find the inverse of the matrix (if it exists). (if an answer does not exist, enter dne.) 1 2 5 9

The rule of the volume of the hemisphere is

r is the radius of it

Since the diameter of the hemisphere is double the radius, then we can find the radius then multiply it by 2 to find it

Since the volume of the hemisphere is 841 cm^3, then

Substitute V by 841

Divide both sides by 2/3pi

Take cube root to both sides

Multiply it by 2 to find the diameter, then round it to the nearest tenth

The diameter of the hemisphere is 14.8 cm

Answer:

11.3057558

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

4(x-1) = 2(6-2x)

x=2

Answer:

x=2

Step-by-step explanation:

4(x-1)=2(6-2x)

4x-4=12-4x

Add 4 to both sides

4x=16-4x

Add 4x to both sides

8x=16

Divide by 8 on both sides

x=2

Answer: =

x

2

−

4

x

−

21

Step-by-step explanation: (

x

+

3

)

.

(

x

−

7

)

=

(

x

)

.

(

x

−

7

)

+

(

3

)

.

(

x

−

7

)

ANSWER

x^2-4x-21

EXPLAIN

First expand the brackets by multiplying the number from the first bracket to the second bracket

you will get this = x^2 + 3x- 7x- 21 ,then u collect the like terms which is (3x & -7x).

your answer ( x^2 - 4x - 21 ).

Answer:

x+3

Step-by-step explanation:

combine like terms then simple math

Answer:

Simple Algebra.

Step-by-step explanation:

x2 + 5x + 6/

X + 2

= −3

The question is incomplete:

The sum of the average amounts spent for veterinary expenses for​ dogs, cats, and birds in a recent year was ​$293 The average expenditure per dog exceeded the sum of the averages for cats and birds by ​$113. The amount spent per cat was 9 times the amount spent per bird. Find the average amount spent on each type of animal.

Answer:

The average amount spent in dogs is $203, in cats is $81 and in birds is $9.

Step-by-step explanation:

From the information given, you can write the following equations:

x+y+z=293 (1)

x-y-z=113 (2)

y=9z (3)

You can replace (3) in (1) and (2):

x+9z+z=293

x+10z=293 (4)

x-9z-z=113

x-10z=113 (5)

Now, you have the following equations:

x+10z=293 (4)

x-10z=113 (5)

Then, you can isolate x in (4):

x=293-10z (6)

Next, you can replace (6) in (5):

293-10z-10z=113

293-20z=113

293-113=20z

180=20z

z=180/20

z=9

Now, you can replace the value of z in (6) to find x:

x=293-10z

x=293-10(9)

x=293-90

x=203

Finally, you can replace the value z in (3) to find y:

y=9*(9)

y=81

According to this, the answer is that the average amount spent in dogs is $203, in cats is $81 and in birds is $9.

The solution to the linear system is unique solution which is  x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.

The correct answer is option  A.

To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:

[1  -4  5  |  23]

[2   1   1  |  10]

[-3  2  -3 |  -23]

We'll apply row operations to transform this matrix into echelon form:

1. Multiply Row 2 by -2 and add it to Row 1:

[1  -4   5   |  23]

[0   9   -9  |  -6]

[-3  2  -3  |  -23]

2. Multiply Row 3 by 3 and add it to Row 1:

[1  -4  5   |  23]

[0   9  -9  |  -6]

[0   -10 6  |  -68]

3. Multiply Row 2 by 10/9:

[1  -4  5    |  23]

[0   1   -1   |  -2/3]

[0   -10 6  |  -68]

4. Multiply Row 2 by 4 and add it to Row 1:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  -10 6  |  -68]

5. Multiply Row 2 by 10 and add it to Row 3:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  0   -4  |  -34/3]

Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:

From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.

From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.

From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.

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27 well if you're asking that then

Answer:

The area is 452.3

Step-by-step explanation:

A= 3.14r2

A= 3.14 times 12~2

A= 452.2

Answer:

2x + 2 + h.

