Given the following system of linear equations, do Part A and Part B below. Part A: Using the method of your choice (graphing, substitution or addition), find the solution to the system of linear equations. Include all of your work in your final answer. Part B: In two or more complete sentences, explain why you chose the specific method you used to find the solution to the system. WRITER

The transition matrix from B to B':

\(\left[\begin{array}{ccc}1&1/2&1/2\\0&1&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}1&1&2\\11&-1&6\\-23&-3&-5\end{array}\right]\)

A row-echelon matrix means that Gaussian elimination is performed on the rows, and a column-echelon form means that Gaussian elimination is performed on the columns. That is, if the transpose of a matrix is ​​in row form, then it is in column form. Therefore, in the rest of this article, only the row-echelon form is considered. Similar columnar properties can be easily derived by transposing all the matrices.

According to the Question:

Consider the given matrices:

B = {(1,2,7),(-1,2,0), (2,4,0) }

B' = {(0,2,1) ,(-2,1,0), (1,1,1)}

The objective is to find the transition matrix from B to B′.

Step 2

Consider the given matrices:

B = {(1,2,7),(-1,2,0), (2,4,0) }

B' = {(0,2,1) ,(-2,1,0), (1,1,1)}

Now,

BB' = \(\left[\begin{array}{ccc}0&-2&1\\2&1&1\\1&0&1\end{array}\right] \left[\begin{array}{ccc}1&-1&2\\2&2&4\\7&0&0\end{array}\right]\)

      = \(\left[\begin{array}{ccc}2&1&1\\0&-2&1\\1&0&1\end{array}\right] \left[\begin{array}{ccc}2&2&4\\1&-1&2\\7&0&0\end{array}\right]\)

Now, reducing it into Echelon’s form:

Interchange the first row and second row:

    \(\left[\begin{array}{ccc}1&1/2&1/2\\0&-2&1\\1&0&1\end{array}\right] \left[\begin{array}{ccc}1&1&2\\1&-1&2\\7&0&0\end{array}\right]\)  

= \(\left[\begin{array}{ccc}1&1/2&1/2\\0&-2&1\\0&-1/2&1/2\end{array}\right] \left[\begin{array}{ccc}1&1&2\\1&-1&2\\6&-1&-2\end{array}\right]\)

Multiply the second row by -1/2

 =  \(\left[\begin{array}{ccc}1&1/2&1/2\\0&1&-1/2\\0&0&1/4\end{array}\right] \left[\begin{array}{ccc}1&1&2\\-1/2&1/2&1\\23/4&-3/4&-5/4\end{array}\right]\)

Multiply the third row by 4 and add -1/2 times the third row to the second row:

 = \(\left[\begin{array}{ccc}1&1/2&1/2\\0&1&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}1&1&2\\11&-1&6\\-23&-3&-5\end{array}\right]\)

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Answer:

true

Step-by-step explanation:

The parametric equations for a circle of radius 4 centered at (2,−5) are:

x = 2 + 4 cos(t)

y = -5 + 4 sin(t)

where t is a parameter that ranges from 0 to 2π.

Parametric equations are equations that describe the coordinates of a point as a function of time. In this case, the point is moving around a circle of radius 4 centered at (2,−5). The parameter t controls the angle of the point on the circle. When t=0, the point is at the top of the circle. As t increases, the point moves counterclockwise around the circle. When t=2π, the point is back at the top of the circle.

The equations can be derived using the following steps:

The center of the circle is (2,−5).

The radius of the circle is 4.

The angle of the point on the circle is t.

The x-coordinate of the point is x=2+4cos(t).

The y-coordinate of the point is y=−5+4sin(t).

Parametric equations can be used to represent a variety of curves, including circles, ellipses, parabolas, and hyperbolas. They can also be used to represent motion, such as the motion of a particle around a circle.

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The parametric equations for a circle of radius 4 centered at (2,−5) are:

x = 2 + 4 cos(t)

y = -5 + 4 sin(t)

where t is a parameter that ranges from 0 to 2π.

Parametric equations are equations that describe the coordinates of a point as a function of time. In this case, the point is moving around a circle of radius 4 centered at (2,−5). The parameter t controls the angle of the point on the circle. When t=0, the point is at the top of the circle. As t increases, the point moves counterclockwise around the circle. When t=2π, the point is back at the top of the circle.

The equations can be derived using the following steps:

The center of the circle is (2,−5).

The radius of the circle is 4.

The angle of the point on the circle is t.

The x-coordinate of the point is x=2+4cos(t).

The y-coordinate of the point is y=−5+4sin(t).

