0

(a-b)(a+b) = 0 .... difference of squares rule

a-b = 0 or a+b = 0

a = b or a = -b

So whatever solution z = a+bi is, it must have either a = b or a = -b.

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If a = b, then the 2abi portion on the left side turns into 2a^2*i

Set this equal to 2i on the right hand side and isolate 'a'

[tex]2a^2*i = 2i\\\\2a^2 = 2\\\\a^2 = 1\\\\a = 1 \text{ or } a = -1\\\\[/tex]

So a = 1 leads to b = 1

Or a = -1 leads to b = -1

Two complex solutions so far are:   z = 1 + i   and   z = -1 - i  based on those two cases above.

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Now consider the case that a = -b

We'll effectively have the same steps as the previous section, but the equation to solve now is [tex]-2a^2*i = 2i\\\\[/tex]

The only difference is that negative is out front. You should find that it leads to a^2 = -1, but this has no solutions because we stated earlier that a,b were real numbers.

So if a = -b, then it concludes with a,b being nonreal numbers. Ultimately we rule out the case that a = -b is possible.

Put another way, note how -2a^2 is always negative which clashes with the idea that the right hand side is positive (ignore the 'i' portions). This contradiction means that no real values of 'a' will make the equation [tex]-2a^2*i = 2i\\\\[/tex] to be true.

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To wrap things up, we only have two solutions and they are  

z = 1 + i   and   z = -1 - i

You can use a tool like WolframAlpha to confirm this.

Answer:

Step-by-step explanation:

For a function given as,

f(x)= 2x + 2

Domain of the given function is → {-5, -1, 2, 3}

For the Range of the given function,

f(-5) = 2(-5) + 2

      = -8

f(-1) = 2(-1) + 2

      = -2 + 2

      = 0

f(2) = 2(2) + 2

     = 6

f(3) = 2(3) + 2

     = 8

Therefore, set for the range will be → {-8, 0, 6, 8}

Now plot the ordered pairs on the graph,

(-5, -8), (-1, 0), (2, 6), (3, 8)

Answer:

[tex]7x {}^{2} + 5x[/tex]

Step-by-step explanation:

[tex]9x {}^{2} + 8x - (2x {}^{2} + 3x) \\ \\ = 9x {}^{2} + 8x - 2x {}^{2} - 3x (remove \: brackets) \\\ \\ = 7x {}^{2} - 5x [/tex]

Answer:

C has a zero slope

Step-by-step explanation:

A horizontal line has a slope of zero

A vertical line has an undefined slope

A positive slope goes up from left to right

A negative slope goes down from left to right

Answer:

21

Step-by-step explanation:

5/3=35/x

3 x 35=105

5 x x= 5x

105=5x

105/5=5x/5

21=x

The number of people who bought the more expensive ticket is 21.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

Let the number of people be X so we can form the following expression given below:-

5/3=35/x

3 x 35=105

5 x x= 5x

105=5x

105/5=5x/5

21=x

Therefore the number of people who bought the more expensive ticket is 21.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ2

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Explanation:

Since f(x) is linear, this means f(x) = mx+b

Let's plug in x = 6

[tex]f(x) = mx+b\\f(6) = m*6+b\\f(6) = 6m+b[/tex]

Repeat for x = 2

[tex]f(x) = mx+b\\f(2) = m*2+b\\f(2) = 2m+b[/tex]

Now subtract the two function outputs

[tex]f(6)-f(2) = (6m+b)-(2m+b)\\f(6)-f(2) = 6m+b-2m-b\\f(6)-f(2) = 4m\\[/tex]

The b terms cancel out which is very handy.

