The image represents what geometric construction? A) Copy a triangle construction B) Copy a segment construction C) Parallel lines construction D) Perpendicular bisector and midpoint​

Answer:

6720

Step-by-step explanation:

The writing 8P5 represents the number of permutations of 8 elements  taken 5 at a time.

First Method :

8P5 = 8 × 7 × 6 × 5 × 4

       = 6720

Second Method :

\(8P5=\frac{8!}{\left( 8-5\right)!}\)

\(=\frac{8!}{ 3!}\)

\(=\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3!}{ 3!}\)

\(= 8 \times 7 \times 6 \times 5 \times 4\)

\(= 6720\)

Answer:

a. always, remain

b. always, remain

c. never, not remain, not remain

d. always, an equal distance, all

e. never, would not, all

Step-by-step explanation:

They are all correct, hope this helps -w-

Answer:1

Step-by-step explanation:2

2

The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.

An absolute function is defined as a function which consists of an algebraic expression that is within absolute value symbols.

Here,

The standard form of the absolute value function is written by,

f(x) = a|x|

Given that,

f(x) = 3|x|

Comparing this with the standard form, we get,

a|x| = 3|x|

Therefore, a = 3

Hence,

The value of a when the function f(x) = 3|xl is written in the standard form of an absolute value function is 3.

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Answer:

B. 4.00$

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

See below

Step-by-step explanation:

\(( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) = 1 - 2 { \cos}^{2} \theta \\ \\ LHS = ( \sin \theta - \cos \theta)( \sin \theta + \cos \theta) \\ \\ = \sin^{2} \theta - \cos^{2} \theta \\ \\ =1 - \cos^{2} \theta - \cos^{2} \theta \\( \because \sin^{2} \theta =1 - \cos^{2} \theta) \\ \\ = 1 - 2 { \cos}^{2} \theta \\ = RHS\)

Thus proved

Answer:

don't expect people to help when you comment bs under their questions for points, mad weird

Answer:

so rlly is that a quetion bc we cat solve that

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

Answer:

The answer is most likely A.

The reason why, is because since the earning in 6 hours is $94.50, so the hourly wage would be, $15.75 because:

94.50/6 = 15.75

Graph B, for the first hour, the amount of dollars is correct, but in 11 hours, it says 25.75, which is not correct so Graph B cannot be it.

Graph C, shows that at hour 1, that it is 15.75 dollars, but at hour 2 16.75, as well with hour 3, 17.75. The graph is showing an increase of 1 dollar per hour, which is not correct so graph C is not it.

Graph D shows that at hour 6, there is $94.50, which is correct, but at hour 12, its 100.50. This is not true because , the hour has increased by 6, and when it increased by 6, the amount of pay increased by 6 as well, which is not the right way in which you would do so.

Option A is correct!

Step-by-step explanation:

Hope it helps! =D

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

(3, 0) and (−1, −8)

Equation's:

2x − (x² − 9) = 6

2x - x²  + 9 = 6

-x² + 2x + 9 - 6 = 0

-x² + 2x + 3 = 0

x² - 2x - 3 = 0

x² - 3x + x - 3 = 0

x(x - 3) + 1(x - 3) = 0

(x + 1)(x - 3) = 0

x = -1, x = 3

If x = -1, then y = (-1)² - 9 = -8

If x = 3, then y = (3)² - 9 = 0

(x, y) = (-1, -8), (3, 0)

Answer:

In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.

To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.

Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.

The selection that comes closest to the correct value of the compound interest is option (c), which equals Rs. 1776.

To calculate the compound interest earned by the money lender on Rs. 7,000 for 3 years, we need to use the formula:

A = \(P(1 + r/n)^(nt)\)

where A is the amount after t years, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Let's first calculate the amount after 1 year at 7% interest compounded annually:

\(A = 7000(1 + 0.07/1)^(1*1) = Rs. 7490\)

Now, we can use this amount as the principal for the second year, and calculate the amount after 1 year at 8% interest compounded annually:

\(A = 7490(1 + 0.08/1)^(1*1) = Rs. 8087.20\)

Finally, we can use this amount as the principal for the third year, and calculate the amount after 1 year at 8.5% interest compounded annually:

\(A = 8087.20(1 + 0.085/1)^(1*1) = Rs. 8773.11\)

The compound interest earned over 3 years is the difference between the final amount and the principal:

CI = 8773.11 - 7000 = Rs. 1773.11

So the answer is (c) Rs. 1776, which is the closest option to the actual value of the compound interest.