Parametric equations can be used to represent a variety of curves, including circles, ellipses, parabolas, and hyperbolas. They can also be used to represent motion, such as the motion of a particle around a circle.

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The increase in surface area is 0.6 times the sum of the length and width of the box.

A rectangular prism is a 3-dimensional shape with six rectangular faces. The surface area of a rectangular prism is calculated by finding the sum of the areas of all six faces. The formula for surface area is:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

In this case, we know that the height of the box is 33 cm, and it increases by 0.3 cm. Therefore, the new height is 33.3 cm.

To find the increase in surface area, we need to calculate the surface area before and after the height increase.

Let's assume that the length and width of the box remain constant. In that case, the surface area before the height increase is:

SA1 = 2lw + 2lh + 2wh = 2lw + 2(33)(w) + 2(33)(l)

Similarly, the surface area after the height increase is:

SA2 = 2lw + 2l(33.3) + 2w(33.3)

To find the increase in surface area, we subtract SA1 from SA2:

SA2 - SA1 = [2lw + 2l(33.3) + 2w(33.3)] - [2lw + 2(33)(w) + 2(33)(l)]

Simplifying the expression, we get:

SA2 - SA1 = 2(33.3 - 33)(l + w)

SA2 - SA1 = 0.6(l + w)

Therefore, the increase in surface area is 0.6 times the sum of the length and width of the box.

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Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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El valor que satisface D es 188.

El modelo matemático será así:

D/d = 12(resto 8)

si escribimos 8 como resto de D, entonces:

(D-8) /d=12

D-8= 12d o se puede escribir D= 12d+8

luego sustituya D= 12d+8 por D+d= 203

D+d= 203

(12d +8) +d= 203

13d= 203-8

13d= 195

re=15

sustituir d=15 en D+d= 203

D+d= 203

D+15=203

D=203-15

D=188

El modelo matemático es una forma de interpretación humana al traducir o formular problemas existentes en forma matemática, de modo que el problema pueda resolverse utilizando las matemáticas.

El uso principal de los modelos matemáticos es ayudar a las personas a comprender los problemas y simplificarlos para que puedan resolverse.

, los siguientes son algunos de los usos que se obtienen al utilizar un modelo matemático, a saber:

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Answer:

Step-by-step explanation:

The experimental probability of the cube landing on three is 1/10.

Answer:

60 feet

Step-by-step explanation:

Perimeter is the sum of the four sides of a rectangle

the formula for the perimeter of a rectangle = 2 x (length + breadth)

2 x (10 + 20)

2 x (30)

= 60 feet

Alternatively, you can add the sides together : 10 + 10 + 20 + 20 = 60 feet

The smallest possible weight in grams of the phone and case combined is 325.6 grams.

Kyle buys a mobile phone that weighs 310 g. He puts the phone inside a

protective case that weighs 15.6 g.

Therefore, the smallest possible total weight in grams of the phone and case combined can be calculated as follows:

Hence,

weight of the phone and case study = 310 + 15.6

weight of the phone and case study = 325.6

weight of the phone and case study = 325.6 grams

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Answer:

hope this helps you

Caspian Sea is elevated at 92 feet (or 28 meters) below sea level. (globally preferred unit is meters)

On the scale of sea levels, a certain height has been assigned zero elevation. This acts as a reference point for rest of the measurements and is called Mean Sea Level (MSL). It is also known as still water level.

Caspian Sea at 92 feet below sea level means it is 92 feet below MSL. Thus, its elevation is considered 92 feet below sea level.

Global MSL is calculated using the spatial average of the complete ocean's level.

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Answer:

The volume of the larger solid can't be determined with the information provided.

This is because you only know the volume and surface area of one solid, but you don't know the shape or dimensions of either solid. The volume and surface area are not enough to determine the shape, size or the volume of the larger solid.

In general, the relationship between the volume and the surface area of a solid is dependent on the shape of the solid. For example, a cube has a constant ratio of surface area to volume, while a sphere has a different ratio. So, knowing the surface area alone doesn't allow us to calculate the volume.

The answers based on the given information:

1. Output per worker (Y/L) is given as 100. Capital per worker (K/L) is given as 40,000.

2. Investment per worker (I/L) can be calculated using the savings rate (s). I/L = s * (Y/L). Since the savings rate is 20% (0.20), I/L = 0.20 * 100 = 20.

3. Depreciation per worker can be calculated using the depreciation rate (d) and capital per worker (K/L). Depreciation per worker = d * (K/L). Since the depreciation rate is 4% (0.04), Depreciation per worker = 0.04 * 40,000 = 1,600.

