o TP & E Write the augmented matrix of the system and use it to solve the system. If the system has an infinite number of solutions, express them in terms of the parameter z. X = y = Z= - 3x + - 2x + y 4y 4y + - 2z = -8 7z = 26 8z = 30 Question Help: Video 1 Video 2 M Message instructor​

Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note the perimeter of the rectangle is:

2 x Length + 2 x Width.

Answer:

2 x Length + 2 x Width.

Step-by-step explanation:

This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

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According to the information, it can be inferred that the option that the quote explains is: The outcome... is situational irony because the opposite of what was expected is what happening.

To identify the correct option that explains the quote we must read the text carefully and the options. Once we have read and understood this information, we can infer which option explains the quote.

In accordance with the above, option A would be the one that explains the quote because options B and C by discarding are fragments of the quote. So these fragments could not explain the same quote that is being used in the text. On the contrary, the paragraph of option A does explain the situation clearly.

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An equation for a line perpendicular to the line 2 = 10 can be found by finding the slope of that line and then finding the slope of the perpendicular line. The slope of the line 2 = 10 is 0, so the slope of the perpendicular line would be undefined.

The equation of a line with slope m passing through the point (x1, y1) can be written in the form:

y - y1 = m(x - x1)

Since the slope of the line is undefined, the equation of the line would be in the form:

x - x1 = constant

To find the equation of the line that passes through the point (3, 2), we substitute the values into the equation:

x - 3 = constant

So the equation of the line that is perpendicular to the line 2 = 10 and passes through the point (3, 2) is:

x - 3 = constant

or simply:

x = 3.

Zion Sun Chairs must sell each chair for at least $75.21 to earn a monthly profit of $65,000.

To determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $65,000, we can use the following formula:

Total Profit = Total Revenue - Total Cost

We know that the monthly fixed costs are $17,363.50, and the variable cost per chair is $52.17. Therefore, the total cost to produce 3,575 beach chairs each month can be calculated as follows:

Total Cost = Fixed Cost + (Variable Cost per Chair x Number of Chairs)

Total Cost = $17,363.50 + ($52.17 x 3,575)

Total Cost = $203,871.25

To earn a monthly profit of $65,000, we can set up the equation as follows:

$65,000 = Total Revenue -  $203,871.25

Total Revenue =$268,871.25

To find the minimum sales price per chair, we can divide the total revenue by the number of chairs:

Minimum Sales Price per Chair = Total Revenue / Number of Chairs

Minimum Sales Price per Chair = $268,871.25 / 3,575

Minimum Sales Price per Chair ≈ $75.208

Therefore, Zion Sun Chairs must sell each chair for at least$75.21 to earn a monthly profit of $65,000, given the monthly fixed costs, variable cost per chair, and production quantity.

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The volume of the cone shown can be described to be A. 513 π cubic units

The volume of a cone can be found by the formula :

= π x radius ² x height / 3

The radius of this cone is 9 units and the height is 19 units.

The volume of this cone then is :

= π x radius ² x height / 3

= π x 9 ² x 19/ 3

= π x 81 x 19/ 3

= π x 513

= 513 π cubic units

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Answer:

49u² - 154u + 121  factored is  (7u - 11)²

Step-by-step explanation:

To factor the given quadratic expression, 49u² - 154u + 121, rewrite in the form a² - 2ab + b².

Rewrite 49 as 7² and 121 as 11²:

[tex]\implies 7^2u^2-154u+11^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^n \cdot c^n=(ac)^n:[/tex]

[tex]\implies (7u)^2-154u+11^2[/tex]

Rewrite 154u as 2 · 7u · 11 :

[tex]\implies (7u)^2-2 \cdot 7u \cdot 11+11^2[/tex]

Compare with the form a² - 2ab + b²:

Apply the perfect square formula: a² - 2ab + b² = (a - b)²

[tex]\implies (7u)^2-2 \cdot 7u \cdot 11+11^2=(7u-11)^2[/tex]

Answer:

Step-by-step explanation:

square = a plane figure with four equal straight sides and four right angles.

so

7x + 13 = 90

7x = 90 - 13

7x = 77

x = 77 : 7

x = 11

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

check

7 x 11 + 13 =  90

90 = 90

the answer is good

Answer: The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.

For the function f(x) = -2√x + 5 + 1, as x approaches positive infinity, the square root of x approaches positive infinity as well. So, the function approaches negative infinity as x approaches positive infinity:

lim x → ∞ f(x) = lim x → ∞ -2√x + 5 + 1 = -∞

As x approaches negative infinity, the square root of x approaches 0, so the function approaches:

lim x → -∞ f(x) = lim x → -∞ -2√x + 5 + 1 = 7

Therefore, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity, and it approaches 7 as x approaches negative infinity.

Step-by-step explanation:

1. The difference between the temperature is 14°C.

2. The value of the expression will be -3x - 6y + 27.

The difference between the temperature will be:

= -10 + 24

= 14°C.

