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Using Gauss-Jordan method, the value of x, y and z are 0, -2 and 1

To solve the system of equations using the Gauss-Jordan method, we'll perform row operations to transform the augmented matrix into row-echelon form and then further transform it into reduced row-echelon form. Here are the steps:

1. Write the augmented matrix for the system of equations:

  [1  -2   4  |  20]

  [1   1  13  | -31]

  [-2   6  -1 | -69]

2. Perform row operations to transform the matrix into row-echelon form:

  R2 = R2 - R1

  R3 = R3 + 2R1

  [1  -2   4  |  20]

  [0   3   9  | -51]

  [0   2   7  | -29]

3. Perform row operations to further transform the matrix into reduced row-echelon form:

  R2 = R2 / 3

  R3 = R3 - 2R2

  [1  -2   4  |  20]

  [0   1   3  | -17]

  [0   0   1  |   1]

4. Perform row operations to obtain a diagonal of 1s from left to right:

  R1 = R1 + 2R2 - 4R3

  R2 = R2 - 3R3

  [1  0  0  |   0]

  [0  1  0  |  -2]

  [0  0  1  |   1]

The resulting matrix corresponds to the system of equations:

x = 0

y = -2

z = 1

Therefore, the solution to the given system of equations is x = 0, y = -2, and z = 1.

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Answer:

Step-by-step explanation:

The general equation for an ellipse with center (h, k) is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]

If a > b, the ellipse is horizontal.

If b > a, the ellipse is vertical.

Given equation:

[tex]\dfrac{(x-5)^2}{4}+\dfrac{(y+5)^2}{9}=1[/tex]

As b > a, the ellipse is vertical. Therefore:

Comparing the given equation with the standard form, we get:

Therefore:

To graph the ellipse:

A) The probability that a randomly selected student studies only mathematics would be 20/75.

B) The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.

C) The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.

D) The exact probability that a student studies mathematics and physics cannot be determined without knowing the number of students who study both subjects.

To determine the requested probabilities, we will use the information provided about the group of 75 students.

a) Study only mate:

We know that there are 20 students studying mathematics and physics, so the number of students studying only mathematics would be the total number of students studying mathematics (20) minus the number of students studying both subjects. Since no information is provided on the number of students studying both subjects, we will assume that none of the students study both subjects. Therefore, the number of students studying only mathematics would be 20 - 0 = 20.

The probability that a randomly selected student studies only mathematics would be 20/75.

b) Study math or physics:

To determine this probability, we need to add the number of students who study mathematics and the number of students who study physics, and then subtract the number of students who study both subjects (we again assume that none of the students study both subjects).

Number of students studying mathematics = 20

Number of students studying physics = X (not given)

Number of students studying both subjects = 0 (assumed)

Therefore, the number of students studying mathematics or physics would be 20 + X - 0 = 20 + X.

The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.

c) That he does not study either:

The number of students not studying either subject would be the complement of the number of students studying mathematics or physics. So it would be 75 - (20 + X).

The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.

d) To study math and physics:

Since no information is provided on the number of students studying both subjects, we cannot determine the exact probability that a student will study mathematics and physics.

In summary:

a) The probability that a randomly selected student studies only mathematics would be 20/75.

b) The probability that a randomly selected student studies mathematics or physics would be (20 + X) / 75.

c) The probability that a randomly selected student does not study either of the two subjects would be (75 - (20 + X)) / 75.

d) The exact probability that a student studies mathematics and physics cannot be determined without knowing the number of students who study both subjects.

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Answer:

-27+15 (N-1)

Step-by-step explanation:

-27, -12, 3, 18

Take the second term and subtract the first term to find the common difference

-12 - (-27)

-12+27 = 15

The common difference is +15

We are adding 15 each time

The formula for an arithmetic sequence is

an = a1+d(n-1)

an = -27 +15(n-1)

Answer:

0

Step-by-step explanation:

Use the following models to show the equivalence of the fractions 35 and 610 a) Set model

The amount of snow accumulated between 2 am and 5 am is: 1.25 inches

The general formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the given graph attached, we see that the y-axis gives the amount of snow at different specific times.

Meanwhile the x-axis gives the time in hours after midnight

At 2am, the y-axis value is 1.25 inches, and as such at 2am snow accumulation was 1.25 inches.

At 5 am, the y-axis value reads 2.5 inches, and as such at 5am snow accumulation was 2.5 inches.

The difference in both snow accumulations is:  2.5 - 1.25 = 1.25

Hence, 1.25 inches snow accumulated between 2 am and 5 am.

