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What does origin mean in term of complex numbers

Therefore, the value of q(α) is 0.

Let p(x) = x³ + ax² + bx + c be a polynomials with distinct roots α, β, and γ, where α, β, and γ are real numbers and α, β, and γ are also roots of another polynomial q(x)

.To find: the value of q(α).

Given:p(x) = x³ + ax² + bx + c

has three distinct roots α, β, and γ such that α, β, and γ are real numbers and α, β, and γ are also roots of q(x).

The root of p(x) are:

α, β, and γThe root of q(x)

are:α, β, and γ

Since α, β, and γ are the roots of q(x),

we have:q(x) = (x - α) (x - β) (x - γ) ... (1)

Let's evaluate q(α) using equation (1)

q(α) = (α - α) (α - β) (α - γ)q(α) = 0

(Since α, β, and γ are distinct)

Therefore, the value of q(α) is 0. Hence, the correct option is (D).

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Answer:

\(33\frac{1}{3}\)

Step-by-step explanation:

square is just multiplying things twice

(-3 1/3)(-3 1/3)

(-10/3)(-10/3)

100/3

33 1/3

Hopes this helps

Answer: 1

Step-by-step explanation:

(-3 1/3)= (-1/3)+(-1/3)+(-1/3) = -1

(-3 1/3)^2 = (-1)^2 = (-1)(-1) = 1

No, a Norman window is not a semicircle above a rectangular window.

A Norman window, also known as a "Normandy window" or "Romanesque window," is a specific architectural feature that consists of a rounded arch at the top with a rectangular opening below it. It is characterized by its combination of curved and rectangular elements.

The top portion of a Norman window is indeed a semicircular arch, which reflects the influence of Romanesque architectural styles. The arch is typically constructed using stone or other masonry materials and adds a sense of grandeur and elegance to the window design.

The semicircular arch can vary in size and may feature intricate detailing or decorative elements.

Below the semicircular arch, a rectangular opening is incorporated, which is the main area for letting in light. The rectangular section is usually wider than the arch and can be divided into smaller sections by mullions or transoms.

The rectangular shape of the lower portion provides a practical and functional space for placing glass panes or other materials.

Overall, the combination of the semicircular arch and rectangular opening in a Norman window creates a visually appealing and harmonious design. It is a distinctive feature commonly found in architectural styles inspired by Romanesque and Norman traditions.

In summary, a Norman window consists of a semicircular arch at the top and a rectangular opening below it, rather than a semicircle above a rectangular window.

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When slave starting a disabled vehicle, the term that serves an important safety consideration is c. The slaving vehicle engine must be running while connecting the slave cable

The dead car is started while the live vehicle's engine is running by inserting a slave cable into the receptacle on each vehicle.

Vehicles with manual transmissions rely heavily on the clutch slave cylinder. When the pedal is depressed, the clutch is disengaged and the transmission is shifted thanks to the slave and clutch master cylinders.

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This is because convenience samples are chosen based on the ease of access to participants and are not necessarily representative of the entire population.

This is because convenience samples are chosen based on the ease of access to participants and are not necessarily representative of the entire population.

In general, it is not expected that a convenience sample would provide an accurate representation of the full population.

A more accurate representation of the full population would require a random sample, which would ensure that every member of the population has an equal chance of being selected for the sample.

This would provide a more representative sample and allow for more accurate statistical analysis.

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Step-by-step explanation:

use substitution method so it will now look like

8x + 5(-4x) = 24

8x + (-20x) = 24

-12x = 24 (divide both sides by 12)

-x = 2 (multiply both sides by negative 1)

x = -2

substitute to find y

y= -4(-2)

=8

Answer:

\(x=-2\\y=8\)

Step-by-step explanation:

\(8x+5y=24\\y=-4x\)

We already have y in terms of, so the easiest way to do is by plugging that value in the first equation.

\(8x+5y=24\\8x+5(-4x)=24\\8x-20x=24\\-12x=24\\x=\frac{24}{-12} \\x=-2\)

After having found the value of x, replace it in the second equation to find y.

\(y=-4(-2)\\y=8\)

Answer: The average amount of pocket change per person is $2.06.

Step-by-step explanation:

To find the average amount of pocket change per person, we need to first add up all the amounts and then divide by the number of people (which is 7 in this case).

Adding up the amounts: $0.00 + $1.25 + $0.02 + $2.00 + $10.75 + $0.40 + $0.00 = $14.42

Dividing by the number of people: $14.42 ÷ 7 = $2.06 So the average amount of pocket change per person is $2.06.

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To find the percent of Lana's gross pay that is take-home pay, we need to subtract her total deductions from her gross pay and then calculate the percentage.

Gross pay = $3776

Deductions = $1020.33

Take-home pay = Gross pay - Deductions = $3776 - $1020.33 = $2755.67

To calculate the percentage, we divide the take-home pay by the gross pay and multiply by 100:

Percentage = (Take-home pay / Gross pay) * 100 = ($2755.67 / $3776) * 100 ≈ 72.94%

Therefore, approximately 72.94% of Lana's gross pay is her take-home pay.

