The shape on the left is transformed to the shape on the right.

Triangle W X Y is rotated to triangle W prime X prime Y prime.

Which of the following statements describes the transformation?
W prime X prime Y prime right-arrow W X Y
W X Y right-arrow W prime X prime Y prime
W X Y right-arrow Y prime X prime W prime
X prime Y prime W prime right-arrow W X Y

The vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.

The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.

It is given that:

The coordinates are:

Rectangle EFGH has vertices E(−3, 4), F(−2, 4), G(−2, −2), and H(−3, −2).

After applying dilation with a scale factor of 3:

E(−3, 4) → E'(-3x3, 4x3) = E'(-9, 12)

Similarly,

F(−2, 4) → F'(-6, 12)

G(−2, −2) → G'(-6, -6)

H(−3, −2) → H'(-9, -6)

Thus, the vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.

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Answer:

resistant

because the median is not affected by the size of an outlier and does not change even if a particular outlier is replaced by an even more extreme value, we say the median is resistant to outliers.

Part a:  What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost

The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)

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a.  P(X > 4) is approximately 0.3713. b. P(X = 2) is approximately 0.1465. c. P(X < 1) is approximately 0.9817.

a. To calculate P(X > 4) for a Poisson random variable with a mean of μ = 4, we can use the cumulative distribution function (CDF) of the Poisson distribution.

P(X > 4) = 1 - P(X ≤ 4)

The probability mass function (PMF) of a Poisson random variable is given by:

P(X = k) = (e^(-μ) * μ^k) / k!

Using this formula, we can calculate the probabilities.

P(X = 0) = (e^(-4) * 4^0) / 0! = e^(-4) ≈ 0.0183

P(X = 1) = (e^(-4) * 4^1) / 1! = 4e^(-4) ≈ 0.0733

P(X = 2) = (e^(-4) * 4^2) / 2! = 8e^(-4) ≈ 0.1465

P(X = 3) = (e^(-4) * 4^3) / 3! = 32e^(-4) ≈ 0.1953

P(X = 4) = (e^(-4) * 4^4) / 4! = 64e^(-4) / 24 ≈ 0.1953

Now, let's calculate P(X > 4):

P(X > 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))

        = 1 - (0.0183 + 0.0733 + 0.1465 + 0.1953 + 0.1953)

        ≈ 0.3713

Therefore, P(X > 4) is approximately 0.3713.

b. To calculate P(X = 2), we can use the PMF of the Poisson distribution with μ = 4.

P(X = 2) = (e^(-4) * 4^2) / 2!

        = 8e^(-4) / 2

        ≈ 0.1465

Therefore, P(X = 2) is approximately 0.1465.

c. To calculate P(X < 1), we can use the complement rule and calculate P(X ≥ 1).

P(X ≥ 1) = 1 - P(X < 1) = 1 - P(X = 0)

Using the PMF of the Poisson distribution:

P(X = 0) = (e^(-4) * 4^0) / 0!

        = e^(-4)

        ≈ 0.0183

Therefore, P(X < 1) = 1 - P(X = 0) = 1 - 0.0183 ≈ 0.9817.

Hence, P(X < 1) is approximately 0.9817.

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Logarithm ln3 is approximately 1.682.

Logarithm, the exponent or power to which a base must be raised in order to produce a specific number.

The linear approximation of the natural logarithm function near x=e is given by y ≈ ln(e) + (y'(e))(x-e), where y'(e) is the derivative of the logarithm function at x=e.

Since ln'(x) = 1/x, we have y'(e) = 1/e.

Substituting x=3 and e=2.71828... into the approximation, we get:

ln(3) ≈ ln(e) + (1/e)(3-e) = ln(e) + (3-e)/e

ln(e) = 1, so the result is:

ln(3) ≈ 1 + (3-e)/e ≈ 1 + 0.682 ≈ 1.682.

Hence, ln3 = 1.682.

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The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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Answer:

bff

Step-by-step explanation:

amnsnsmsms.s.s.s.d.d..xx.dontmind

The area between the curves y = 2x^2 and y = x^3 from x = 0 to x = 1/2 is 5/96 square units.