Set this equal to 12, since f(6)-f(2) = 12, and solve for m

[tex]f(6)-f(2) = 12\\4m = 12\\m = 12/4\\m = 3\\[/tex]

So the slope of f(x) is m = 3

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Next, plug in x = 12

[tex]f(x) = mx+b\\f(12) = m*12+b\\f(12) = 12m+b[/tex]

We can then say:

[tex]f(12)-f(2) = (12m+b)-(2m+b)\\f(12)-f(2) = 12m+b-2m-b\\f(12)-f(2) = 10m\\[/tex]

Lastly, we plug in m = 3

[tex]f(12)-f(2) = 10m\\f(12)-f(2) = 10*3\\f(12)-f(2) = 30\\[/tex]

Answer:

0.6

Step-by-step explanation:

In this question, the | symbol means "given", so we can phrase the question as "Find the probability that a student watches more than one hour of TV given that they are in the 6th period class"

Next, because there is a 100% chance that the student is in the 6th period class, we can disregard the results of the 3rd period class.

Given that the student is in the 6th period class, there are 15 total students (as 9+6=15 = the sum of the yes and no answers for 6th period) and 9 students that said yes. Therefore, there is a 9/15 = 3/5 = 0.6 probability that a student watches more than 1 hour of TV given that they are in the 6th period class

Answer:

Step-by-step explanation:

[tex]R(x)=\frac{x+3}{x-5} \geq 0\\R(x)=0,gives~x+3=0,x=-3\\R(x)>0 ,if~both~numerator ~and~denominator~are~of~same~sign.\\let~x+3>0,x>-3\\and~x-5>0,x>5\\combining \\x>5\\\\again~let~x+3<0,x<-3\\x-5<0,x<5\\combining\\x<-3\\Hence~R(x)\geq 0\\if ~x \in ~[- \infty,-3]U(5,\infty)[/tex]

Answer:

Option B.

Step-by-step explanation:

3 points are collinear if we can draw a line that connects the points.

And we know that any 2 or 3 points are always coplanar because we can find a plane such that the 2 or 3 points belong to it.

In the image we can see that B, A, and E are at the same y-value, thus these points are collinear, then the points define a line, and these are 3 points, thus we know that are coplanar.

Then points A, B, and E are collinear and coplanar.

The correct option is B.

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Answer:

  30°

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°.

  230° +C +50° +50° = 360°

  C = 360° -330° = 30°

  m∠C = 30 degrees

Answer:

no i dont think it is

Step-by-step explanation:

Answer:

The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 7 - 1 = 6

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.9432.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.9432\frac{0.16}{\sqrt{7}} = 0.12[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.12 = 2.68 pounds.

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.12 = 2.92 pounds.

The 90% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.68 and 2.92 pounds.

Answer:

Step-by-step explanation:

This is nice and simple. I'm going to walk through it like I do when teaching this concept to my class for the first time. This is a good problem for that.

We are given a square and we are looking for the rate at which the area is increasing when a certain set of specifics are given. That means that the main equation for this problem is the area of a square, which is:

[tex]A=s^2[/tex] where s is a side.

Since we are looking for the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], we need to take the derivative of area formula implicitly:

[tex]\frac{dA}{dt}=2s\frac{ds}{dt}[/tex] that means that if [tex]\frac{dA}{dt}[/tex] is our unknown, we need values for everything else. We are given that the initial area for the square is 49. That will help us determine what the "s" in our derivative is. We plug in 49 for A and solve:

[tex]49=s^2[/tex] so

s = 7

We are also given at the start that the sides of this square are increasing at a rate of 8cm/s. That is [tex]\frac{ds}{dt}[/tex]. Filling it all in:

[tex]\frac{dA}{dt}=2(7)(8)[/tex] and

[tex]\frac{dA}{dt}=112\frac{cm^2}{s}[/tex]

The surface area of a square of side L is given by

[tex]A = L^2[/tex]

The rate of change of the area per unit time is

[tex]\dfrac{dA}{dt} = 2L\dfrac{dL}{dt}[/tex]

We can express the length L on the right hand side in terms of the area A [tex](L = \sqrt{A})[/tex]:

[tex]\dfrac{dA}{dt} = 2\sqrt{A}\dfrac{dL}{dt}[/tex]

[tex]\:\:\:\:\:\:\:=2(\sqrt{49\:\text{cm}^2})(8\:\text{cm/s})[/tex]

[tex]\:\:\:\:\:\:\:=112\:\text{cm}^2\text{/s}[/tex]

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Answer:

  (b)  (negative 2, StartFraction 5 over 3 EndFraction)

Step-by-step explanation:

The value of x is given, so you only need to substitute that into the first equation to find y.

  y = 2/3(-2) +3 = -4/3 +9/3

  y = 5/3

The solution is (x, y) = (-2, 5/3).

