I’m stuck on this question

(a) A basis for a subspace is a set of linearly independent vectors that span the subspace. To find a basis for this subspace, we can use the following steps:

Write the given set of vectors as the rows of a matrix, with each vector as a row.

Use row-reduction (Gaussian elimination) to put the matrix in row-echelon form.

The non-zero rows of the row-echelon form matrix form a basis for the subspace.

So, we get the matrix:

| 6a - 2c | -5b - 5c | -6a + 5b + 2c | -6a + 2c |

Using row-reduction, we can simplify the matrix to:

| 1 - 1/3 | 0 | 1/3 | -1/3 |

The non-zero rows are {[ 1 - 1/3 0 1/3 -1/3 ]}

So, a basis for the subspace is:

{[ 1 - 1/3 0 1/3 -1/3 ]}

(b) The dimension of a subspace is the number of linearly independent vectors in a basis for the subspace. In this case, the basis for the subspace has only one vector, so the dimension of the subspace is 1.

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Answer:

20 groups

Step-by-step explanation:

There are 20 groups of 1/5 in 4 because you have to divide (4)/(1/5) so aplying the ear law you obtain 20.

Answer:

True.

Step-by-step explanation:

Answer:

True.

The statement "The amount of water in the tank is decreasing at 600 gallons per hour" is true. It means that the water level in the tank is going down by 600 gallons per hour, which means that the water is being used or drained out of the tank at a rate of 600 gallons per hour.

Step-by-step explanation:

The relation between effort force and the force of gravity can be represented as,   Fₐ < Fₙ

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Given that,

A student lifts up a spring scale attached to a block on a table

The block is still resting on the table

The relation between effort force to the force of gravity = ?

Suppose,

The effort force = Fₐ

The force of gravity =  Fₙ

block is still resting on the table,

it means effort force is less than the force of gravity,

To move upward, it is required to apply more effort force,

but, here effort force is less

So, It can be written as,

Fₐ < Fₙ

Hence, the relation between both the forces is  Fₐ < Fₙ

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Answer:

24.53

Step-by-step explanation:

d = (1/2)gt²

First man travels 1 sec + 2 sec = 3 sec

d = (1/2)(9.81 m/s²)(3 s)² = 44.15 m

Second man travels 2 sec

d = (1/2)(9.81 m/s²)(2 s)² = 19.62 m

Distance between the 2 men:

44.15 m - 19.62 m = 24.53 m

Answer: Murr's annual social security deduction is the amount of money he pays in social security taxes. Social security tax is 6.2% of Murr's annual salary. To find the annual social security deduction, we can multiply Murr's annual salary by the social security tax rate:

57,285.50 x 6.2% = 3,541.829

Murr's annual social security deduction is 3,541.829

Note that Medicare tax is 1.45% and it's calculated separately, if you want to calculate it you can use the same formula:

57,285.50 x 1.45% = 829.4078

So the total Social security and Medicare tax is 3,541.829 + 829.4078 = 4,371.2368

It's important to note that these are the federal Social Security and Medicare taxes, there might be additional state taxes or deductions that are not included.

Step-by-step explanation:

Answer: 44 5/8

Step-by-step explanation:

Regular Volume: (3.5)(8.5)(15)= 446.25

Individual Volume (1/10 of regular): 446.25/10= 44.625

44.625 as Fraction: 44 5/8

Because a cubic function is a polynomial function, which are continuous curves, the domain of a cubic function is all real numbers.

All odd-degree polynomials have at least one real root; a cubic function has one to three real roots, which may or may not be distinct. A cubic function's graph always has one inflection point. It might have a local minimum and local maximum as its two critical points.

The cubic function [tex]f(x) = x^3 + x^2 + x + 1[/tex]  has a local maximum at x = 1 and a local minimum at x = 1/3. A cubic function can also have two local extreme values (1 max and 1 min).