The area between the curves y = 2x^2 and y = x^3 from x = 0 to x = 1/2 can be found by subtracting the area under the curve y = x^3 from the area under the curve y = 2x^2 over the given interval.

To calculate the area, we need to integrate the difference between the two functions. Let's proceed with the calculation:

The area, A, is given by:

A = ∫[0, 1/2] (2x^2 - x^3) dx

To find the antiderivative of each term, we use the power rule of integration:

∫x^n dx = (1/(n+1))x^(n+1) + C

Applying the power rule to each term, we have:

A = [(2/3)x^3 - (1/4)x^4] evaluated from 0 to 1/2

Substituting the limits of integration, we get:

A = [(2/3)(1/2)^3 - (1/4)(1/2)^4] - [(2/3)(0^3) - (1/4)(0^4)]

Simplifying further:

A = [(2/3)(1/8) - (1/4)(1/16)] - [0 - 0]

A = (1/12) - (1/64)

A = 8/96 - 3/96

A = 5/96

Therefore, the area between the curves y = 2x^2 and y = x^3 from x = 0 to x = 1/2 is 5/96 square units.



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The area of the shaded part in figure A is 24 square units and the area of the shaded part in figure B is 27 square units.

The given figure A can be divided into two rectangles.

One rectangle has length=6 units and breadth= 2 units.

So, area of a rectangle = 6×2 =12 square units

Second rectangle has length=4 units and breadth= 3 units.

So, area of a rectangle = 4×3 =12 square units

Total area = 12+12 =24 square units

In the given figure B,

Area of a large square is side² = 6²

= 36 square units

Area of a large square is side² = 3²

= 9 square units

Area of shaded = 36-9

= 27 square units

Therefore, the area of the shaded part in figure A is 24 square units and the area of the shaded part in figure B is 27 square units.

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The partial derivatives of f(x, y) are:

∂f/∂x = \(y^2/(x^2+y^2)^(3/2)\)

∂f/∂y = \(x^2/(x^2+y^2)^(3/2)\)

To find the partial derivatives of \(f(x, y) = xy/sqrt(x^2 + y^2)\), we need to differentiate with respect to x and y while treating the other variable as a constant.

Partial derivative with respect to x:

To find the partial derivative of f(x, y) with respect to x, we differentiate the function with respect to x while treating y as a constant. Using the quotient rule, we get:

∂f/∂x = y(√( \((x^2+y^2)) - x y(x^2+y^2)^(-1/2)(2x))/((x^2+y^2))\)

Simplifying the expression, we get:

∂f/∂x = \(y^2/(x^2+y^2)^(3/2)\)

Partial derivative with respect to y:

To find the partial derivative of f(x, y) with respect to y, we differentiate the function with respect to y while treating x as a constant. Using the quotient rule, we get:

∂f/∂y = (x(√\((x^2+y^2)) - xy(x^2+y^2)^(-1/2)(2y))/((x^2+y^2))\)

Simplifying the expression, we get:

∂f/∂y = \(x^2/(x^2+y^2)^(3/2)\)

Therefore, the partial derivatives of f(x, y) are:

∂f/∂x = \(y^2/(x^2+y^2)^(3/2)\)

∂f/∂y = \(x^2/(x^2+y^2)^(3/2)\)

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The maximum area of the rectangle inside the ellipse is 2ab.

Given that,

Ellipse = x2 / a2 + y2 / b2 = 1

we know the general coordinates of any point in an ellipse of the equation

x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)

So, we take general vertices of rectangles as

(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)

So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ

So, its area will be ab4sinθcosθ (Length x Breadth)

Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A

Now A=2absin2θ

Now as the area is the maximum given in the question, we have to differentiate it with respect to θ

dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)

Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ =  π / 2 and θ=π / 4

So now we to put θ=π / 4 in the equation of area which is A=2absin2θ

We get as A=2absin2π / 4=2absinπ / 2=2ab

Hence the max area of the rectangle inside the ellipse is 2ab.

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Angle-Angle (AA) similarity postulate,  if two angles of one triangle are congruent to two angles of another, then the triangles are similar.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

As per the diagram,

Triangles RPQ & RST are similar since

∠P = ∠S & ∠Q = ∠T

Side - side - side (SSS) similarity theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Triangles RPQ & RST are similar since

RP/RS = RQ/RT = ST/PQ

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The volume of the cylinder after the prism is cut out is 593 cm^3.

