What is this one for factor to this?

The correct choice is C. It is a known theorem that if A is invertible, then A⁻¹ must also be invertible. According to the Invertible Matrix Theorem, if a matrix is invertible, its columns form a linearly independent set. Therefore, the columns of A⁻¹ are linearly independent.

When a matrix A is invertible, it means that there exists a matrix A⁻¹ (A inverse) such that A⁻¹A = AA⁻¹ = I, where I is the identity matrix. This implies that A⁻¹ undoes the effect of A, and vice versa.

To understand why the columns of A⁻¹ are linearly independent, we can consider the properties of matrix inverses. If the columns of A were linearly dependent, it would imply that there is a non-trivial linear combination of the columns that equals zero. However, applying the inverse A⁻¹ to this equation would yield A⁻¹(0) = 0, which contradicts the property of the identity matrix.

Therefore, since A is invertible, its columns are linearly independent. Consequently, the inverse matrix A⁻¹ will also have linearly independent columns, ensuring that the columns of A⁻¹ are linearly independent. So, the correct answer is C.

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--The given question is incomplete, the complete question is given below " If A is invertible, then the columns of A⁻¹are linearly independent. Explain why. Select the correct choice below.

A. The columns of A⁻¹ are linearly independent because A is a square matrix, and according to the Invertible Matrix Theorem, if a matrix is square, it is invertible and its columns are linearly independent.

B. If A is invertible, then the rows of A are linearly independent, which implies that the columns of A⁻¹ are linearly independent.

C, It is a known theorem that if A is invertible then A⁻¹ must also be invertible. According to the Invertible Matrix Theorem, if a matrix is invertible its columns form a linearly independent set. Therefore, the columns of A⁻¹ are linearly independent.

D. According to the Invertible Matrix Theorem, if a matrix is invertible its columns form a linearly dependent set. When the columns of a matrix are linearly dependent, then the columns of the inverse of that matrix are linearly independent. Therefore, the columns of A are linearly independent. "--

Answer:  not sure. but as long as he saves his money wisely and doesn't spend frivilously

Step-by-step explanation:

Answer:

m + 7

Step-by-step explanation:

→ Collect like terms

3.8m - 2.8m + 7

→ Simplify

m + 7

Answer:

rectangle

6 faces

12 edges

8 vertices

10ft height

hope this helps

Answer:

2/5

Step-by-step explanation:

Look at where the lines lay on coordinate plane correctly.

The two sided confidence interval on mean is 3.56 and 4.80.

What is confidence interval?

The proportion of probability, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.

The given data is  3.7, 4.5, 4.1, 4.7, 3.9.  Here n = 5

=> σ = 1- 95% = 5% = 0.05

We know that the confidence interval is

=> CI = \(\overline x {\displaystyle \pm }\frac{z(\sigma)}{\sqrt n}\)

Here 95% confidence level so z= 1.96

Mean \(\overline x = \frac{3.7+4.5+4.1+3.9+4.7}{5} = 4.18\) and σ = 0.5

Here  n<30 so we can use t instead of z then t-value = 2.776.

Now confidence level CI = \(\ 4.18 {\displaystyle \pm }\frac{2.776\times0.5}{\sqrt 5}\)

=> CI = 4.18 \(\display \pm\) 0.62 = ( 3.56 , 4.80)

Hence the two sided confidence interval on mean is 3.56 and 4.80.

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For the linear transformation we have:

Basis for the kernel of T (Ker(T)): {[t² - t]}

Basis for the range of T (Range(T)): {[1, 1], [1, 0], [0, 1]}

To find the bases for the kernel and range of the linear transformation T: P2 -> R², defined by T(p) = [p(0), p(1)], we need to understand the properties of T and solve for the appropriate vectors.

Kernel of T (Nullspace):

The kernel of T, denoted as Ker(T), consists of all polynomials p in P2 such that T(p) = [p(0), p(1)] = [0, 0]. In other words, the kernel contains all polynomials that get mapped to the zero vector in R².

Let's solve for the kernel by setting up the system of equations:

p(0) = 0

p(1) = 0

Since we are dealing with polynomials of degree at most 2, let's consider a general polynomial p(t) = at² + bt + c.

