NEED HELP ASAP!!! At a movie theater, the price of 2 adult tickets and 4 child tickets is $48. The price of 5 adult tickets and 2 child tickets is $64.

Let x be the cost of an adult ticket and let y be the cost of a child ticket. Write and solve a system of equations to find the ticket price for one adult and for one child.

Answer:

Rotation of 180° clockwise around the origin

Step-by-step explanation: if you rotate the first triangle 90 degrees, it will be in the lower quarter, so you need to rotate it 1 more time.

The transformations are clockwise rotation 180° and translation down by 1 unit.

Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.

From the given graph, the coordinates of triangle PQR are P(2, 1), Q(4, 6) and R(4, 1).

Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise direction, we have (-x,-y).

Here,

P(2, 1) → P'(-2, -1)

Q(4, 6) → Q'(-4, -6)

R(4, 1) → R'(-4, -1)

The translation down by 1 unit, we get (x, y-k)

P'(-2, -1) → P'(-2, -2)

Q'(-4, -6) → Q'(-4, -7)

R'(-4, -1) → R'(-4, -2)

The coordinates of triangle P'Q'R' are P'(-2, -2), Q(-4, -7) and R'(-4, -2)

Therefore, the transformations are clockwise rotation 180° and translation down by 1 unit.

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The general solution of the differential equation x'(t) = Ax(t), where A is the matrix [0 -1; 1 0], is x(t) = [(c₁² - c₂² + 2ic₁c₂)[tex]e^{(it)[/tex] + (2c₁c₂ - c₁² + c₂²)[tex]e^{(it)[/tex]][1, i].

To solve the differential equation x'(t) = Ax(t), where A is the given matrix [0 -1; 1 0], we can use the method of finding the eigenvalues and eigenvectors.

Step 1: Find the eigenvalues λ of the matrix A by solving the characteristic equation |A - λI| = 0.

The characteristic equation for A is:

|0-λ -1| = 0

|1 0-λ|

Expanding the determinant gives:

(-λ)(-λ) - (-1)(1) = 0

λ² + 1 = 0

Solving the equation, we get two eigenvalues: λ₁ = i and λ₂ = -i.

Step 2: Find the eigenvectors corresponding to each eigenvalue.

For λ₁ = i:

(A - λ₁I)u₁ = 0

|0- i -1| |x₁| = |0|

|1 0- i| |x₂| |0|

Simplifying the equation gives:

-ix₁ - x₂ = 0

x₁ - ix₂ = 0

Solving this system of equations, we get the eigenvector u₁ = [1, i].

For λ₂ = -i:

(A - λ₂I)u₂ = 0

|0+i -1| |x₁| = |0|

|1 0+i| |x₂| |0|

Simplifying the equation gives:

ix₁ - x₂ = 0

x₁ + ix₂ = 0

Solving this system of equations, we get the eigenvector u₂ = [1, -i].

Step 3: Write the general solution as x(t) = c₁x₁(t) + c₂x₂(t), where c₁ and c₂ are constants.

The general solution to the differential equation x'(t) = Ax(t) is:

x(t) = c₁[1, i][tex]e^{(i\lambda_1 t)[/tex] + c₂[1, -i][tex]e^{(i\lambda_2 t)[/tex]

= c₁[1, i][tex]e^{(it)[/tex] + c₂[1, -i][tex]e^{(it)[/tex]

Expanding and simplifying the solution:

x₁(t) = c₁[tex]e^{(it)[/tex] + c₂[tex]e^{(it)[/tex]

x₂(t) = ic₁[tex]e^{(it)[/tex] - ic₂[tex]e^{(it)[/tex]

Therefore, the general solution is:

x(t) = c₁[c₁[tex]e^{(it)[/tex] + c₂[tex]e^{(it)[/tex]][1, i] + c₂[ic₁[tex]e^{(it)[/tex] - ic₂[tex]e^{(it)[/tex]][1, -i]