Step-by-step explanation:

F(x+h) is f(x) where x+h replaces x:-

f(x + h) = (x + h)^2 + 2(x + h) - 3

[f(x+h) - f(x)] / h

= (x + h)^2 + 2(x + h) - 3 - (x^2 + 2x - 3)  /  h

= [x^2 + 2hx + h^2 + 2x + 2h - 3 - x^2 - 2x + 3] / h

= (2hx + h^2 + 2h) / h

= 2x + 2 + h

The limit of [f(x+h) - f(x)] / h as h ----> 0 is 2x + 2.

We refer to 2x + 2 as the derivative of x^2 + 2x - 3.

Answer:

-5x+(- 15 ) = 20

x=-7

Step by Step

-5x+(-15)= 20 becomes

-5-15=20 add 15 tp (15 and 20)

-5x=35 ( divide by 51

x=-7

a) The congruent sides are:

As they have the same lengths.

b) The diagonals AC and BD are congruent.

Congruent figures are figures that have the same side lengths, that is, the side lengths of the figures have the same numerical measures.

The lengths of each side will be obtaining using the formula for the distance between two points, \((x_1,y_1)\) and \((x_2, y_2)\), given as follows:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates of the vertices of the rectangle are given as follows:

A(0,3), B(3,6), C(9,1), D(6,-2).

Hence the lengths of each segment is given as follows:

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The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:

1. Calculate the perimeter of the given rectangular field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120 meters + 80 meters)

            = 2 * 200 meters

            = 400 meters

2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:

  Side length = Perimeter / 2

             = 400 meters / 2

             = 200 meters

3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.

4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:

  Width = Perimeter / 2 - Length

        = 400 meters / 2 - 200 meters

        = 200 meters - 200 meters

        = 0 meters

5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.

In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.

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Yes, if the geometric multiplicity of each eigenvalue equals its algebraic multiplicity, then the matrix is diagonalizable.

1. Eigenvalues: Scalar values associated with a matrix that, when multiplied by a non-zero vector (eigenvector), only result in a scaled version of that vector.

2. Geometric multiplicity: The number of linearly independent eigenvectors associated with a specific eigenvalue.

3. Algebraic multiplicity: The number of times a specific eigenvalue appears as a root of the characteristic polynomial of the matrix.

4. Matrix diagonalizable: A matrix is diagonalizable if it can be transformed into a diagonal matrix through a similarity transformation (using an invertible matrix P).


A matrix is diagonalizable if and only if there are enough linearly independent eigenvectors to form a basis for the matrix's domain. This means that the sum of the geometric multiplicities of all eigenvalues must equal the dimension of the matrix. If the geometric multiplicity of each eigenvalue equals its algebraic multiplicity, it ensures that there are enough linearly independent eigenvectors to form a basis. Consequently, the matrix is diagonalizable.

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The area of the surface obtained by rotating the curve x = 20 cos(3θ), y = 20 sin(3θ), where 0 ≤ θ ≤ π/2, about the x-axis is calculated using the formulA for surface area of revolution

To find the area of the surface, we can use the formula for the surface area of revolution. Given a curve defined parametrically by x = f(θ) and y = g(θ), where α ≤ θ ≤ β, the surface area obtained by rotating the curve about the x-axis is given by:

A = ∫[α,β] 2πy √(1 + (f'(θ))²) dθ

In this case, we have x = 20 cos(3θ) and y = 20 sin(3θ), with 0 ≤ θ ≤ π/2. Taking the derivatives, we find f'(θ) = -60 sin(3θ) and g'(θ) = 60 cos(3θ).

Plugging these values into the surface area formula and simplifying, we get:

A = ∫[0,π/2] 2π(20 sin(3θ))(√(1 + (-60 sin(3θ))²)) dθ

Evaluating this integral will give us the exact value of the surface area of the rotated curve about the x-axis within the given range of θ.

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When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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Answer:

C) 8, 15, 17

Step-by-step explanation:

\(8^2 +15^2 = 17^2\\\)

Differential equations are mathematical equations that involve derivatives. They describe the relationship between an unknown function and its derivatives, helping to model and understand dynamic systems in physics, engineering, and other scientific disciplines.

To find the general solution of the given system of differential equations by decoupling, we first need to rewrite the given equation in a more standard form. The equation provided is: x1' = x1 * x.