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Answer:

See below ~

Step-by-step explanation:

For the question with colored rectangles, it asks to find the area.

The area can be found by multiplying the dimensions of the rectangle.

Blue rectangle :

Green rectangle :

Question 13 :

a. The distribution of x1 x2 is z1z2 ~ Cauchy(0,1). (b) The probability that x1 x2 is greater than 16 is 0.1056. (c) The distribution of 3x1 + 2x2 + x3, is given as N(38, 29).

A probability density function (PDF) expresses the likelihood that a continuous random variable will take a specified value or fall within a predetermined range of values. It is a derivative of the cumulative distribution function (CDF), which is the likelihood that a random variable will have a value that is less than or equal to a certain value.

The CDF is a function that converts every potential value of the random variable to a probability between 0 and 1, and it is defined for both discrete and continuous random variables.

a. Covert the x1 and x3 into standard normal variables by subtracting their means and dividing by their standard deviations:

z1 = (x1 - 4) / 2 ~ N(0,1)

z2 = (x2 - 8) / 3 ~ N(0,1)

The product is thus:

z1z2 ~ Cauchy(0,1)

b. The probability that x1 x2 is greater than 16:

Y / z1 ~ Cauchy(0,1)

Now,

z1 = Y / (z1z2) ~ Cauchy(0,1)

Here, the probability that x1 x2 > 16 is:

P(x1 x2 > 16) = P(Y / z1 > 16 / z1) = P(z1 < -Y / 16) + P(z1 > Y / 16)

= 2 * P(z1 < -Y / 16)

Substituting the value of z1 and Y we have:

P(x1 x2 > 16) = 2 * P(z1 < -16z1z2 / (9)) = 2 * Φ(-16z2 / 3) ≈ 0.1056

Hence, the probability that x1 x2 is greater than 16 is 0.1056.

c) The distribution of 3x1 + 2x2 + x3, is given as:

\(3x1 + 2x2 + x3 \~ N(34 + 28 + 12, 3^22^2 + 2^23^2 + 4^2) = N(38, 29)\)

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Answer:

im Pretty sure it’s 20 I did this awhile ago

Step-by-step explanation:

we have that

\(y=-x^2+36\)

we know that

Is the equation of a vertical parabola open down

so

the vertex is a maximum

step 1

convert the equation of the parabola in the vertex form

\(y=-x^2+36\)

\(y-36=-x^2\)

the vertex (h,k) is the point (0,36)

Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)

Part b) The points on the graph where the height of the tunnel is zero feet is when y=0

so

for y=0

\(-x^2+36=0\)

\(x^2=36\)

\(x=(+/-)6\)

the points are (-6,0)  and (6,0)

see the attached figure

Answer:

Step-by-step explanation:

To find the equation of the linear function that passes through the point (e, f(e)) on the graph of f(x) = -ln(x) and has a slope of m = -1/e, we will use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. In this case, the point is (e, f(e)) and the slope is m = -1/e.

Substituting the values into the point-slope form, we have:

y - f(e) = -1/e(x - e).

Since our function is f(x) = -ln(x), we can substitute f(e) with -ln(e), which simplifies to -1. Therefore, the equation becomes:

y + 1 = -1/e(x - e).

Rearranging the equation, we get:

y = -1/e(x - e) - 1.

So, the equation of the linear function that passes through the point (e, f(e)) and has a slope of -1/e is y = -1/e(x - e) - 1.

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The solution of the system goes to infinity as t gets large.

Consider the given system of differential equations: dx/dt = 3x + 4ydy/dt = −x − 2yNow, find the solution of the system:(2)   dx/dt + 2 dy/dt = 7xObserve the second equation and multiply it by 2:2  dy / dt = −2x − 4y(3)   dx/dt + 2 dy/dt = 3x − 4ySubstitute the value of dy/dt from (3) into (2):(2)   dx/dt + 3x − 4y = 7xSimplify this equation:dx/dt − 4x = 4yTake the laplace transform of both sides: Laplace{dx/dt − 4x} = Laplace{4y} ⇒ sX(s) − x(0) − 4X(s) = 4Y(s) ⇒ X(s) = {4Y(s)}/{s − 4}Now, find the Laplace transform of y(s):(1)   dy/dt = −x − 2y ⇒ Laplace{dy/dt} = −Laplace{x} − 2Laplace{y} ⇒ sY(s) − y(0) = −X(s) − 2Y(s) ⇒ Y(s) = {−X(s)}/{s + 2}Substitute the value of X(s) in the above equation, we get:Y(s) = {−4Y(s)}/[(s − 4)(s + 2)]Simplify this equation:Y(s) = {A}/{s − 4} + {B}/{s + 2}Now, find the values of A and B:Multiplying the above equation by (s − 4) and (s + 2), we get:Y(s) = A(s + 2) + B(s − 4)Simplify this equation:Y(s) = (A + B)s + 2A − 4BAs per the equation (3), we can say A + B = 0, 2A − 4B = −4On solving, we get A = 2, B = −2Therefore, the value of Y(s) is:Y(s) = {2}/{s − 4} − {2}/{s + 2}Now, substitute the value of X(s) and Y(s) in the following equation:dx/dt − 4x = 4yThe solution of the above differential equation is:x(t) = {2}/{3}e^{4t} − {5}/{3}e^{-2t}The above is the general solution of the given system of differential equations.Now, find what happens to the system as t gets large?As t gets large, the term {5}/{3}e^{-2t} will tend to zero and {2}/{3}e^{4t} will tend to infinity.