Answer:

negative 2, StartFraction 5 over 3 EndFraction)

Step-by-step explanation:

Answer:

X = 101.48

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Average of 62 seconds with a standard deviation of 24.5 seconds.

This means that [tex]\mu = 62, \sigma = 24.5[/tex]

If the manager wants to advertize that 95% of the time, they serve customers within X seconds, what is the value of X?

This is the 95th percentile of times, which is X when Z has a p-value of 0.95, so X when Z = 1.645.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.645 = \frac{X - 62}{24.5}[/tex]

[tex]X - 62 = 1.645*24[/tex]

[tex]X = 101.48[/tex]

Answer:

0.000000073

Step-by-step explanation:

Given number is,

7.3E - 8

In scientific notation number will be,

7.3 × 10⁻⁸

In standard form the number will be,

0.000000073

Given:

Pattern x: Starting number 5. Rule: Multiply by 3.

Pattern y: Starting number 20. Rule: Multiply by [tex]\dfrac{1}{2}[/tex].

To find:

The values for the given table.

Solution:

First value of x is 5.

The rule for pattern x is "number is multiply by 3".

Second value of x is:

[tex]5\times 3=15[/tex]

Third value of x is:

[tex]15\times 3=45[/tex]

The first value of y is 20.

The rule for pattern y is "number is multiply by [tex]\dfrac{1}{2}[/tex]".

Second value of y is:

[tex]20\times \dfrac{1}{2}=10[/tex]

Third value of y is:

[tex]10\times \dfrac{1}{2}=5[/tex]

Therefore, the values in the table are 5, 15, 45 and the y-values are 20, 10, 5 respectively.

Answer: I dont know if this is right

Step-by-step explanation:

EC/CA= ED/DB

EC/EA = DE/BA

EB/ED= AE/DE

DB/EB = CD/AE

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

Technician __Shutdown

Taylor, T___4

Rousche, R _ 3

Hurley, H__ 3

Huang, Hu___2

Gupta, ___ 5

The Numbe of samples of 2 possible from the 5 technicians :

We use combination :

nCr = n! ÷ (n-r)!r!

5C2 = 5!(3!)2!

5C2 = (5*4)/2 = 10

POSSIBLE COMBINATIONS :

TR, TH, THu, TG, RH, RHu, RG , HHu, HG, HuG

Sample means :

TR = (4+3)/2 = 3.5

TH = (4+3)/2 = 3.5

THu = (4+2) = 6/2 = 3

TG = (4 + 5) = 9/2 = 4.5

RH = (3+3) = 6/2 = 3

RHu = (3+2) /2 = 2.5

RG = (3 + 5) = 8/2 = 4

HHu = (3+2) = 2.5

HG = (3+5) = 8/2 = 4

HuG = (2+5) / 2 = 3.5

Mean of sample mean (3.5+3.5+3+4.5+3+2.5+4+2.5+4+3.5) / 10 = 3.4

Population mean :

(4 + 3 + 3 + 2 + 5) / 5 = 17 /5 = 3.4

Population Mean and mean of sample means are the same.

This distribution should be approximately normal.

Answer:

Option B

Step-by-step explanation:

Option A

a² - b² = (a+ b)(a - b)

It's a polynomial identity.

Option B

a³ + b³ = (a - b)(a² - ab + b²)

It's not a polynomial identity.

Because the identity is,

a³ + b³ = (a + b)(a² - ab + b²)

Option C

a³ - b³ = (a - b)(a² + ab + b²)

It's a polynomial identity.