For the second part of your question, to clear the parenthesis in the expression "12 - 3(x + 2y - 5)", you can first simplify the expression inside the parenthesis:

x + 2y - 5

Next, multiply this expression by 3:

3(x + 2y - 5) = 3x + 6y - 15

Finally, substitute this back into the original expression:

12 - 3(x + 2y - 5) = 12 - (3x + 6y - 15) = 12 - 3x - 6y + 15 = -3x - 6y + 27

So, the final expression after clearing the parenthesis and combining like terms is -3x - 6y + 27.

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Answer:

Step-by-step explanation:

To calculate the percentage increase in the estimated number of millionaire households from 2017 to 2018, we need to follow these steps:

Determine the estimated number of millionaire households in 2017 and 2018. Let's call these numbers A and B, respectively.

Subtract the 2017 number from the 2018 number: B - A = C

Divide the result from step 2 by the 2017 number: C / A = D

Multiply the result from step 3 by 100 to convert it to a percentage: D * 100 = E

Round the result from step 4 to the nearest tenth of a percent.

In this case, we are given the percentage increase, so we can skip steps 1-4 and simply round the given percentage increase to the nearest tenth of a percent.

The solution of the question sin(50)sin(80)cos(50)cos(80) is cos^2(80o), the correct option is D.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot. Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).

Given;

sin(50)sin(80)cos(50)cos(80)

Now,

=sin(20°)cos(80°) – cos(20°)sin(80°)

=sin(A-B) = sinA.cosB – cosA.sinB

=sin(20°-80°)

=sin(-60°)

=cos^2(80o)

Therefore, by trigonometry the answer will be cos^2(80o).

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Answer:

Step-by-step explanation:

(X=the number)

2x+13=-21

(-21)-13=34

34x2=68

On solving the provided question, we can say that By BODMAS, 2.4of4.5-5.6/1.4+3.8*2 => 10.8-5.6/1.4+3.8*2 => 10.8-4+3.8*2 = > 14.4

The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.

By BODMAS

2.4of4.5-5.6/1.4+3.8*2

10.8-5.6/1.4+3.8*2

10.8-4+3.8*2

10.8-4+7.6

14.4

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The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).

By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.

Given function is xy²= 4. The given expression will be different as below,

dy / dx ( xy² ) - 4 = 0

2xy( dy / dx) + y² = 0

dy / dx = -y / 2x

Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).

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Answer:

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{6}~,~\stackrel{y_1}{3})\qquad P2(\stackrel{x_2}{-3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{(~~-3 - 6~~)^2 + (~~5 - 3~~)^2} \implies P1P2=\sqrt{( -9 )^2 + ( 2 )^2} \\\\\\ P1P2=\sqrt{ 81 + 4 } \implies P1P2=\sqrt{ 85 }[/tex]

The statistical measurement known as the Z-score describes the connection between a value and the mean of a set of values and the required z-score to the three decimal places is −2.714.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score.

Standard deviations from the mean are used to measure Z-score.

A Z-score of zero means the data point's score is the same as the mean score.

Your observed value is 2.5 standard deviations from the mean if your Z-score is 2.5, and so on.

Your value is more closely aligned with the mean the closer your Z-score is to zero.

Your value is further from the mean the farther your Z-score is from zero.

So, let's say Rosetta wins the game on Thursday with 110 points.

When x=110, the z-score is -2.714.

The average is 148.

You can see from this z-score that x=110 is 2.714 standard deviations away from the mean.

This formula can be used to determine the z-score:

z = x−μ/σ

=110−148/14

=−38/14

≈−2.714

Therefore, the required z-score to the three decimal places is −2.714.

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The expression  x²−−6 can be factored as:

[tex]x^{2} - 6 = (x + \sqrt{6} )(x - \sqrt{6})[/tex]

What is Factoring an expression?

A numerical or algebraic expression is factored when it is written as a product of factors. The distributive property can be used to factor expressions.

The expression  x²−−6 can be factored as:

[tex]x^{2} - 6 = (x + \sqrt{6} )(x - \sqrt{6})[/tex]

The solutions for this equation would be x = √6 or x = -√6. These are the values of x that make the expression equal to zero.

Factoring the expression in this way can be useful in solving related equations or in finding the roots of a quadratic function. It also helps in visualizing the graph of the function, as the factored form shows the x-intercepts, which are the points where the graph crosses the x-axis.

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a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.

b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.

c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.

A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.

A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.

The current total world oil reserves, R = 2,090 billion barrels

Average decrease per year = 18 billion barrels

a) Linear equation for R is 2,090 - 18t

b) In 15 years, the total oil reserves = 2,090 - 18(15)

= 2,090 - 270

= 1,820

c) The constant rate of decrease = 18 billion barrels per year

The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).

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12 hours

If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours

Answer:

5.333 hours.