4. Net investment per worker can be calculated by subtracting depreciation per worker from investment per worker. Net investment per worker = (I/L) - Depreciation per worker = 20 - 1,600 = -1,580.

5. Since the net investment per worker is negative, capital per worker is decreasing.

7. If capital per worker is 360,000, net investment can be calculated by multiplying the savings rate by the new output per worker (assuming it stays the same) and then subtracting the depreciation. Net investment = (s * (Y/L)) - (d * 360,000) = (0.20 * 100) - (0.04 * 360,000) = 20 - 14,400 = -14,380.

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Answer:

The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where r is the radius and h is the height. In this case, the volume is 500 ml, or 0.5 liters. To convert liters to cm, we can use the conversion factor 1 liter = 10 cm^3. Therefore, the height of the jug can be calculated as follows:

0.5 liters = 0.5 x 10 cm^3 = 500 cm^3

V = πr^2h

500 = π x (3 cm)^2 x h

h = 500 / (π x (3 cm)^2)

Approximating π as 3.14, we get:

h = 500 / (3.14 x (3 cm)^2)

h = 500 / (3.14 x 9 cm^2)

h = 500 / 28.26 cm^2

h = 17.67 cm

So the height of the cylindrical measuring jug is approximately 17.67 cm. Therefore, the distance between each marking, which represents 100 ml of volume, is 17.67 cm / 5 = 3.534 cm.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

To determine the distance between each of the markings, we need to determine the height of the jug for each 100 ml increment.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. We know the volume of the jug is 500 ml, or 0.5 liters, and the radius is 3 cm, so we can solve for the height:

0.5 liters = π * (3 cm)^2 * h

h = 0.5 liters / π * (3 cm)^2

h = 0.5 liters / 9π cm^2

Now that we have the height of the jug per 100 ml, we can divide it by 5 to determine the height between each marking:

Marking height = h / 5

= 0.5 liters / 9π cm^2 / 5

= 0.1 liters / 9π cm^2

So the distance between each of the markings is the height of the jug for each 100 ml increment divided by 5.

Answer:

0.9821

Step-by-step explanation:

Probability that a randomly selected value will be less than 2.1 deviations from the mean ; this means the Zscore = 2.1

Hence, using :

P(Z < 2.1) = 0.9821 (standard normal table

= 0.9821

Answer:

Mi-Ling saves more money.

Step-by-step explanation:

At 3 weeks Mi-Ling has saved $45, whereas Daniel at 3 weeks has only saved $30

i. The equation of the plane is 4x + 8y - 4z + 48 = 0. ii.The line crosses the z-axis at the point (0, 0, 12).

The equation of the plane determined by the points (-5,-1,5), (1,-3,7), and (-7,-1,3) can be found by solving a system of equations. We can write the equation of the plane in the form Ax + By + Cz + D = 0, where A, B, C, and D are constants.

To find the equation, we need to find the normal vector to the plane. We can obtain the normal vector by taking the cross product of two vectors formed by the given points. Let's choose the vectors (-5,-1,5) to (1,-3,7) and (-5,-1,5) to (-7,-1,3):

Vector A = (1-(-5), -3-(-1), 7-5) = (6, -2, 2)

Vector B = (-7-(-5), -1-(-1), 3-5) = (-2, 0, -2)

Taking the cross product of A and B, we get the normal vector N = A × B:

N = (4, 8, -4)

Now, we can substitute one of the given points and the normal vector into the equation of the plane to find D. Let's use the point (-5,-1,5):

4(-5) + 8(-1) + (-4)(5) + D = 0

-20 - 8 - 20 + D = 0

D = 48

Therefore, the equation of the plane is 4x + 8y - 4z + 48 = 0.

To determine where the line crosses the z-axis, we need to find the point where the line intersects the plane when x and y are both zero. Substituting x = y = 0 into the equation of the plane, we can solve for z:

4(0) + 8(0) - 4z + 48 = 0

-4z + 48 = 0

-4z = -48

z = 12

Thus, the line crosses the z-axis at the point (0, 0, 12).

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To show that the limit does not exist, we need to show that it has different limits as it approaches (0,0) along different paths. Let x = y: We can use the denominator of the fraction to write \((x^2 + y^2)\) as \(2x^2\). Substituting this in the numerator, we get \((x^2 - x^2) = 0.\)

To show that the limit does not exist, we need to show that it has different limits as it approaches (0,0) along different paths. Let x = y: We can use the denominator of the fraction to write \((x^2 + y^2) as 2x^2.\) Substituting this in the numerator, we get \((x^2 - x^2) = 0\). Therefore, the limit reduces to the following:

\(y^2}{x^2 + y^2})^2\) = \((\frac{0}{2x^2})^2\)

= 0\]Let

x = ky, where k is a constant: Substituting in the limit, we get:\(\[\lim_{(x,y) \to (0,0)} (\frac{x^2 - y^2}{x^2 + y^2})^2\)

\(= \lim_{y \to 0} (\frac{(k^2 - 1)y^2}{(k^2 + 1)y^2})^2\)

= \((\frac{k^2 - 1}{k^2 + 1})^2\]\) The limit does not exist as it has different limits as it approaches (0,0) along different paths.