Substituting into the equations:

(0)a + (0)b + c = 0 -> c = 0

(1)a + (1)b + c = 0 -> a + b = 0 -> b = -a

Thus, any polynomial of the form p(t) = at² - at, where a is a scalar, will be in the kernel of T. Therefore, a basis for the kernel is [t² - t].

Range of T:

The range of T, denoted as Range(T), consists of all vectors in R² that can be obtained by applying the linear transformation T to some polynomial in P2.

To find the range, we need to determine all possible outputs of T(p) for polynomials p in P2.

Let's consider a general polynomial p(t) = at² + bt + c and apply T(p):

T(p) = [p(0), p(1)] = [a(0)² + b(0) + c, a(1)² + b(1) + c] = [c, a + b + c]

So, any vector [x, y] in the range of T must satisfy x = c and y = a + b + c for some a, b, c.

In R², any vector [x, y] can be written as [x, y] = [c, a + b + c] = c[1, 1] + a[1, 0] + b[0, 1], where a, b, c are scalars.

So, the basis for the range of T is {[1, 1], [1, 0], [0, 1]}.

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Answer:

144 in^2

Step-by-step explanation:

Using the A = s^2 and the text says that s= 12in

 the answer is 12 in * 12 in = 144 in^2

Answer:

-20j+ 6j=-14j

-14j + 18j=4j

4j-9j=-5j

-5j=-3-17

-5j =-20

j =-20÷-5

j =4

Diogo's optimal bundle is q1 ≈ 12.77 units of chocolate candy and q2 ≈ 74.46 units of slices of pie.

To find Diogo's optimal bundle, we need to maximize his utility function subject to his budget constraint. The budget constraint is given by:

p1q1 + p2q2 = Y

Substituting the given values:

2q1 + 1q2 = 100

We can rewrite this as:

q2 = (100 - 2q1) / 1

Now, let's maximize Diogo's utility function:

U(q1, q2) = q1^0.2 * q2^0.8

Substituting the expression for q2:

U(q1) = q1^0.2 * [(100 - 2q1) / 1]^0.8

To find the optimal bundle, we need to find the value of q1 that maximizes U(q1). We can do this by taking the derivative of U(q1) with respect to q1 and setting it equal to zero:

dU(q1) / dq1 = 0.2q1^(-0.8) * [(100 - 2q1) / 1]^0.8 - 0.8q1^0.2 * [(100 - 2q1) / 1]^(-0.2) * (-2 / 1) = 0

Simplifying the equation:

0.2[(100 - 2q1) / q1]^0.8 = 0.8

[(100 - 2q1) / q1]^0.8 = 4

Taking both sides to the power of 1/0.8:

(100 - 2q1) / q1 = 4^(1/0.8)

Solving for q1:

100 - 2q1 = 4^(1/0.8) * q1

100 = (4^(1/0.8) + 2) * q1

q1 = 100 / (4^(1/0.8) + 2)

Calculating the value of q1:

q1 ≈ 12.77

Now we can substitute this value back into the budget constraint to find q2:

2q1 + q2 = 100

2(12.77) + q2 = 100

25.54 + q2 = 100

q2 = 100 - 25.54

q2 ≈ 74.46

Therefore, Diogo's optimal bundle is q1 ≈ 12.77 units of chocolate candy and q2 ≈ 74.46 units of slices of pie.

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Answer to the second question.

9

Step-by-step explanation:

3⁴ simply means 3×3×3×3=81

3² 3×3=9

81/9=9

The inequality to model the situation will be 24b ≤ 250

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality to model the situation will be 24b ≤ 250. The number of baseball will be:

24b ≤ 250

b ≤ 250 / 24

b ≤ 10

The number of baseball will be 10 or less.

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Sawarasenai kimi wa shoujo na no?~

Boku Wa yaRcHin BiCChi nO oSu Da YO!~~

The living room area of Monica's home is  0.645 ft².

The floor area of her current home is  1.3975 ft²

The total floor area of Monica's dream home should be 2.150 ft².

Monica wants the living room to be 30% of the total area. Therefore, the living room area will be as follows:

living room area = 30 / 100 × 2.150 = 64.5 / 100 = 0.645 ft²

Her current house has only 65% of the floor area of her dream house. Therefore, the floor area of her current home is as follows:

Floor area of her current home = 65 / 100 × 2.150

Floor area of her current home = 139.75 / 100

Floor area of her current home = 1.3975 ft²

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An equation that depicts a straight line on a graph is said to be linear line.