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The percent decrease from June 2022 to August 2022 was 15%.

The percentage is defined as a ratio expressed as a fraction of 100.

During the month of June 2022, the average price per gallon of gas was $4.42.

During August of 2022, the average price per gallon of gas dropped to $3.75.

As per the question, the required solution would be as:

100 × (4.42 - 3.75) / 4.42

= 15.1583

Rounding to the nearest percent, we get

= 15%

Thus, the percent decrease was 15%.

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Answer:

The answer is that a(t) is decreasing from 5 to 6 minutes.

Step-by-step explanation:

The other answers do not make sense, except for one which may be confusing. That answer is that a(t) is negative from 5 to 6 minutes.

The graph, however, while decreasing, is never negative, as the distance can never be a negative measurement. Nor is the graph slanted up and to the left.

This could result in an unexpected transformation. Therefore, the order of the matrices must be taken into account when combining them.

Matrix is a mathematical entity composed of elements arranged in rows and columns. It is used to represent and manipulate various types of data and is commonly used in scientific and engineering applications. Matrices are useful for representing linear equations and transformations of vector spaces, such as scaling and rotation. They can also be used to store data and perform calculations on that data.
Matrix A is a scaling matrix which is used to change the size of an object. This transformation is achieved by multiplying each component of the vector by a value, resulting in a larger or smaller object.

Matrix B is a rotation matrix which is used to rotate an object. This transformation is achieved by multiplying each component of the vector by a coefficient which is then added to the other components, resulting in a rotated object.

Matrix D is a combination of matrices A and B, where the effects of matrix A are applied first and then the effects of matrix B are applied. Care must be taken when combining the two matrices because the order of the transformations matters; applying the effects of matrix B first would result in a different transformation than applying the effects of matrix A first. If matrix B is applied first, it will rotate the object before it is scaled, meaning that the scaling will be applied to the already-rotated object. This could result in an unexpected transformation. Therefore, the order of the matrices must be taken into account when combining them.

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The measure of angle x is  30°

Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is concerned with the measurement of angles and the calculation of sines, cosines, and tangents of those angles.

These ratios are known as trigonometric functions and they are used to relate the ratios of the sides of a right triangle to the angles opposite or adjacent to the right angle.

cos(x) = (√3)/2

x = cos⁻¹((√3)/2) = 30°

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The new coordinates of point D after the transformation(-4 -4)

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Using the general depreciation calculation, y = A(1 - r)^t, the car will be worth $12528.15 after 4 years.

Y = A(1 - r)^t, is the general depreciation formula, which is used to solve the car's worth.

Description of the variables

y is the current value and where =?

Original cost was $24,000,

rate of depreciation was 15%, and

time was measured in years. = 4 years

plugging in the values

current value, y = A(1 - r)^t

current value, y = 24000 * (1 - 0.15)^4

current value, y = $12528.15

The car has been depreciated to $12528.15

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complete question

The general equation for depreciation is given by y = A(1 – r)t, where y = current value,

A = original cost, r = rate of depreciation, and t = time, in years.

The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years?

The statement "The output is three less than the input x" as an expression is y = x - 3

From the question, we have the following parameters that can be used in our computation:

A mathematical statement

The mathematical statement is given as

The output is three less than the input x

Less than here means minus

So, we have the following representation

The output is three less than the input x = x - 3

The question does not require that we solve the expression

So, we leave it at x - 3

Introduce the output varianle

y = x - 3

Hence, the required expression is y = x - 3

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Answer:

a = 6 , b = 17

Step-by-step explanation:

using Pythagoras' identity.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

using right triangle ABD , then

a² + 8² = 10²

a² + 64 = 100  ( subtract 64 from both sides )

a² = 36 ( take square root of both sides )

a = [tex]\sqrt{36}[/tex] = 6

using right triangle ABC

note that BC = a + 9 = 6 + 9 = 15

b² = 8² + 15² = 64 + 225 = 289 ( take square root of both sides )

b = [tex]\sqrt{289}[/tex] = 17

The diagram that models the story is given as follows:

Right diagram.