To show that the limit does not exist, we need to show that it has different limits as it approaches (0,0) along different paths. Let x = y: We can use the denominator of the fraction to write \((x^2 + y^2) as 2x^2\). Substituting this in the numerator, we get \((x^2 - x^2) = 0\). Therefore, the limit reduces to the following:\(\[\lim_{(x,y) \to (0,0)}\)(\frac{x^2 - y^2}{x^2 + \(y^2})^2 = (\frac{0}{2x^2})^2\)

= 0\]Let

x = ky, where k is a constant: Substituting in the limit, we get:\(\[\lim_{(x,y) \to (0,0)} (\frac{x^2 - y^2}{x^2 + y^2})^2 = \lim_{y\)\to 0} \((\frac{(k^2 - 1)y^2}{(k^2 + 1)y^2})^2 = (\frac{k^2 - 1}{k^2 + 1})^2\]\) The limit does not exist as it has different limits as it approaches (0,0) along different paths.

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If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b)  \(15x+12y = 348\) and \(8x+8y = 200\) .

let the number of jackets purchased be = x ;

let the number of pairs of sweatshirts purchased be = y ;

the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,

that means the equation that represents the situation is :

\(15x+12y = 348\) .

Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,

that means the equation that represents the situation is :

\(8x+8y = 200\) .

Therefore , the system of equations are \(15x+12y = 348\) and \(8x+8y = 200\) .

The given question is incomplete , the complete question is

A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?

(a) 8x + 8y = 200  ;  12x + 15y = 348   ;

(b) 8x + 8y = 200  ; 15x + 12y = 348 ;  

(c) 8x + 8y = 348  ;  12x + 15y = 200 ;  

(d) 8x + 8y = 348 ;  15x + 12y = 200 .

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Answer:

100 packets

Step-by-step explanation:

Given :

Cost = fixed cost + variable cost

Fixed cost = $500

Variable cost = $10

Sales price = $15

Let :

Number of packets = x

To break even :

fixed cost + variable cost = sales made

500 + 10x = 15x

500 = 15x - 10x

500 = 5x

x = 500 / 5

x = 100

100 packets

Using the conversion factor we know that Michale needs to 21 feet of fabric.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

For instance, 12 inches equals one foot when converting between inches and feet.

So, convert yards into feet using the conversion factor as follows:

1 yard = 3 feet

11.5 = 34.5 feet

Michael needs: 34.5 feet

Michael has: 13.5 feet

More fabric Micael needs:

34.5 feet - 13.5 feet

21 feet

Therefore, using the conversion factor we know that Michale needs to 21 feet of fabric.

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The area of the shaded region is the one in the third option; 18π

We can see that if we add the two shaded regions, we get half of a circle.

Remember that the area of a circle of radius R is:

A = πR²

And the area of half of a circle is half of what we wrote above.

Here we can see that the radius of the composite circle is:

R = 4 + 2= 6 units.

Replacing that in the area formula, and dividing by 2, we will get:

Area =  π(6)²/2 = 18π

Then the correct option is the third one, counting from the top.

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TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.

This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.

When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.

To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.

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If you want to eliminate x than multiply equation 1 by 4 and equation 2 by 3 and subtract them or,

If you want to eliminate y than mutiply equation 1 by 8 and equation 2 by 11 and subtract them.

Answer:

b=19

Explanation:

Answer:19

Step-by-step explanation:14+5=19

The maximum value attained by the sum of the expression is 169 when N is the two-digit number 98.

Let N be a two-digit number with digits a and b. Then, the sum of N and the product of its digits is N + ab, and the sum of N's digits is a + b. Therefore, the expression we want to maximize is:

Substituting N = 10a + b, we get:

To maximize this expression, we want to maximize a and b. Since a and b are digits, they must be between 1 and 9. If we set a = 9 and b = 8, we get:

Therefore, the maximum value attained by the expression is 169 when N is the two-digit number 98.

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Answer:

Step-by-step explanation:

AREA OF CIRCLE = 660.185CM^2

HOPE IT HELPS