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Answer:

The range of this graph is (-4, 6], or

-4 < y < 6.

The range of the graph is [-4, 6].

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

This ultimately implies that, a range simply refers to the set of all possible output numerical values (real numbers), which are shown on the y-coordinate (y-axis) of a graph.

Based on the information provided in this scenario, the domain and range of the graph of this equation can be determined are as follows:

Domain = [1, 10] or 1 ≤ x < 10

Range = [-4, 6], or -4 < y ≤ 6.

Therefore, the range can be rewritten as [-4, 6].

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Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts

Step-by-step explanation:

Answer:

perimeter = 75 cm , area ≈ 28.3 in²

Step-by-step explanation:

23 (a)

since the figure is being enlarged by a scale factor of 5

then the perimeter is increased by a factor of 5.

perimeter of larger shape = 5 × 15 = 75 cm

24

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{90}{360}[/tex]

  = π × 6² × [tex]\frac{1}{4}[/tex]

  = 36π × [tex]\frac{1}{4}[/tex]

  = 9π

  ≈ 28.3 in² ( to 1 decimal place )

Using the given operations and nine 9s, you can make 1001.

To make 1001 using nine 9s, you can use the following mathematical operations:

1. (9 + 9 + 9) * 9 * 9 - 9 - 9 - 9 = 1001

- Adding three 9s together: (9 + 9 + 9) = 27

- Multiplying the sum by two 9s: (27 * 9 * 9) = 2187

- Subtracting three 9s: (2187 - 9 - 9 - 9) = 2160

- Adding one 9: (2160 + 9) = 2169

- Adding 832 (which is (9 * 9 * 9 + 9 * 9 + 9)) to 2169: (2169 + 832) = 3001

- Subtracting two 9s: (3001 - 9 - 9) = 2983

- Adding nine 9s: (2983 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9) = 1001

Therefore, using the given operations and nine 9s, you can make 1001.

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Para representar gráficamente los vectores 2u, -3v y 1/4, necesitamos utilizar los vectores dados A(-1,3), B(-2,4), C(0,-2) y D(8,1).

Vector 2u:

El vector 2u se obtiene al multiplicar el vector u por 2. Si conocemos las coordenadas de u, podríamos multiplicar cada componente por 2. Sin embargo, no se proporciona información sobre las coordenadas de u, por lo que no podemos realizar este cálculo específico.

Vector -3v:

Similar al caso anterior, para obtener el vector -3v, debemos multiplicar el vector v por -3. Sin información sobre las coordenadas de v, no podemos realizar este cálculo específico.

Vector 1/4:

El vector 1/4 se obtiene al multiplicar cada componente de los vectores A, B, C y D por 1/4. Podemos calcular las nuevas coordenadas de estos vectores:A' = (-1/4, 3/4)

B' = (-1/2, 1)

C' = (0, -1/2)

D' = (2, 1/4)

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Answer:

Any equation that has the power of x at 1

Step-by-step explanation:

Since the function f(x) = -2x -3 +8 has an infinite range, so any other equation that only contains x^1 would work

Answer:

∠1 = 100

∠2 = 110

Step-by-step explanation:

∠1  + 80 = 180(angles on a straight line add to 180)

∠1 = 180 - 80

∠1 = 100

∠2 = 110 (vertically opposite angles are equal)

The algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2).  Option B.

To translate a figure 3 units to the left and 2 units up, we need to adjust the coordinates of the figure accordingly. The algebraic rule that represents this translation can be determined by examining the changes in the x and y coordinates.

When we move a figure to the left, we subtract a certain value from the x coordinates. In this case, we want to move the figure 3 units to the left, so we subtract 3 from the x coordinates.

Similarly, when we move a figure up, we add a certain value to the y coordinates. In this case, we want to move the figure 2 units up, so we add 2 to the y coordinates.

Taking these changes into account, we can conclude that the algebraic rule for translating the figure 3 units left and 2 units up is (x-3, y+2). The x coordinates are shifted by subtracting 3, and the y coordinates are shifted by adding 2. SO Option B is correct.

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Answer:

18.84 in

Step-by-step explanation:

The circumference of a circle = pi * diameter = 6*3.14 = 18.84 in.

Answer:

Only one scalene triangle with side lengths of 12 in, 15 in, and 18 in exists. Therefore, exactly one unique triangle exists with the given side lengths.

Step-by-step explanation:

The function that satisfies the given condition is y = 3x + 2.

The correct answer to the given question is option B.

We are to find the function that satisfies the condition: When x increases from a to a + 2, y increases by a difference of 6.