Step 1: Rewrite the equation
x1' = x1 * x can be rewritten as dx1/dt = x1 * x, where x1 is a function of time t.

Step 2: Separate variables
Now, we separate variables by dividing both sides of the equation by x1, and then multiplying both sides by dt:
(dx1/x1) = x * dt

Step 3: Integrate both sides
Now we can integrate both sides of the equation with respect to their respective variables:

∫(dx1/x1) = ∫(x * dt)

After integrating, we get:
ln|x1| = (1/2) * x^2 + C₁, where C₁ is the constant of integration.

Step 4: Solve for x1
To find the general solution for x1, we need to exponentiate both sides of the equation to eliminate the natural logarithm:

x1(t) = Ce^(1/2 * x^2), where C = e^(C₁) is a new constant.

So, the general solution of the given system of differential equations is x1(t) = Ce^(1/2 * x^2), where C is an arbitrary constant.

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Answer:

Step-by-step explanation:

Given the sets of side lengths of a triangle:

To verify whether each set of side lengths could be the sides of a right triangle, we use the Pythagorean Theorem. Note that the longest side is always taken as the hypotenuse.

In the set of side lengths 10.5 cm, 20.8 cm, 23.3 cm

\(23.3^2=20.8^2+10.5^2\\542.89=432.64+110.25\\542.89=542.89\)

Clearly these satisfies the required theorem and thus are side lengths of a right triangle.

In the set of side lengths 6 cm, 22.9 cm, 20.1 cm

\(22.9^2=20.1^2+6^2\\524.41\neq 440.01\)

Clearly these does not satisfy the required theorem and thus are not side lengths of a right triangle.

Given that biology is the subject, the Probability of being on time is 32.8%.

In this case:

P(on-time arrival in class | biology) = P(on-time arrival in class and biology) / P(biology) is the result of applying the conditional probability formula.

According to the table, 82.4% of students will be on time for biology class. Since there are four topics listed, each with an equal weight, the likelihood of biology is 25%. Therefore, we have:

P(on-time arrival in class | biology) = 82.4% / 25% = 0.328 = 32.8%

Therefore it can be concluded that the probability of on-time arrival in class given that the subject is biology is 32.8%.

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The value of x in the given system of linear equations, 5x - 8y = 16 and 21x + 12y = 28, rounded to one decimal place, is approximately 0.7.

To find the value of x in the system of linear equations, we can use the method of elimination or substitution. Let's use the method of elimination:

Multiply the first equation by 21 and the second equation by 5 to eliminate the variable y.

105x - 168y = 336

105x + 60y = 140

Subtract the second equation from the first equation to eliminate x:

-228y = 196

Solve for y:

y ≈ -0.8596

Substitute the value of y back into either equation to solve for x. Using the first equation:

5x - 8(-0.8596) = 16

5x + 6.8768 = 16

5x = 9.1232

x ≈ 1.8246

Rounded to one decimal place, the value of x is approximately 0.7.

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(x+2)(3x+1)

x(3x+1)+2(3x+1)

3x²+x+6x+2

3x²+7x+2

(3x²+7x+2)(x-3)

x(3x²+7x+2)-3(3x²+7x+2)

3x³+7x²+2x-9x²-21x-6

3x³+7x²-9x²+2x-21x-6

3x³-2x²-19x-6

Answer:

The perimeter of a shape is the total measurement of all the edges of a shape e.g. a triangle has three edges, so its perimeter is the total of those three edges added together.

Step-by-step explanation:

difference means minus

12-(-58)

12+58=70

The probability of winning something on each of the two plays of the game is 2/3, since there are 6 possible outcomes and 4 of them result in a win.

The probability of winning something on each of the two plays of the game can be calculated by taking the number of outcomes that result in a win (4) divided by the total number of possible outcomes (6). Thus, the probability of winning something on each of the two plays of the game is 4/6, or 2/3. For each play of the game, there is a 1/6 chance of rolling a 6, a 1/6 chance of rolling a 5, a 1/6 chance of rolling a 4, and a 1/6 chance of rolling a 3. Thus, the total probability of winning something is 1/6 + 1/6 + 1/6 + 1/6 = 4/6 = 2/3.

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