The equation that models the story is given as follows:

c = 12 x 8.

The story is modeled applying the proportions from the units given in the context of the problem.

We have that the parameters are given as follows:

Hence the total number of charms that she purchased is given as follows:

c/12 = 8.

c = 12 x 8. (which is the equation that models this situation).

c = 104.

The diagram that represents a multiplication of 12 by 8 is the diagram that is composed by a successive addition of twelve times the number 8, hence it is the right diagram.

The complete problem is given by the image presented at the end of the answer.

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The greatest common factor of the expression 5x²a + 5xa² is 5xa

To find the greatest common factor (GCF) of the expression 5x²a + 5xa², we need to find the greatest term that can divide into both terms in the expression.

In this case, the GCF is 5xa, as it can divide into both 5x²a and 5xa².

We can check this by dividing both terms with 5xa:

5x²a + 5xa² = (5xa)(x) + (5xa)(a) = 5xa (x + a)

Thus, the GCF of 5x²a + 5xa² is 5xa.

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According to the information, it can be inferred that the total matches that would be played in total are 160,461.

A combination is a term to refer to an arrangement of elements in no particular order. For example:

When we put together a sandwich with salami, ham and turkey. The order in which the deli meats are placed does not matter as long as they are in a sandwich. There is only one way to stack the meat on the sandwich when the order doesn't matter.

To calculate how many matches will be played in total we have to perform the following procedure:

[tex]= ^{567} C_{2} \\= \frac{(567)!}{2!565!} \\= \frac{567 * 566 * (565)!}{2 * (565)!} \\= 567 * 283\\= 160,461\\\\[/tex]

As we can see after the combination, the number of games that would be played in this tournament would be 160,461.

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On solving the provided question we can say that the solution required angle bisector  ∠BCE=50°.

An angle bisector or the bisector of an angle is a ray that divides an angle into two equal parts. For example, if a ray AX divides an angle of 60 degrees into two equal parts, then each measure will be equal to 30 degrees. Every angle has an angle bisector.

The sum of all the three angles of the triangle is 180°.

∠BAC=70° and ∠ABC=60°.

We know that in a triangle there are three angles and the sum of all the three angles is 180°.

∠ABC+∠BAC+∠BCE=  180°

Putting the values of the given angles we have,

60°+70°+∠BCE=180°

on adding the angles,

130°+∠BCE=180°

aking 130° to the right-hand side,

∠BCE=180°-130°

on solving we have,

∠BCE=50°

Therefore, the required angle is 50°.

The required angle ∠BCE=50°.

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On solving the provided question we can say that the solution required angle bisector  ∠BCE=50°.

An angle bisector or the bisector of an angle is a ray that divides an angle into two equal parts. For example, if a ray AX divides an angle of 60 degrees into two equal parts, then each measure will be equal to 30 degrees. Every angle has an angle bisector.

The sum of all the three angles of the triangle is 180°.

∠BAC=70° and ∠ABC=60°.

We know that in a triangle there are three angles and the sum of all the three angles is 180°.

∠ABC+∠BAC+∠BCE=  180°

Putting the values of the given angles we have,

60°+70°+∠BCE=180°

on adding the angles,

130°+∠BCE=180°

aking 130° to the right-hand side,

∠BCE=180°-130°

on solving we have,

∠BCE=50°

Therefore, the required angle is 50°.

The required angle ∠BCE=50°.

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Answer:

Step-by-step explanation:

12 ÷ (4 − (6 × 2 − ((3 + 3) × 2 − 1)))

12 ÷ (4 − (12 − ((3 + 3) × 2 − 1)))

12 ÷ (4 − (12 − ((6) × 2 − 1)))

12 ÷ (4 − (12 − (12 − 1)))

12 ÷ (4 − (12 − 11)))

12 ÷ (4 − (1))

12 ÷ (4 − 1)

12÷3

4

The width of the rectangle is 1 in.

