(Q2) The set of line segments _____ meet the requirements to form a triangle.8 cm4 cm3 cm

one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

Answer:

g = 2d - 8

g + d = 46

Step-by-step explanation:

It is given that the guitarist wrote eight less than twice as many songs as the drummer did, hence one would multiply by the number of songs the drummer wrote by two, and subtract eight.

It is also given that the combined total of songs that they both wrote is 46, hence one would add up the songs that they wrote, and attain a result fo 46.

Answer:

c

Step-by-step explanation:

Tim weighting this bc it said

Answer:

Angle b = 30 degrees

Step-by-step explanation:

3x = 90.

X= 30

Angle b = 30 degrees

Answer:

45

Step-by-step explanation:

because in total it's a 90-degree agle half of 90 is 45.

Answer:

Exact Form:

(41036433850368 ^6  x  2419 ^54 )− 328

Decimal Form:

2.48516121  x  10 ^264

Answer:

Heyyy T-T

Step-by-step explanation:

Answer:

41.9%

Step-by-step explanation:

percent change = (new number - old number)/(old number) × 100%

new number = 44

old number = 31

percent change = (44 - 31)/31 × 100%

percent change = 13/31 × 100%

percent change = 0.41935 × 100%

percent change = 41.9%

The particular solution to the differential equation subject to the given initial condition is B(t) = 15e^(-0.3t).

To find the particular solution to the differential equation subject to the given initial condition, dB/dt + 0.3B - 30 = 0 and B(3) = 6, follow these steps:

Step 1: Rewrite the given differential equation as dB/dt = -0.3B + 30.

Step 2: Solve the homogeneous equation dB/dt = -0.3B. This is a first-order linear differential equation, and the solution is B(t) = Ce^(-0.3t), where C is the integration constant.

Step 3: Substitute the initial condition B(3) = 6 into the equation B(t) = Ce^(-0.3t) to find the value of C. So, 6 = Ce^(-0.3(3)).

Step 4: Solve for C. First, find the value of e^(-0.9) ≈ 0.40657. Then, divide both sides of the equation by this value: C ≈ 6 / 0.40657 ≈ 14.75. Round C to the nearest integer, which is 15.

Step 5: Substitute the value of C back into the equation B(t) = Ce^(-0.3t) to find the particular solution: B(t) = 15e^(-0.3t).

So, the particular solution to the differential equation subject to the given initial condition is B(t) = 15e^(-0.3t).

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Given that a square pyramid has a surface area of 10 cm², and a dilation of the pyramid has a surface area of 90 cm², we are to find the scale factor of the dilation.

Step 1: Recall the formula for the surface area of a square pyramid, which is given by: S.A. = l² + 2 × l × sHere, l is the slant height of the pyramid, and s is the length of the base.

Step 2: Let the scale factor of the dilation be k. Therefore, the new slant height of the pyramid after dilation is kl, and the new length of the base is ks.

Step 3: Recall that the surface area of a pyramid is proportional to the square of the slant height, and also proportional to the product of the slant height and the length of the base.

Therefore, we can say:S.A. ∝ (slant height)² × (base length)S.A. = k²l² + 2k²lsAnd since we know that the initial surface area is 10 cm² and the new surface area is 90 cm², we can form the equation:10 = l² + 2ls90 = k²l² + 2k²ls

Step 4: Solve for k by dividing the second equation by the first:90/10 = k²l² + 2k²ls / (l² + 2ls)9 = k²l² + 2k²ls / (l(l + 2s))9 = k² + 2ks / (l + 2s)9(l + 2s) = k²l + 2ks k² = (9l + 18s) / l² + 2sl²k² = 9(l / l² + 2s / l) + 18(s / l² + 2s / l)k² = 9 / l + 18 / s k = √(9 / l + 18 / s)

Therefore, the scale factor of the dilation is: k = √(9 / l + 18 / s)

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Answer:

RT || AB

Step-by-step explanation:

The answer to your question is that segment RT is parallel to AB.

And for those of you who encounter AB || ?

The answer is RT.

Both questions are rewrites.

RT || AB if R and T are the midpoints of AC and BC. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

R, S, and T are midpoints of AC, AB, and CB.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

A line is parallel to the right side if it divides any two triangles sides in a similar ratio.

RT || AB if R and T are the midpoints of AC and BC. Then the correct option is C.

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A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels towards as it approaches infinity.

Set the denominator to zero and solve for x to discover the vertical asymptotes. Set each factor to zero and solve as this has already been factored. The asymptotes are expressed as equations of lines since they are lines. Asymptotes for the vertical line are x = 3 and x = 1.

An asymptote of a curve in analytic geometry is a line where the distance between the curve and the line gets closer to zero as one or both of the x or y coordinates tends to infinity.

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9.) The transformation performed in the function\(f(x) = \frac{1}{2}^{-x}\) is a reflection across the x-axis.

10.) The transformations performed in the function \(f(x) = -log_5(x-2)+17\)are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞.