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Answer:

x2−x−6

Step-by-step explanation:

Answer:

(x-3)(x+2)

Step-by-step explanation:

The probability of James rolling a 1 on the red cube and a 1 on the blue cube is 1/36, or approximately 2.78%.

The probability that James rolls a 1 on the red cube and a 1 on the blue cube can be calculated using the formula P(A and B) = P(A) x P(B). In this case, the probability of rolling a 1 on the red cube (P(A)) is 1/6, and the probability of rolling a 1 on the blue cube (P(B)) is also 1/6. Multiplying these two probabilities together gives us \(P(A and B) = (1/6) x (1/6) = 1/36\). This means that the probability of James rolling a 1 on the red cube and a 1 on the blue cube is 1/36, or approximately 2.78%.

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The expression that is equivalent to negative three raised to the fourth power divided by negative three raised to the second power is (-3⁴) / (-3²)

Expression:

Expressions are the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Negative three raised to the fourth power divided by negative three raised to the second power.

Here we need to find the expression for this statement.

First, we have to divide the statement into two like,

"Negative three raised to the fourth power"

It can be written as,

=> (-3⁴)

And the for the next part,

"Negative three raised to the second power."

It can be written as,

=> (-3²)

Now we have to divide these two terms, the we get,

=> (-3⁴) / (-3²)

Therefore, the expression is (-3⁴) / (-3²).

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Answer:

265 miles

Step-by-step explanation:

Divide 106 by 2 and get 53. Now you know that Andre rides 53 miles per hour.

To find your answer, Multiply 106 by 2 and get 212. Add 53 to 212.

Result: 265 miles per 5 hours

Therefore, 265 would be your answer.

-kiniwih426

Answer:

ΔTFS ≅ ΔRFS (sas) because:

+) FT = FR (given)

+) FS ≅ FS (in the picture)

+) ∠TFS = ∠RFS ( SF bisects ∠TFR)

Step-by-step explanation:

I need a little more information is there anymore that you could give me?

Answer:

According to Stephen Few, charts reveal more than a collection of individual values. Because of their visual nature, they show the overall shape of your data. This is when you should use charts instead of tables: The message is contained in the shape of the values (e.g. patterns, trends, exceptions).

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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Answer:

domain[-infinity, infinity]

range[2, infinity]

The value of a₄₃ is 3.

Matrices is a plural form of a matrix, which is a rectangular array or a table where numbers or elements are arranged in rows and columns.

Here,  aₓₙ is the element of matrix in which x represents the number of row and n represents the number of column of element.

So, a₄₃ means element from 4th row and 3rd column.

4th row  =  [2  9   3   7]

3rd column = \(\left[\begin{array}{ccc}8\\6\\1\\3\end{array}\right]\)

the common value between them is 3.

Thus, the value of a₄₃ is 3.

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Step-by-step explanation:

30 days period multiply by 7 days

=210 therefore our answer is =210

Answer:

Following are the solution to the given question:

Step-by-step explanation:

\(\to 18000=2000 \times i \times 10 \\\\\to 18000=200000 \times i\\\\\to i=\frac{18000}{200000}\\\\\to i= \frac{18}{200}\\\\ \to i= \frac{9}{100}\\\\ \to 0.09\\\\\)

Calculating the percentage:

\(\to 0.09\times 100=9\%\)

The compensating variation is $13.52.

The compensating variation is the amount of money that Greg would need to be compensated for a price increase in order to maintain his original level of utility. In this case, Greg's utility function is u = x^0.38x^0.962. His income is $83.00, and he faces these prices: (P1, P2) = (4.00, 1.00). If the price of x increases by $1.00, then the new prices are (P1, P2) = (5.00, 1.00).

To calculate the compensating variation, we can use the following formula:

CV = u(x1, x2) - u(x1', x2')

where u(x1, x2) is Greg's original level of utility, u(x1', x2') is Greg's new level of utility after the price increase, and CV is the compensating variation.

We can find u(x1, x2) using the following steps:

Set x1 = 83 / 4 = 20.75.

Set x2 = 83 - 20.75 = 62.25.

Substitute x1 and x2 into the utility function to get u(x1, x2) = 22.13.

We can find u(x1', x2') using the following steps:

Set x1' = 83 / 5 = 16.60.

Set x2' = 83 - 16.60 = 66.40.

Substitute x1' and x2' into the utility function to get u(x1', x2') = 21.62.

Therefore, the compensating variation is CV = 22.13 - 21.62 = $1.51.

To two decimal places, the compensating variation is $13.52.

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