= (c₁c₁[tex]e^{(it)[/tex] + c₁c₂[tex]e^{(it)[/tex] + ic₁c₁[tex]e^{(it)[/tex] - ic₁c₂[tex]e^{(it)[/tex])[1, i] + (ic₁c₁[tex]e^{(it)[/tex] - ic₁c₂[tex]e^{(it)[/tex] - c₂c₁[tex]e^{(it)[/tex] - c₂c₂[tex]e^{(it)[/tex])[1, -i]

= [(c₁² - c₂² + 2ic₁c₂)[tex]e^{(it)[/tex] + (2c₁c₂ - c₁² + c₂²)[tex]e^{(it)[/tex]][1, i]

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The question is -

What's the general solution (c1x1(t) +c2x2(t)) of a differential equation x'(t) = Ax(t) with a matrix A = [0 -1; 1 0]?

Answer:

a= −1/9y+64/9

Answer:

86.6

Step-by-step explanation:

Add them all up and divide by how many scores

the coordinates of the reflected point are (4, 2).

When a point is reflected about the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

The original point is (-4, 2). If we reflect this point about the y-axis, the x-coordinate becomes positive, and the y-coordinate remains unchanged.

Negating the x-coordinate, we get:

x-coordinate: -(-4) = 4

y-coordinate: 2 (unchanged)

Given the point (-4, 2), reflecting it about the y-axis would result in the x-coordinate changing its sign while the y-coordinate remains unchanged.

Therefore, the coordinates of the reflected point are (4, 2).

Among the options provided, the correct answer is (c) (4, 2).

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Answer:

maybe it meane 11/a

Step-by-step explanation:

Answer:

The bracket is the binomial.

The definition is: [tex]\binom{n}{k} = \frac{n!}{k!\cdot (n-k)!}[/tex]

Note that [tex]\binom{n}{k} = \binom{n}{n-k}[/tex]

The meaning is "if we have n elements, how many ways are there to choose k of them?" From this definition it should be obvious that [tex]\binom{n}{k} = \binom{n}{n-k}[/tex] - if you're picking k, it's just as many ways as choosing the (n-k) that you're not picking.

The coefficient can be found by realizing that to get x^9, we need to choose (from the full multiplication):

There's [tex]\binom{11}{9}[/tex] ways to do that, so the component for x^9 will be:

[tex]\binom{11}{9} \cdot 3^2 \cdot x^9 = \frac{11!}{2!\cdot 9!} \cdot 3^2 \cdot x^9 = \frac{10\cdot 11}{2} \cdot 3^2 \cdot x^9 = 55 \cdot 9 \cdot x^9 = 495x^9[/tex]

So:

a = 2

Coefficient is 495

Answer:

516 miles

Step-by-step explanation:

Answer:

quizlet or quizzes

Step-by-step explanation:

Answer:

y=2^x

Step-by-step explanation:

Answer:

The lateral surface area of the prism shown is 1021 unit^2.

Step-by-step explanation:

2((21*9)/2) + (17*16) + (21*16) + (14*16) = 1021 unit^2

Answer: The lateral surface area of a prism is the sum of the areas of its lateral faces. The total surface area of a prism is the sum of the areas of its lateral faces and its two bases

=ph where p represents the perimeter of the base and h represents the height of the prism.

Answer:

An insurance actuary is a professional that analyzes financial risk using mathematics, statistics, and financial theories.

Step-by-step explanation:

Most actuaries work in the insurance industry and help insurance companies create and price insurance policies based on the likelihood that they will have to pay out claims.

Hope this helped!!!

Answer:

2,7

Step-by-step explanation:

To solve this type of problem you simply plug the left number or x value in the ordered pair into the function and then see if it equals the right or y value. So we would plug 4 in for x and get 16, you then do the same thing for the other two pairs and find out that when you plug 2 into the equation, it does not equal 7

Answer:

10

Step-by-step explanation:

The principal, real, root of:

100−−−√2

=10

All roots:

10

−10

100 is a perfect square

Answer:

The answer is D

Step-by-step explanation:

:))))))))

Answer:

D is not true

Step-by-step explanation:

you can tell because 19-11 is 8 and that don't equal 10

Answer:

A

Step-by-step explanation:

Answer: I would say it's B

Step-by-step explanation: The reason is because whiskers are primary to have, Sharp claws is a tool for animals to get food, and large beaks are used to pick at the food so they don't eat the wrong things.