Option D

(a²+ b²)(c² + d²) = (ac - bd)² + (ad + bc)²

                         = a²c² - 2abcd + b²d² + a²d² + b²c² + 2abcd

                         = a²c² + b²c² + b²d² + a²d²

                         = c²(a² + b²) + d²(a² + b²)

                         = (a²+ b²)(c² + d²)

Therefore, it's a polynomial identity.

Option B will be the answer.

Answer:

Option C

Step-by-step explanation:

Step 1:  Find the correct method

Option A is incorrect because we don't have m + 6 and 5m - 2

Option B is incorrect because that wouldn't show us the correct value

Option C is correct, once we solve for v, we can plug in v and get the value of m.  For example:  v + 6 = 5v - 2 → v + 8 = 5v → 8 = 4v → 2 = v.  Then we plug it into the other equation m = 2 + 6 → m = 8

Option D is incorrect because that wouldn't show us the correct value.

Answer: Option C

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Answer:

  (c) $72

Step-by-step explanation:

Each tile is 8/12 ft = 2/3 ft on a side. Then 8/(2/3) = 12 tiles will fit along each edge of the square area to be tiled. That is ...

  12 × 12 = 144

tiles will be needed to cover the area.

The cost of 144 tiles at $0.50 each is ...

  (144)($0.50) = $72.00

Answer:

See answers below

Step-by-step explanation:

From the given functions, the equivalent function for when x = 0 is -(x-1)²

h(x) = -(x-1)²

h(0) = -(0-1)²

h(0)= -(-1)²

h(0) = -1

when x = 2, the equivalent function is -1/2x - 1

h(x) =  -1/2x - 1

h(2) =  -1/2(2) - 1

h(2) = -1-1

h(2) = -2

when x = 5, the equivalent function is -1/2x - 1

h(x) =  -1/2x - 1

h(5) =  -1/2(5) - 1

h(5) = -5/2-1

h(5) = -7/2

Answer:

horizontal expansion factor of 2

2^x =2(2)=4

2^4=2×2×2×2= 16

Answer:

I AM VERY SORRY AARUSH KAPUSH

Step-by-step explanation:

9514 1404 393

Answer:

  c. 11

Step-by-step explanation:

The sum of all 6 numbers is ...

  6 × average of 6 = total of 6

  6 × 6 = 36 = total of 6

Then the remaining number is ...

  total of 5 + sixth number = total of 6

  25 + sixth number = 36

  sixth number = 36 -25 = 11

Answer:

i would switch

Step-by-step explanation:

your chance of picking the right door that has the grand price is 33.33% because 1 out of 3 doors has the prize and you have a 66.66% chance of being wrong.

*just know that the host will never reveal the grand prize first because then the tension of the game show is gone, etc *

after knowing the door that has a goat, are my chances of winning 50/50 (1 out of 2 doors) ?

no.

Always switch!

your chances are still the same as before (33.33%). like i mentioned the host won't reveal the grand prize first.

I will refer to 3 doors: X, Y, Z

So if your 1 out of 3 pick wasn't the money(you chose x), and the money is in, let's say door Y, then the host will reveal Z. If the money is in Z, the host reveals Y. IF you chose the money the first time (X), then the host can reveal either Y or Z.  no matter what, you are still stuck in that initial 33.33% chance that you chose right the very first time. But if you switch, regardless of the prize, you are now in the 66.66% zone. you have actually doubled your chances of winning.

to think about it in another way, when you are being asked to switch, you are given a dilemma : do you want to keep one envelope of do you want both of the others? you already know what is inside one of them (the goat). But since the one that will be revealed won't have the money in it, the chances that the other envelope has the prize are twice as high.

Answer:

0.9113

Step-by-step explanation:

Given :

Sample standard deviation of Stock X = 4.665

Sample standard deviation of Stock Y = 8.427

Sample Covariance = 35.826

The Correlation Coefficient, R is related to sample covariance and standard deviation using the formular :

R = Covariance(X, Y) / (SD(X) * (SD(Y))

R = 35.826 / (4.665 * 8.427)

R = 35.826 / 39.311955

R = 0.9113

Hence, correlation Coefficient, R = 0.9113 which depicts a strong positive relationship.

AS IN THE PICTURE.............