A statement such as this represents a linear function, where y increases at a constant rate with respect to the increase in x.Let y = mx + b, be a linear function.

We know that when x increases from a to a + 2, y increases by a difference of 6. In other words, we can express this relationship using the following equation:

2m + b − m − b = 6 ⇒ m = 3

The function has been found to be y = 3x + b.

To find the value of b, we need to use the fact that when x increases from a to a + 2, y increases by a difference of 6: y(a + 2) − y(a) = 6 ⇒ 3(a + 2) + b − 3a − b = 6 ⇒ 6 = 6

Therefore, the function that satisfies the given condition is y = 3x + 2. The correct option is B) y = 3x + 2.

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Answer/Step-by-step explanation:

C., the first proof we would be given if a little box is shown, which indicates a 90 degree angle at the place where to lines touch  in a T kind of manor. So C is the answer.

Answer: C

b = 6; JG = 34; HF = 29

Answer:

[tex] \frac{a}{2x - 3} + \frac{b}{3x +4} = \frac{x + 7}{ 6{x}^{2} - x - 12} [/tex]

[tex](3x + 4)a + (2x - 3)b = x + 7[/tex]

3a + 2b = 1---->9a + 6b = 3

4a - 3b = 7---->8a - 6b = 14

--------------- ----------------

17a = 17

a = 1, b = -1

The total liabilities and stockholders' equity for Deacon Company as of March 31st is $275,400.

To calculate the total liabilities and stockholders' equity, we need to add the amounts of accounts payable, common stock, and retained earnings. Accounts Payable: The balance sheet provides the information that the accounts payable is $71,100.

Common Stock: The balance sheet states that the common stock is $70,000.

Retained Earnings: The balance sheet shows that the retained earnings are $134,300.

Calculate the total liabilities and stockholders' equity: Add the amounts of accounts payable, common stock, and retained earnings.

Total liabilities and stockholders' equity = Accounts payable + Common stock + Retained earnings

= $71,100 + $70,000 + $134,300

= $275,400

Therefore, the total liabilities and stockholders' equity for Deacon Company as of March 31st is $275,400.

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Answer: D: The cost of one hand towel is $8 and the cost of one bath towel is $5.

Step-by-step explanation:

Let's assume the cost of one hand towel is 'x' dollars and the cost of one bath towel is 'y' dollars.

For the first hotel, Mr. Miller ordered 27 hand towels and 48 bath towels, resulting in a bill of $540. This can be expressed as the equation:

27x + 48y = 540 ...(equation 1)

For the second hotel, Mr. Miller ordered 50 hand towels and 24 bath towels, resulting in a bill of $416. This can be expressed as the equation:

50x + 24y = 416 ...(equation 2)

To solve this system of equations, we can use any suitable method such as substitution or elimination. Let's use the elimination method:

Multiplying equation 1 by 2 and equation 2 by 3, we get:

54x + 96y = 1080 ...(equation 3)

150x + 72y = 1248 ...(equation 4)

Now, subtracting equation 4 from equation 3, we have:

(54x + 96y) - (150x + 72y) = 1080 - 1248

-96x + 24y = -168

Dividing both sides of the equation by -24, we get:

4x - y = 7 ...(equation 5)

Now, we have a system of equations:

4x - y = 7 ...(equation 5)

50x + 24y = 416 ...(equation 2)

Solving this system of equations, we find that x = 8 and y = 5.

Therefore, the cost of one hand towel is $8 and the cost of one bath towel is $5.

So, the correct answer is option D: The cost of one hand towel is $8 and the cost of one bath towel is $5.

Answer:

Step-by-step explanation:

Total cost of hand towels for first hotel = 27 * $5 = $135

Total cost of bath towels for first hotel = 48 * $8 = $384

Total cost of hand towels for second hotel = 50 * $5 = $250

Total cost of bath towels for second hotel = 24 * $8 = $192

Total cost of all hand towels = $135 + $250 = $385

Total cost of all bath towels = $384 + $192 = $576

Total number of hand towels = 27 + 50 = 77

Total number of bath towels = 48 + 24 = 72

Average cost of one hand towel = $385 / 77 = $5

Average cost of one bath towel = $576 / 72 = $8

Answer:

89

Step-by-step explanation:

Take half of 177 and round up, which is 177/2 = 88.5 = 89

This is because 89+88=177 and 89>88, so there will be a majority.