Answer:

The answer is "Option C"

Step-by-step explanation:

Please find the complete question in the attached file.

In this question its value of P is 0.0644, the significance level is higher than 0.05. Which doesn't reject [tex]H_o[/tex],

Answer: C

Step-by-step explanation: EDGE 2022

Answer:

a part

Step-by-step explanation:

Attachment added....

Hope it helps :)

Answer:

1/2c

Step-by-step explanation:

A breakfast chef used different amounts of ill when

making pancakes, depending on the number of panes ordered. The results are shown below.

1/2c, 1/4c, 1/2c, 3/4c, 1/2c, 3/4c, 1/2c, 1/4c, 1/2c, 1/2c

What is the average amount of milk used for an order of pancakes?

Average amount of milk used for an order of pancakes = {1/2c + 1/4c + 1/2c + 3/4c + 1/2c + 3/4c + 1/2c + 1/4c + 1/2c + 1/2c} ÷ 10

= {6(1/2c) + 2(1/4c) + 2(3/4c)} ÷ 10

= {6/2c + 2/4c + 6/4c} ÷ 10

= {3c + 1/2c + 3/2c} ÷ 10

= {(6+1+3) / 2}c ÷ 10

= 10/2c ÷ 10

= 5c ÷ 10

= 5/10c

= 1/2c

The average amount of milk used for an order of pancakes = 1/2c

Answer:

3rd choice

Step-by-step explanation:

You start with: aebt = c

Divide both sides by a: ebt = c/a

Take the natural log: ln(ebt) = ln(c/a)

which gives you: bt = ln(c/a)

Divide by b: t = ln(c/a) / b.

Answer:

What is the lenght and the other things?

Step-by-step explanation:

Brainliest?

Answer:

see photo

Step-by-step explanation:

Answer:

7238 units^3

Step-by-step explanation:

The formula for the volume of a sphere of radius 12 units is

V = (4/3)(pi)r^3.  

Here, with r = 12 units,

V = (4/3)(pi)(12 units)^3 = 7238 units^3

Answer:

V = 2304π units³

Step-by-step explanation:

V = (4/3)πr^3

V = (4/3)π(12)^3

V = (4/3)π(1728)

V = 2304π units³

The statement A, E, G , H and L describes state of nature whereas, statement B, C, D, F, I, J and K describes decision alternative.

A. Government regulations: State of nature - Government regulations are external factors that affect the operations of manufacturing companies. These are not decisions that companies make on their own.

B. Hiring options: Decision alternative - It involves decisions made by the manufacturing company regarding the selection and recruitment of potential candidates.

C. Management bonuses: Decision alternative - Decisions is made by the manufacturing company regarding the allocation of bonuses to its management team.

D. New plant location: Decision alternative - Decision is taken by the manufacturing company regarding set up of new plant.

E. Win or lose a court case: State of nature - Court outcome in a case is not in the control of the manufacturing company.

F. Challenge or settle a lawsuit: Decision alternative - Choosing whether to challenge or settle a lawsuit this decision is taken by the manufacturing company.

G. Demand level at 50, 60, 70+:  State of nature - Demand level is determined by market forces and consumer behavior which are external factors.

H. Supply level at 50, 60, 70+: State of nature - Similar to demand level, the supply level is determined by external factors such as availability of resources etc.

I.  Advertising budget level: Decision alternative - Decision is made by the manufacturing company regarding the allocation of financial resources and budget for advertising.

J. Type of gasoline to use: Decision alternative - Decision is made by the manufacturing company regarding the selection of fuel to use.

K. Suppliers to purchase from: Decision alternative - Decisions is made by the manufacturing company regarding the choice of suppliers for purchase of raw materials, components, or other goods.