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The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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Answer:

At least 3/4 of the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours.

Step-by-step explanation:

Chebyshev's Theorem states that:

1) at least 3/4 of the data lie within two standard deviations of the mean, that is, in the interval with endpoints x bar ±2s for samples and with endpoints μ±2σ for populations;

2) at least 8/9 of the data lie within three standard deviations of the mean, that is, in the interval with endpoints x bar ±3s for samples and with endpoints μ ± 3σ for populations;

3) at least 1−1/k² of the data lie within k standard deviations of the mean, that is, in the interval with endpoints x bar ± ks for samples and with endpoints μ ± kσ for populations, where k is any positive whole number that is greater than 1.

1) endpoints μ ± 2σ for populations;

μ = mean = 4

σ = standard deviation = 0.8

= 4 ± 2(0.8)

= 4 ± 1.6

= 4+ 1.6 = 5.6

= 4 - 1.6 = 2.4

Therefore, the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours is at least 3/4

Answer:

3/4

Step-by-step explanation:

The pairs of coordinates arranged from least to greatest based on the differences between the points are:

(-1,-2) and (1,-4)

(4,1) and (2,2)

(-5,2) and (-3,-2)

(3,-4) and (-2,1)

(5,-2) and (-1,-1)

Let's calculate the differences and arrange the pairs accordingly:

(4,1) and (2,2):

Difference in x-coordinates: 4 - 2 = 2

Difference in y-coordinates: 1 - 2 = -1

(-5,2) and (-3,-2):

Difference in x-coordinates: -5 - (-3) = -2

Difference in y-coordinates: 2 - (-2) = 4

(3,-4) and (-2,1):

Difference in x-coordinates: 3 - (-2) = 5

Difference in y-coordinates: -4 - 1 = -5

(-1,-2) and (1,-4):

Difference in x-coordinates: -1 - 1 = -2

Difference in y-coordinates: -2 - (-4) = 2

(5,-2) and (-1,-1):

Difference in x-coordinates: 5 - (-1) = 6

Difference in y-coordinates: -2 - (-1) = -1

Now let's arrange them in order from least to greatest based on the differences in the points:

(3,-4) and (-2,1) (difference: 5)

(-1,-2) and (1,-4) (difference: 2)

(4,1) and (2,2) (difference: 2)

(-5,2) and (-3,-2) (difference: 4)

(5,-2) and (-1,-1) (difference: 6)

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Answer:

B) 4,700

Step-by-step explanation:

6000 - 4000 = 2000

2000 in 15 year, find how much for each year

2000/ 15 = 133.3333333

133.3333333 estimated = 133

133 approximately for each year

1975 to 1980 is five years

133 x 5 = 665

4000 + 665 = 4665

4665 rounded the the nearest hundred

4700

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The equation z = 30x represents a direct variation the two variables, z and x, are directly proportional to each other. a.

Direct variation can be defined as a relationship between two variables where their values increase or decrease at the same rate.

In the case of the given equation, as x increases, z also increases proportionally.

Similarly, if x decreases, z will also decrease proportionally.

Direct variation can be represented as y = kx, where y and x are the variables, and k is the constant of variation.

In the given equation, we can see that z is the dependent variable, and x is the independent variable.

We can rewrite the equation as z = kx, where k = 30.

To understand how direct variation works, let's consider an example. Suppose we have an equation y = 5x, where y represents the cost of buying x apples at $5 per apple.

Here, the cost of buying apples is directly proportional to the number of apples purchased.

For instance, if we buy 10 apples, the total cost will be 10 × $5 = $50.

Similarly, if we buy 20 apples, the total cost will be 20 × $5 = $100.

Thus, we can see that the cost increases as the number of apples purchased increases, and vice versa.

The given equation z = 30x represents a direct variation is a type of relationship between two variables where their values increase or decrease proportionally.