To calculate the volume of the cylinder after the prism is cut out, we need to first determine the volume of the prism that will be removed. This can be found by multiplying the length, width, and height of the prism. Once we have this value, we can subtract it from the original volume of the cylinder.

For example, if the cylinder has a radius of 5 cm and a height of 10 cm, and the prism to be removed has a length of 6 cm, a width of 4 cm, and a height of 8 cm, we can calculate the volume of the prism as follows:

Volume of prism = length x width x height
Volume of prism = 6 cm x 4 cm x 8 cm
Volume of prism = 192 cm^3

To find the volume of the cylinder after the prism is cut out, we simply subtract the volume of the prism from the original volume of the cylinder:

Volume of cylinder = pi x radius^2 x height
Volume of cylinder = 3.14 x 5^2 x 10
Volume of cylinder = 785 cm^3

Volume of cylinder after prism is cut out = 785 cm^3 - 192 cm^3
Volume of cylinder after prism is cut out = 593 cm^3

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======================================

Work Shown:

1 inch = 0.35 miles

3.5*(1 inch) = 3.5*(0.35 miles)

(3.5*1) inches = (3.5*0.35) miles

3.5 inches = 1.225 miles

---------------

Another way to solve:

(1 inch)/(0.35 miles) = (3.5 inches)/(x miles)

1/0.35 = 3.5/x

1*x = 0.35*3.5

x = 1.225

Answer: B. Start with 45 tiles and separate them into 15 same-sized groups

Step-by-step explanation:

In this case, 45 is divided by 15

#1 we should start with the total amount (dividend) that is going to be divided which is 45

#2 we should separate the dividend into the divisors amount which is 15

with all the steps, we will get the 3 groups of 15 which will be the answer

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Answer:

its b sorry im late

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

when x is 0.5 then y value is 3, x is 1.5 then y is 9 and x is 4.5 then y is 27.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other

In the given table the value of x is 0.5 and value of y is 3

y/x=3/0.5=6

In the second row the value of x is 1.5 we need to find value of y.

3/0.5=y/1.5

4.5=0.5y

Divide both sides by 0.5

y=9

In third row the value of x is 4.5 and y is 27

Hence, when x is 0.5 then y is 3, x is 1.5 then y value is 9 and x is 4.5 then y is 27.

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Answer:

D hopefully this have helped you !

Step-by-step explanation:

The solution is Option B.

The total net-worth of Emily is given by the equation A = $ 87,025

An individual's net worth is the difference between their assets (both long-term and short-term) and their liabilities (long-term and short-term).

The net worth of a company is equivalent to its equity, which refers to the net assets owned by the stockholders after paying off all debts.

So , Net Worth = Assets - Liabilities

Given data ,

Let the net worth of Emily be represented as A

Now , the equation will be

The assets of Emily are = Checking account $750 + Automobile (current value) $8,950 + House (current value) $92,500 + Savings account $1,350 + Investments $4,000

The total assets of Emily = $107,550

And , the liabilities of Emily are = Credit card debt $3,800 + Student loans $15,750 + Personal loans $975 + Total Liabilities $20,525

Now , the total liabilities of Emily = $20,525

So , the net worth = Assets - Liabilities

Substituting the values in the equation , we get

Net worth of Emily A = $107,550 - $20,525

On simplifying the equation , we get

Net worth of Emily A = $ 87,025

Hence , the net worth of Emily is $ 87,025

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Point U would be (1, 1)

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow these steps:

Calculate the characteristic equation by subtracting the identity matrix I multiplied by the scalar λ from matrix A, and set the determinant of this resulting matrix equal to zero. The characteristic equation is given by det(A - λI) = 0.Solve the characteristic equation to find the eigenvalues (λ).

Let's assume we have a 2x2 matrix A:

  | a  b |

A = | c d |

To find the eigenvalues, we need to calculate the characteristic equation:

det(A - λI) = 0,

where I is the 2x2 identity matrix and λ is the eigenvalue.