L. Frequency of machine breakdown: State of nature - Occurrence of unplanned breakdowns or malfunctions of machinery is beyond the control of the manufacturing company.

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The condition number for the problem of evaluating the function f(x) = 1/cos(x) near the point x = 1.5708 is approximately 10 raised to power 16

This means that a small change in the input x can cause a large change in the output f(x).

The condition number of a function is a measure of how sensitive the function is to changes in its input. The larger the condition number, the more sensitive the function is to changes in its input. The condition number for the function f(x) = 1/cos(x) can be estimated as follows:

K = |f'(x)| / |f(x)|

where f'(x) is the derivative of f(x) and f(x) is the value of f(x) at the point x. At the point x = 1.5708, f'(x) = -1 and f(x) = 0.017453292519943295. Therefore, the condition number is approximately:

K = |-1| / |0.017453292519943295| = 10 raised to power 16

This means that a small change in the input x can cause a large change in the output f(x). For example, if the input x is changed by 1e raised to power of -16, the output f(x) will change by approximately 10 raised to power of 16.

This large condition number is due to the fact that the function f(x) = 1/cos(x) is very sensitive to changes in the input x near the point x = 1.5708. This is because the cosine function is very close to zero at this point.

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The spring constant, k = 27 N/m. The system is critically damped. The position function of the object is x(t) = e-6t(cos √3t + √3/3 sin √3t).

(a) Given, m = 1 kg, c = 12 and the spring is stretched 0.5 meters by a force of 13.5 N. We need to find the spring constant k. Let's consider the force applied on the spring, F = -kx

Here, x = 0.5 m and F = 13.5 N. So, 13.5 = -k (0.5) => k = -27 N/m

Since, we cannot have negative spring constant. Therefore, k = 27 N/m.

(b) The given differential equation is x" + 12x' + 27x = 0.

On comparing with the general equation of a damped mass-spring system, we get m = 1 kg, c = 12, k = 27.

The damping factor is defined as β = c/2m = 6.

Using the damping factor we can determine the type of the system. c2 - 4mk > 0 - overdamped systemc2 - 4mk = 0 - critically damped systemc2 - 4mk < 0 - underdamped system In this case, c2 - 4mk = 12^2 - 4(1)(27) = 0

This indicates that the system is critically damped.

(c) The general equation for a damped mass-spring system is x(t) = e-βt(A cos ωdt + B sin ωdt)

Where, A and B are constants that are determined using initial conditions. x(0) = A = 1 and x'(0) = -βA + ωdB/dt = -2 => B = (1/ω) (-βA + 2)

Now, we need to determine ω.ω2 = k/m - β2/4m2 = 27/1 - (12/2)2/4(1)(27) = 3ω = √3

Substitute the value of A, B and ω in the general equation, we get x(t) = e-6t(cos √3t + √3/3 sin √3t)

Hence, the position function of the object is x(t) = e-6t(cos √3t + √3/3 sin √3t).

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Answer:

The equation to solve to find the number of yellow marbles =

3y + y = 500

4y = 500

The number of yellow marbles = 125

Step-by-step explanation:

Let the number of

Blue marbles = x

Yellow marbles = y

A large jar contains 500 marbles.

x + y = 500

All of the marbles in the jar are either blue or yellow, and there are 3 times as many blue marbles as yellow marbles.

3y = x

Hence, we substitute 3y for ymx in the above equation

3y + y = 500

4y = 500

y = 500/4

y = 125

The number of yellow marbles = 125

The number of snowboards that must be sold for the company to break even is: 9000

The function that models the profit is given as:

P(x) = -5x² - 30x + 675

where:

P(x) is the profit in thousands of dollars

x is the number of snowboards sold in thousands

For the company to break even, it means that P(x) = 0. Thus:

-5x² - 30x + 675 = 0

Using quadratic formula to solve this gives us":

x = [-(-30) ± √((-30)² - 4(-5 * 675)]/(2 * -5)

x = 9

This is in thousands and means the break even will be when the sold amount is 9000 snowboards

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Answer:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.