A rectangle is a type of parallelogram, having each angle right angle and equal diagonal.

Given that, A rectangle has a length that is five times longer than its width. and the perimeter of the rectangle is 12 inches

Perimeter of a rectangle = 2(length+width)

Let the width be w then length will be (5w)

Therefore,

(w+5w)2 = 12

6w = 6

w = 1

Hence, the width of the rectangle is 1 in.

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Answer:-7

Step-by-step explanation:

3 to -4 the difference is -7

The answer is -7

Answer: 0

Step-by-step explanation:

c2+2c−24=0

Answer:

7.

Step-by-step explanation:

Mean = (2+10+9)/3

= 21/3

= 7.

Answer:

the mean is 7

Brief explanation:

To find the Mean of a set we add all the numbers first.

Remember that the Mean relies on a sum.

So we just add up 2 + 10 + 9 = 21

Then divide 21 by 3 (3 because there are 3 numbers in this set) :

21 : 3 = 7

 We take all the numbers in the set, and divide by how many numbers we have in this set.

--

The length KM is equivalent to 8.61 ft.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

Given is that JKLM is a parallelogram such that JN = 5 ft and KN = 7 ft.

We can write that -

KM² = JN² + KN²

KM² = 5² + 7²

KM² = 25 + 49

KM² = 74

KM = √74

KM = 8.61

Therefore, the length KM is equivalent to 8.61 ft.

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Answer:

-792

Step-by-step explanation:

According to PEMDAS, you would multiply 8 x 100 first making the equation

1+1+1-5+2+2+2+4-800+1

then combine like terms, 8-800+1

Since 8 is smaller than 800, you would get a negative number, -792

then you add 1, making your answer -792

The answer is:

1. n = m ........ .There is not enough information to tell.

2. n > m  .........T is a one-to-one transformation.

3. n < m ......... There is not enough information to tell.

The transformation matrix is a matrix that transforms one vector into another vector. The positional vector of a point is changed to another positional vector of a new point, with the help of a transformation matrix.

he transformation matrix transforms a vector into another vector, which can be understood geometrically in a two-dimensional or three-dimensional space. The frequently used transformations are stretching, squeezing, rotation, reflection, and orthogonal projection.

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a) The y-intercept of the line is 25.66, which represents the predicted number of wins when yards allowed is 0.

b) The Seattle Sea hawks, the observed number of wins (10) is 4.12 less than the predicted number of wins based on the least-squares regression line.

c) It will increase the R-Sq and R-Sq(adj) and decrease the S.

The equation of the least-squares regression line is given by:

Number of wins = 25.66 - 0.003131 * (Yards_allowed)

This equation shows the relationship between the number of wins for a team (the dependent variable) and the number of yards allowed by the team (the independent variable).

The slope of the line is -0.003131, which means that for every 1 yard increase in yards allowed, the number of wins decreases by 0.003131. The y-intercept of the line is 25.66, which represents the predicted number of wins when yards allowed is 0.

b) To calculate the residual for the Seattle Seahawks, we can use the equation of the least-squares regression line and the data for the team:

Residual = Observed value - Predicted value

Residual = 10 - (25.66 - 0.003131 * 4668)

Residual = 10 - (25.66 - 14.12)

Residual = -4.12

This means that for the Seattle Seahawks, the observed number of wins (10) is 4.12 less than the predicted number of wins based on the least-squares regression line.

c) The point representing the Carolina Panthers (5167 yards allowed, 15 wins) has a positive effect on the equation of the least-squares regression line because it is above the line.

This means that the team performed better than expected based on the number of yards allowed. Since this point is an outlier, it will increase the R-Sq and R-Sq(adj) and decrease the S.

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