Linear refers to a straight line. Straight-line graphs called linear graphs are used to show the relationship between two values. The single straight lines on this graph assist to represent a result. The phrase "linear" refers to a straight line and excludes the usage of curves, dots, bars, etc.

A linear line can include more than one variable. Linear lines with two variables, for example, are those that have two variables in them. 2x - 3 = 0 and 2y = 8 are few examples of linear lines.

Steps to draw a linear graph are described below:

Examine the line to see if it is straight or curved. A straight line indicates a linear equation. A nonlinear equation is one that is curved.

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The probability that the number of homicide deaths for a randomly selected day is:

a) 0: 0.18,

b) 1: 0.35,

c) 2: 0.27

The Poisson distribution is used to simulate the likelihood that a certain number of events will occur within a predetermined window of time or space.

In this instance, the Poisson distribution can be used to simulate the number of homicide deaths that occurred in Richmond, Virginia over the course of a year.

The Poisson distribution can be used to determine the likelihood of 0, 1, and 2 homicides happening on any given day.

One homicide occurs on a randomly chosen day with a 0.18 percent chance, one homicide occurs on a randomly chosen day with a 0.35 percent chance, and two homicides occur on a randomly selected day with a 0.27 percent chance.

Complete Question:

In one year, there were 116 homicide deaths in Richmond, Virginia. Using the Poisson distribution, find the probability that the number of homicide deaths for a randomly selected day is:

a) 0

b) 1

c) 2

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Therefore , the solution of the given problem of inequality comes out to be x = 12.5°.

An inequality in mathematics is a linear relationship or a set of integers even without equal sign. Equilibrium follows equity ineluctably. Inequality exists between two variables when they are not equal. There are distinctions between equality and inequality. I've selected the most prevalent symbol because when variables aren't identical or comparable (). Any number of inequalities, no matter how little or large, can be used to compare values.

Here,

Given :4x -10 = 40

=> 4x = 40 + 10

=>  4x =50

=> x  =50/4

=>x= 12.5°

Therefore , the solution of the given problem of inequality comes out to be x = 12.5°.

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Answer:

y intercept=5

Definition of a rectangle. Opposite sides of a parallelogram are congruent. Reflexive Property of congruent , SSS, option D.

Every component of the set is connected to itself, according to the reflexive feature of sets. The reflexive property of congruence is known when the relation specified on a set is congruence, and the reflexive property of equality is known when the relation defined on a set of numbers is equality. When this occurs, the relation can be referred to as a reflexive relation or as a reflexive property being satisfied on that set.

Any geometric figure compared to itself is congruent to itself so this is why:

AC ≅ CA

∠B ≅ ∠B

Since we have a parallelogram, therefore we can say:

BC ≅ DA

BA ≅ Dc

CA ≅ AC

Both triangles ABC and CDA satisfy the side to side to side congruence, since their 3 sides are congruent.

So, It's D.

Notice that the angle measure information is not included in the data above that's why we cannot say it is SAS congruence.

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Complete question:

Given: ABCD is a rectangle.

Prove: ΔABC is congruent to ΔCDA ABDC is a rectangle.

ABCD is a parallelogram. AB is congruent to DC and BC is congruent to DA AC is congruent to AC ΔABC is congruent to ΔCDA Given Definition of a rectangle. Opposite sides of a parallelogram are congruent. _____________________ _____________________

A. Symmetric Property of congruent; SAS

B. Reflexive Property of congruent to; SAS

C. Symmetric Property of congruent; SSS

D. Reflexive Property of congruent; SSS

The distance from the base of the telephone pole to point B is approximately 65 feet.

We can take care of this issue utilizing the Pythagorean hypothesis, which expresses that in a right triangle, the amount of the squares of the lengths of the two more limited sides is equivalent to the square of the length of the longest side (the hypotenuse).

Let's call the distance from point C to point B "x". Then we have:

AB² + BC² = AC² (using the Pythagorean theorem)

x² + 54² = 83²

x² = 83² - 54²

x² = 4225

x = √4225

x = 65

As a result, the distance between point B and the base of the telephone pole is approximately 65 feet, which has been rounded to the nearest tenth of a foot.