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Answer:

3 texts by madelyn, there were 2 texts from aubrey

Step-by-step explanation:

the ratio of maddie to aubrey was 18:12 which is 3:2

so 3 by maddie = 2 by aubrey

i used maddie because its shorter

Answer:

6 + 6 is 12 and 12 + 6 is 18 so i think its for every 6 text sent and then 6 again (6 in both boxes)

Step-by-step explanation:

adore your sasha pfp

Answer:

The standard form of the equation of a circle with center at (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

We are given that the center of the circle is (4, -1), so h = 4 and k = -1. We also know that the circle passes through the point (-4, 1), which means that the distance from the center of the circle to (-4, 1) is the radius of the circle.

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So the radius of the circle is:

r = sqrt((-4 - 4)^2 + (1 - (-1))^2) = sqrt(100) = 10

Now we can substitute the values of h, k, and r into the standard form equation of a circle:

(x - 4)^2 + (y + 1)^2 = 10^2

Expanding the equation gives:

x^2 - 8x + 16 + y^2 + 2y + 1 = 100

Simplifying and putting the equation in standard form, we get:

x^2 + y^2 - 8x + 2y - 83 = 0

Therefore, the equation in standard form of the circle with center at (4, −1) and that passes through the point (−4, 1) is:

x^2 + y^2 - 8x + 2y - 83 = 0

Answer:

Step-by-step explanation:

Interest

Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15

The value of the car is solved by using the formula for depreciation which is  y = A(1 – r)t

definition of variables

where

y = current value, = ?

A = original cost, = $24,000

r = rate of depreciation, = 15% and

t = time, in years. = 4 years

substituting the variables

current value, y = A(1 – r)t

current value, y = 24000 * (1 - 0.15)⁴

current value, y = 12528.15

the depreciation is $12528.15

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Answer:

8

Step-by-step explanation:

Thanks I was reading it like "what?" lma oo

But thanks Have a good day!!

Answer:

slope = -5/4

Step-by-step explanation:

Because you have been given two points, you can use point-slope formula to find the slope. In the equation, "m" is the slope.

1st Point: (1,3)

2nd Point: (5, -2)

y₁ - y₂ = m(x₁ - x₂)                    <----- Point-Slope Equation

3 - (-2) = m(1 - 5)                       <----- Plug "x" and "y" values into equation

5 = m(-4)                                   <----- Combine like terms

-5/4 = m                                    <----- Divide both sides by -4

The divergence and the curl

A. Divergence of F is 11

B. The curl of F is (0, 0, 0)

C. The curl of F is (0, 0, 5). It is not possible to find a function f such that F = ∇f

What is Divergence?

Divergence is a vector operator in vector calculus that operates on a vector field to produce a scalar field that contains the quantity of the source of the vector field at each point.

To compute the divergence of a vector field \(F = (F_x, F_y, F_z)\), we use the formula:

\(div F = (dF_x/dx) + (dF_y/dy) + (dF_z/dz)\)

A. For the vector field F = (6x, 2y, 3z), we have:

       \(div F = (d(6x)/dx) + (d(2y)/dy) + (d(3z)/dz)\\= 6 + 2 + 3\\= 11\)

So the divergence of F is 11.

B. To compute the curl of a vector field \(F = (F_x, F_y, F_z)\), we use the formula:

 \(curl F = (dF_z/dy - dF_y/dz) i + (dF_x/dz - dF_z/dx) j + (dF_y/dx - dF_x/dy) k\)

For the vector field F = (6x, 2y, 3z), we have:

\(curl F = (d(3z)/dy - d(2y)/dz) i + (d(6x)/dz - d(3z)/dx) j + (d(2y)/dx - d(6x)/dy) k\\= (0 - 0) i + (0 - 0) j + (0 - 0) k\\= 0i + 0j + 0k\)

So the curl of F is (0, 0, 0).

C. For the vector field F = (3xy, 8y, 5z), we have:

\(curl F = (d(5z)/dy - d(8y)/dz) i + (d(3xy)/dz - d(5z)/dx) j + (d(8y)/dx - d(3xy)/dy) k\\= (0 - 0) i + (0 - 0) j + (8 - 3) k\\= 0i + 0j + 5k\)

So the curl of F is (0, 0, 5).

It is not possible to find a function f such that F = ∇f for either of these vector fields. The divergence and curl operator do not generally have an inverse that allows us to express a given vector field as the gradient of some function.

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