A - λI = | a-λ b |

| c d-λ |

The determinant of this matrix is:

(a-λ)(d-λ) - bc = 0,

which simplifies to:

λ² - (a+d)λ + (ad - bc) = 0.

This quadratic equation gives us the eigenvalues.

Solve the quadratic equation to find the values of λ. The solutions will be the eigenvalues.

Once you have the eigenvalues, substitute each value back into the equation (A - λI)v = 0 and solve for v to find the corresponding eigenvectors.

For each eigenvalue, set up the homogeneous system of equations:

(A - λI)v = 0,

where v is the eigenvector.

Solve this system of equations to find the eigenvectors corresponding to each eigenvalue.

To find the eigenvalues and eigenvectors of a 2x2 matrix, follow the steps mentioned above. The characteristic equation gives the eigenvalues, and by solving the corresponding homogeneous system of equations, you can determine the eigenvectors.

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Answer:

(1) let pen = x

let pencil= y

i) y ≤ 5x

ii) 5x + 2y ≤ 40

Step-by-step explanation:

at most = maximum

The solution to the linear programming problem 0.3x₁ + 0.1x₂ ≤ 1.8 using the simplex method shows that the problem has optimal solutions.)

Convert the inequality into an equation by subtracting 1.8 from both sides:
0.3x₁ + 0.1x₂ - 1.8 ≤ 0

Introduce slack variables to convert the inequality into an equation:
0.3x₁ + 0.1x₂ + s₁ = 1.8

Set up the initial simplex tableau:

┌───┬───┬───┬───┬───┐
│   │ x₁ │ x₂ │ s₁ │  1│
├───┼───┼───┼───┼───┤
│  1│ 0.3│ 0.1│  1  │1.8│
└───┴───┴───┴───┴───┘
```

Select the pivot column. Choose the column with the most negative coefficient in the bottom row. In this case, it is the second column (x₂).

Select the pivot row. Divide the numbers in the rightmost column (1.8) by the corresponding numbers in the pivot column (0.1) and choose the smallest positive ratio. In this case, the smallest positive ratio is 1.8/0.1 = 18. So the pivot row is the first row.


The simplex method is an iterative procedure that systematically improves the solution to a linear programming problem. It starts with an initial feasible solution and continues to find a better feasible solution until an optimal solution is obtained. In each iteration, the simplex method selects a pivot column and a pivot row to perform row operations, which transform the current tableau into a new tableau with improved objective function values. The process continues until the objective function values cannot be further improved or the linear programming problem is unbounded.

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The correct answer is

0.3x1+0.1x2≤2.7→0.3x1+0.1x2≤1.8 Work Through The Simplex Method Step By Step. How The Solution Changes (I.E., LP Has Optimal

32. Solving integral equation using the convolution theoremThe convolution theorem states that the convolution of two signals in the time domain is equivalent to multiplication in the frequency domain.

Therefore, to solve the given integral equation using the convolution theorem, we need to take the Fourier transform of both sides of the equation.

y(t) = ∫_{-∞}^{∞} sinh(−)g() + ∫_{-∞}^{∞} sinh(−−)g()Taking the Fourier transform of both sides, we haveY() = 2π[G()sinh() + G()sinh(−)]where Y() and G() are the Fourier transforms of y(t) and g(t), respectively.Rearranging for y(t), we gety(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]e^(j) d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)](cos()+j sin())d= (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d+ j(1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()dTherefore, the solution to the integral equation is given by:y(t) = (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]cos()d + (1/2π) ∫_{-∞}^{∞} [G()sinh()+G()sinh(−)]sin()d

It is always important to understand the principles that govern an integral equation before attempting to solve them. In this case, we used the convolution theorem to solve the equation by taking the Fourier transform of both sides of the equation and rearranging for the unknown signal. The steps outlined above provide a comprehensive solution to the equation.  33. Fourier series representation of f(x)

The Fourier series representation of a periodic signal is an expansion of the signal into an infinite sum of sines and cosines. To find the Fourier series representation of the given signal, we need to first compute the Fourier coefficients, which are given by:an = (1/T) ∫_{-T/2}^{T/2} f(x)cos(nx/T) dxbn = (1/T) ∫_{-T/2}^{T/2} f(x)sin(nx/T) dxFurthermore, the Fourier series representation is given by:f(x) = a_0/2 + Σ_{n=1}^{∞} a_n cos(nx/T) + b_n sin(nx/T)where a_0, a_n, and b_n are the DC and Fourier coefficients, respectively. In this case, the signal is given as:f(x) = -1, -π

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Answer:

121

Step-by-step explanation:

If x=11 then the equation is:

15(11)-4(11)

First, multiply:

15×11-4×11=164-44

Now, subtract:

164-44= 121

Hope this helps!! <3

Answer:

121

Step-by-step explanation:

15x-4x

15(11) - 4(11)

165 - 44

= 121

The iterated integral is \(\frac{2}{3}\left(1+e^5\right)^{\frac{3}{2}}-\frac{2}{3}\).

What is Integrate?

In calculus, integration is the process of finding the integral of a function. The integral is the inverse of the derivative, and it represents the area under a curve between two points. Integration is a fundamental concept in calculus, and it has many applications in various fields such as physics, engineering, economics, and more.

The integral of a function f(x) over an interval [a, b] is denoted by ∫(a to b) f(x) dx, and it is defined as the limit of a sum of areas of rectangles as the width of the rectangles approaches zero. In other words, it is the sum of infinitely many small areas under the curve.

Integrate with respect to w first, treating v as a constant:

\($$\int_0^{e^v} \sqrt{1+e^v} d w=\left[w \sqrt{1+e^v}\right]_0^{e^v}=e^v \sqrt{1+e^v}\)

\($$2. Integrate the result from step 1 with respect to $\mathrm{v}$ :$$\)

\($$\int_0^5 e^v \sqrt{1+e^v} d v=\left[\frac{2}{3}\left(1+e^v\right)^{\frac{3}{2}}\right]_0^5=\frac{2}{3}\left(1+e^5\right)^{\frac{3}{2}}-\frac{2}{3} .$$\)

Therefore, the value of the iterated integral is