What is the transformation of the function?

The term "transformation of a function" refers to the process of altering the appearance of a function, either by shifting, stretching, or reflecting it along the coordinate axes.

9.) The transformation performed in the function \(f(x) = \frac{1}{2}^{-x}\) is a reflection across the x-axis.

10.) The transformations performed in the function\(f(x) = -log_5(x-2)+17\)are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞. As x approaches positive infinity, the value of 4^x approaches positive infinity, making the value of the function approach positive infinity.

Hence,

9.) The transformation performed in the function\(f(x) = \frac{1}{2}^{-x}\) is a reflection across the x-axis.

10.) The transformations performed in the function \(f(x) = -log_5(x-2)+17\)are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞.

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step 1

$1,000 < $7,000

so

the tax rate is 15%

15%=15/100=0.15

0.15*1,000=$150

therefore

Answer:

\(y = 7\)

\(x = 7 \sqrt{2} \)

Answer:

The first image is the answer and the second image is the explanation.

Step-by-step explanation:

Answer:

The vertex, a maximum, is (25, 2400). It reveals that the maximum profit will result when the tickets are $25, and then the profit will be $2400.

Explanation:

p(d) = -4d² + 200d - 100

Comparing it with quadratic function, ax² + bx² + c

Here given: a = -4, b = 200, c = -100

Using Vertex Formula: x = -b/2a = -200/2(-4) = 25

Then find y = -4(25)² + 200(25) - 100 = 2400

Solution Set : (x, y) → (25, 2400)

As a > 0, the vertex is maximum.

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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The smallest angles of the triangle is angle A

In triangle ABC

The length of the side AB = 6.2 units

The length of the side AC = 9.5 units

The length of the side BC = 5.1 units

The opposite angle of AB is angle C, the opposite angle of AC is angle B and the opposite angle of BC is angle A

We know length of the line is BC which is 5.1 units which is the smallest side of the triangle. Then the opposite angle of BC will be the smallest angle in the triangle ABC

The opposite angle of the side BC is angle A, which is the smallest angle in the triangle

Hence, the smallest angles of the triangle is angle A

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Answer:

3 5/10 or 3 1/2

Step-by-step explanation:

Answer:

-8x-8

Step-by-step explanation:

Answer:

The equation equal to 16x - 12 - 24x + 4 is -8x - 8

Step-by-step explanation:

  16x - 12 - 24x + 4

= 16x - 24x - 12 + 4

= -8x - 8

Answer:

A

Step-by-step explanation:

Answer: A

Step-by-step explanation:

A is correct because u have  to minus 18 if u want x to be by its self

b, is incorrect because we have to do the opposite of each operation since it’s addition its inverse is subtraction

c, incorrect cuz it only minuses 18 from one side but u have to minus from both sides

d, incorrect

Answer:

I think the answer is c. Hope this helps. Please tell me if I am right or wrong.

Step-by-step explanation:

Answer:

5/9

Step-by-step explanation:

brainliest when possible.

Answer:

The answer is B

Step-by-step explanation:

Its 3 ounces of raisins for every 9 but if you simplify it divided by 3 it will be 1 ounce of raisend for every 3 ounces of peanuts.

The fact that certain neurons might respond only to your mother's face but not your father's face highlights the importance of facial recognition and the specificity of neural responses.

Facial recognition is a complex cognitive process that involves the ability to distinguish and identify different faces. The specificity of neural responses to different faces, such as responding exclusively to one's mother's face but not the father's face, highlights the importance of neural specialization and the intricate nature of face perception.

The brain possesses specialized neurons known as face-selective neurons or face cells that are specifically tuned to detect and process facial features. These neurons play a crucial role in facial recognition and contribute to our ability to differentiate and remember faces.

The fact that certain neurons respond selectively to specific faces, like the mother's face, suggests that our brains have developed specialized mechanisms to encode and process important social stimuli, such as faces of close family members. This phenomenon emphasizes the significance of early experiences, bonding, and the formation of neural representations associated with familiar faces, particularly those with strong emotional connections.

In summary, the specificity of neural responses to the mother's face highlights the importance of facial recognition and the specialized neural mechanisms involved in processing and distinguishing familiar faces, contributing to our understanding of social cognition and the complexities of human brain function.

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Answer:

\(y=-2+6x\)

Step-by-step explanation:

\(-3y-6x= -18\)

\((-3y-6x)= -18+6x\)

\(-3y-6x+6x=6x -18\)

\(y=-2+6x\)

Answer:

5

Step-by-step explanation:

A measure of the dispersion of observations in a process distribution is called: range.

This is further explained below.

Generally, The range of a collection of data is the difference between the highest and smallest values in the set. This difference is calculated by subtracting the sample maximum and minimum from the sample size. It is written out using the same units that were used for the data.

In conclusion, The term "range" refers to a measure of the dispersion of observations included within a process distribution.

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Answer:
-1/6

Glad to help :D