Answer:

[tex]\textsf{12)} \quad \text{a.}\;\;m \angle 1 = 107^{\circ}, \quad \text{b.}\;\;m \angle 2 = 107^{\circ}, \quad \text{c.}\;\;m \angle 3 = 73^{\circ}[/tex]

[tex]\textsf{13)} \quad EC = 6[/tex]

[tex]\textf{14)}\quad \text{a.}\;\;x = 33, \quad \text{b.}\;\; x = 8[/tex]

Step-by-step explanation:

As the base angles of an isosceles trapezoid are congruent, the measures of angles E and J are the same. Therefore:

[tex]m\angle 3 = 73^{\circ}[/tex]

The opposite angles of an isosceles trapezoid sum to 180°. Therefore:

[tex]\implies m\angle 1 + m\angle 3 = 180^{\circ}[/tex]

[tex]\implies m\angle 1 + 73^{\circ} = 180^{\circ}[/tex]

[tex]\implies m\angle 1 = 107^{\circ}[/tex]

Since the base angles of an isosceles trapezoid are congruent, the measures of angles A and N are the same. Therefore:

[tex]m\angle 2 = 107^{\circ}[/tex]

[tex]\hrulefill[/tex]

The diagonals of isosceles trapezoid ABCD are AC and BD.

Point E is the point of intersection of the diagonals. Therefore:

[tex]BE + ED = BD[/tex]

[tex]AE + EC = AC[/tex]

As the diagonals of an isosceles trapezoid are the same length, BD = AC. Therefore:

[tex]AE + EC = BD[/tex]

Given BD = 20 and AE = 14:

[tex]\implies AE + EC = BD[/tex]

[tex]\implies 14 + EC = 20[/tex]

[tex]\implies 14 + EC - 14 = 20 - 14[/tex]

[tex]\implies EC = 6[/tex]

[tex]\hrulefill[/tex]

The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides (legs) of the trapezoid.

The formula for the midsegment of a trapezoid is:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Midsegment of a trapezoid}\\\\$M=\dfrac{1}{2}(a+b)$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the midsegment.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides.\\\end{minipage}}[/tex]

a)  From inspection of the given trapezoid:

Substitute these values into the midsegment formula and solve for x:

[tex]x=\dfrac{1}{2}(18+48)[/tex]

[tex]x=\dfrac{1}{2}(66)[/tex]

[tex]x=33[/tex]

Therefore, the value of x is 33.

b)  From inspection of the given trapezoid:

Substitute these values into the midsegment formula and solve for x:

[tex]15=\dfrac{1}{2}(22+x)[/tex]

[tex]30=22+x[/tex]

[tex]x=8[/tex]

Therefore, the value of x is 8.

Answer:

F(5)= -1

if 5 is the value on the x axis it corresponds to -1 on the y axis

The largest possible weight for the package is 11.5 kg.

To find the largest possible weight for the package, we need to consider the range within which the weight lies when rounded to the nearest kilogram.

When the package is weighed at 11 kg to the nearest kilogram, it means the actual weight could be anywhere between 10.5 kg and 11.5 kg. This is because rounding to the nearest kilogram involves considering values halfway between two integers to round up or down.

To determine the largest possible weight, we take the upper limit of this range, which is 11.5 kg. Therefore, the largest possible weight for the package is 11.5 kg.

Keep in mind that when rounding to the nearest kilogram, values from 10.5 kg to 11.4 kg would round down to 11 kg, while values from 11.5 kg to 12.4 kg would round up to 12 kg.

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According to the Committee for the Study of the American Electorate, the four states with lower voter turnout in the 2004 presidential election compared to the 2000 election were Arkansas, Hawaii, Maryland, and Tennessee.

In the 2004 presidential election, voter turnout increased in most states compared to the 2000 election. However, Arkansas, Hawaii, Maryland, and Tennessee experienced a decrease in voter participation. This means that fewer eligible voters in these states cast their ballots in the 2004 election compared to the previous one.

The reasons behind the lower voter turnout in these states could vary and might be influenced by factors such as changes in voter registration laws, campaign strategies, voter demographics, or the overall political climate in each state during that particular election cycle.

It is worth noting that while voter turnout increased in most states, overall voter participation in the United States has been historically lower compared to some other democracies.

Efforts to increase voter engagement and turnout, such as expanding access to voting and improving voter education, continue to be important in ensuring that more eligible citizens exercise their right to vote and have their voices heard in the democratic process.

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Answer:

a. Let tomorrow's temperature be x

b.

[tex] |93 - x | < 10[/tex]

c.

[tex] - 10 < 93 - x < 10 \\ - 103 < - x < - 83 \\ 103 > x > 83[/tex]

Answer:

211%

Step-by-step explanation:

percent = part/whole × 100%

percent = 19/9 × 100%

percent = 211%