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Answer:

Step-by-step explanation:

If I understand this correct the question is:

Solving by collecting like terms:

Answer:

-4a⁴+a²b²-4b⁴ this is your answer. your question is in mess .I don't understand properly.

a⁴+4a²b²-2b⁴......(1)

-3a⁴+5a²b²+2b⁴.........(2)

subtracting equation 1_from 2

Step-by-step explanation:

-3a⁴+5a²b²+2b⁴

a⁴+4a²b²-2b⁴

-

____________

-4a⁴+a²b²-4b⁴

1 mile = 5,280 feet.

45 miles x 5,280 feet = 237,600 total feet.

1 hour = 3600 seconds

237,600/3600 = 66 feet per second.

Answer:

66 feet per second...I think

Step-by-step explanation:

Answer:

88.28

Step-by-step explanation:

applying formula of area of triangle, 1/2 X base X height.

given.= base= 16.9 height=10.4

so keeping value in formula.

1/2 X 16.9 X 10.4

on solving it will be 88.28

Answer:

The Correct Answer Is 87.88

Step-by-step explanation:

10.4*16.9=175.76

175.76/2=87.88

Do not round ft² = 87.88

Hope this helps everyone using Acellus program!

Answer:

y = - 4

Step-by-step explanation:

the given line is horizontal and parallel to the x- axis with slope zero

Parallel lines have equal slopes

a parallel line will therefore be horizontal with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 2, - 4 ) with y- coordinate - 4 , then

y = - 4 ← equation of parallel line

Answer:

C: y = –4

Worked for me on edge

Without calculating the integral, we cannot determine the exact average value of the function f(x) on the interval [2, 20].

To find the average value of a function f(x) over an interval [a, b], we need to compute the definite integral of f(x) over that interval and divide it by the length of the interval (b - a).

In this case, we are given the function f(x) = (9π/x^2)cos(π/x), and we want to find the average value on the interval [2, 20].

Using the definite integral formula, the average value can be calculated as follows:

Average value =\((1/(20 - 2)) * ∫[2,20] (9π/x^2)cos(π/x) dx\)

Simplifying this expression, we have:

Average value =\((1/18) * ∫[2,20] (9π/x^2)cos(π/x) dx\)

Unfortunately, it is not possible to determine the exact value of this integral analytically. However, it can be approximated numerically using methods like numerical integration or software tools like MATLAB or Wolfram Alpha.

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The sequence of transformations that proves the two trapezoids are similar is a dilation by a scale factor of 2 about vertex K followed by a reflection across the y-axis, which is option D.

The sequence of transformations that proves trapezoid HJKL and trapezoid QPRS are similar is a dilation by a scale factor of 2 about vertex K followed by a reflection across the y-axis, which is option D.

Two figures are similar if their corresponding angles are congruent and their corresponding sides are proportional. The two trapezoids have congruent angles, since they are both trapezoids and have the same parallel bases. Therefore, we only need to show that their corresponding sides are proportional.

To do this, we need to apply a series of transformations that map trapezoid HJKL onto trapezoid QPRS. Looking at the two trapezoids, we can see that a dilation by a scale factor of 2 about vertex K would make the sides of trapezoid HJKL proportional to the corresponding sides of trapezoid QPRS. We can then reflect the resulting figure across the y-axis to make the sides of the trapezoids correspond in the same order. Therefore, the sequence of transformations that proves the two trapezoids are similar is a dilation by a scale factor of 2 about vertex K followed by a reflection across the y-axis, which is option D.

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The number of incorrect answers is 8.

linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Let,

number correct of answer = x

number of incorrect answer = y

Given that,

Total number of answer  x+y = 30 ......(1)

Total score = x-\(\frac{1}{4}\)y = 20  .......(2)

In equation (2) multiply by -1 on both side.

-x+\(\frac{1}{4}\)y = -20   .......(3)

Now,

Adding both the equation (1) and (3)

x+y-x+\(\frac{1}{4}\)y = 30-20

\(\frac{5}{4} y\) = 10

y = 8

Hence, The number of incorrect answers is 8.

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