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An invertible matrix P and a diagonal matrix D such that A = PDP⁻¹ is shown below.

To find an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹:

Let \(\lambda\) be an eigenvalue of A. Then:

\(\begin{aligned}0 &=|A-\lambda I| \\&=\left|\begin{array}{ccc}-11-\lambda & 3 & -9 \\0 & -5-\lambda & 0 \\6 & -3 & 4-\lambda\end{array}\right| \\&=-(0)\left|\begin{array}{cc}3 & -9 \\-3 & 4-\lambda\end{array}\right|+(-5-\lambda)\left|\begin{array}{cc}-11-\lambda & -9 \\6 & 4-\lambda\end{array}\right|-(0)\left|\begin{array}{cc}-11-\lambda & 3 \\6 & -3\end{array}\right| \\&=(-5-\lambda)[(-11-\lambda)(4-\lambda)+54] \\&=-(5+\lambda)^{2}(2+\lambda)\end{aligned}\)

Therefore, \(\lambda = -2\) or \(\lambda = -5\).

Let \(\mathbf{v}=\left[\begin{array}{l}a \\b \\c\end{array}\right]\) be an eigenvector associated with the eigenvalue \(\lambda\).\(\lambda = -2\): From \((A+2 I) \mathbf{v}=\mathbf{0}\) we obtain:

\(\left[\begin{array}{ccc}-9 & 3 & -9 \\0 & -3 & 0 \\6 & -3 & 6\end{array}\right]\left[\begin{array}{l}a \\b \\c\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]\)

Applying elementary row operations to find the reduced echelon form of the coefficient matrix, we obtain:

\(\left[\begin{array}{ccc}-9 & 3 & -9 \\0 & -3 & 0 \\6 & -3 & 6\end{array}\right] \stackrel{\left(-\frac{1}{9}\right) R_{1} \rightarrow R_{1}}{\longrightarrow}\left[\begin{array}{rrr}1 & -\frac{1}{3} & 1 \\0 & -3 & 0 \\6 & -3 & 6\end{array}\right] \stackrel{(-6) R_{1}+R_{3} \rightarrow R_{3}}{\longrightarrow}\left[\begin{array}{rrr}1 & -\frac{1}{3} & 1 \\0 & -2 & 0 \\0 & -1 & 0\end{array}\right] \stackrel{\left(-\frac{1}{2}\right) R_{2} \rightarrow R_{2}}{\longrightarrow}\)

\(\left[\begin{array}{ccc}1 & -\frac{1}{3} & 1 \\0 & 1 & 0 \\0 & -1 & 0\end{array}\right] \stackrel{\left(\frac{1}{3}\right) R_{2}+R_{1} \rightarrow R_{1}}{\stackrel{R_{2}+R_{3} \rightarrow R_{3}}{\longrightarrow}}\left[\begin{array}{ccc}1 & 0 & 1 \\0 & 1 & 0 \\0 & -1 & 0\end{array}\right] \stackrel{R_{2}+R_{3} \rightarrow R_{3}}{\longrightarrow}\left[\begin{array}{ccc}1 & 0 & 1 \\0 & 1 & 0 \\0 & 0 & 0\end{array}\right]\)

Hence, we have a + c = 0 and b = 0. Let c = -1 and a = 1.So, \(\left[\begin{array}{c}1 \\0 \\-1\end{array}\right]\) is an eigenvector associated with \(\lambda = -2\).

\(\lambda = -5\): From \((A+5 I) \mathbf{v}=\mathbf{0}\) we obtain:

\(\left[\begin{array}{ccc}-6 & 3 & -9 \\0 & 0 & 0 \\6 & -3 & 9\end{array}\right]\left[\begin{array}{l}a \\b \\c\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]\)

Applying elementary row operations to find the reduced echelon form of the coefficient matrix, we obtain:

\(\left[\begin{array}{ccc}-6 & 3 & -9 \\0 & 0 & 0 \\6 & -3 & 9\end{array}\right] \stackrel{\left(-\frac{1}{6}\right) R_{1} \rightarrow R_{1}}{\longrightarrow}\left[\begin{array}{ccc}1 & -\frac{1}{2} & \frac{3}{2} \\0 & 0 & 0 \\6 & -3 & 9\end{array}\right] \stackrel{(-6) R_{1}+R_{3} \rightarrow R_{3}}{\longrightarrow}\left[\begin{array}{ccc}1 & -\frac{1}{2} & \frac{3}{2} \\0 & 0 & 0 \\0 & 0 & 0\end{array}\right]\)

Hence, we have a - 1/2b + 3/2c = 0. Let b = 2 and c = 0.Then a = 1. Let b = 0 and c = -2. Then a = 3. Therefore,

\(\left[\begin{array}{l}1 \\2 \\0\end{array}\right],\left[\begin{array}{c}3 \\0 \\-2\end{array}\right]\)

are two linearly independent vectors associated with \(\lambda = -5\)

Matrices P and D: Let

\(P=\left[\begin{array}{ccc}1 & 1 & 3 \\0 & 2 & 0 \\-1 & 0 & -2\end{array}\right]\)

be the matrix whose columns are the eigenvectors obtained in the previous step. Set

\(Q=\left[\begin{array}{ccc}-2 & 0 & 0 \\0 & -5 & 0 \\0 & 0 & -5\end{array}\right]\)

to be the diagonal matrix whose diagonal entries are the eigenvalues.

Thus we have, A = PDP⁻¹.

Therefore an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹ is shown.

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The correct question is given below:

Diagonalize matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹.

\(A=\left[\begin{array}{ccc}-11 & 3 & -9 \\0 & -5 & 0 \\6 & -3 & 4\end{array}\right]\)

Using algebraic expression, For the given expression, the height of the scarf will be 2h - 7

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given the height = h

length of the base = 2h - 7

The area will be - 1/2 . B . H

= 1/2 . (2h - 7) . (h)

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Answer:

B

Step-by-step explanation:

since 5 is constant so you can take it out from the summation

Answer: 12

Step-by-step explanation:

The 4 in “-1/4” can be multiplied by three.

Three 3 in “-2/3” can be multiplied by four.

These give you the common denominator of 12!

Don’t forget to multiply the numerator by the amount you multiplied the denominator by!