Step-by-step explanation:

Put this on a chart:

6 people = 8 hours

4 people = ? hours

To find ? Use crisscross multiplication and solve:

? = (4 * 8) / 6

? = 32 / 6

? = 5.333

Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Lets solve ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} = 10[/tex]

[ taking square root on both sides ]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} } = \sqrt{10} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \pm \sqrt{10} [/tex]

Both the values are appropriate here, as the square of both negative or positive value is same [positive value]

[tex] \huge\bold \large \bf{Solution }[/tex]

[tex] \rightarrow \large \displaystyle \sf \: {x}^{2} = 10 \: [/tex]

Transposing square on RHS , We get

[tex]\rightarrow \large \displaystyle \sf \: x \: = \sqrt{10} [/tex]

We know that,

10 does not even have a square root , so,

[tex]\rightarrow \large \displaystyle{\bf{ \pink{x \: = \pm \: \sqrt{10} }}}[/tex]

We know that the value of root is both negative and positive.

[tex] \purple {\rule{190pt}{4pt}}[/tex]

Due to length restrictions, we kindly invite to read the explanation of this question for further details about two numbers related to a given sum and a given product.

In this problem we find 48 case of two numbers that must be found and whose sum and product are given. Mathematically speaking, the expressions describing the problem:

x₁ + x₂ = b

x₁ · x₂ = c

Whose solution can be found by numerical methods.

Now we proceed to determine the values for each cases:

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Correct me if im wrong :)

Hi there, here's your answer:

Given a class is divided into 2 equal groups, i.e. Group A has 1 : 2 of the students in the class and group B has 1 : 2 of the students in the class.

Also [tex]\frac{2}{3} rd[/tex] of group A have an A

While 40% of group B have an A

To find:
Fraction of the class that has A

Solution:

First, we find the % of students in group A who have an A:

Since [tex]\frac{2}{3} rd[/tex] of group A have an A,

[tex]\frac{2}{3}[/tex] × [tex]50[/tex]  (∵ 1 : 2 = 50 : 100)

[tex]= \frac{100}{3} = 33.33[/tex]   (i)

Therefore, % of students in group A who have an A = 33.33%

Now, we find the % of students in group B who have an A:

Since 40% of group B have an A:

[tex]\frac{40}{100}[/tex] × [tex]50[/tex] (∵ 1 : 2 = 50 : 100)

= 4 × 5 = 20   (ii)

Adding (i) and (ii), we get
33.33 + 20 = 53.33%

Thus, the fraction of the class that has an A = [tex]\frac{53.33}{100}[/tex]

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Answer: TASK 1: The answer to how much more of the atmosphere is nitrogen than all other gases combined can be found by measuring the atmospheric composition. Nitrogen makes up the largest fraction of the Earth's atmosphere, at around 78%. Oxygen makes up around 21%, while all other gases make up the remaining 1%. So, nitrogen makes up around 77% more of the atmosphere than all other gases combined.

TASK 2: I'm sorry, but there seems to be a typo in your prompt. Can you please clarify what you meant by "in the Tronosphere was separated out from"?

Step-by-step explanation:

rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.

Let's say that the Persian rug is rectangular, with length "l" and width "w".

The total of a rectangle's four sides is known as the perimeter, and it can be calculated as follows:

Perimeter = 2l + 2w

Given that the distance around it is 22 feet, we can write:

2l + 2w = 22

When we simplify this equation, we obtain:

l + w = 11

A rectangle's area is determined by the product of its length and breadth, which may be written as follows:

l x w = area

Given that the space is 10 square feet, we can write:

l x w = 10

Two equations with two variables are now available:

L+W = 11, and L x W = 10.

To find l and w, we can utilise substitution or elimination. For instance, we can solve for w from the first equation in terms of l:

w = 11 - l

Using this expression as w's replacement in the second equation, we obtain:

l x (11 - l) = 10

The result of expanding and rearrangement is a quadratic equation:

l² - 11l + 10 = 0

Using the quadratic formula or factoring, we can solve this quadratic problem. Factoring results in:

(l - 10)(l - 1) = 0

so either l = 10 or l = 1 is true.

w = 1 if l = 10, otherwise. w equals 10 if l = 1.

As w is always smaller than l, we have

The rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.

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Answer:

The correct answer is D. Step 4 is incorrect and should be 10x = 24.

To find the echelon form of the augmented matrix, we will use row operations to transform the matrix into a triangular form.

Starting matrix:

[ 1  -1  2  |  400 ]

[100 900  1  |   -3 ]

[ 1  -3  7  | -300 ]

Subtracting the first row from the second and third rows, respectively:

[ 1  -1   2  |  400 ]

[ 0 901 -199 | -403 ]

[ 0  -2   5  | -700 ]

Dividing the second row by 901 to get a leading 1:

[ 1  -1    2   |  400 ]

[ 0   1 -199/901 | -403/901 ]

[ 0  -2    5   | -700 ]

Adding 2 times the second row to the third row:

[ 1  -1     2          |  400       ]

[ 0   1  -199/901     | -403/901    ]

[ 0   0  5 - (2*199/901) | -496/901 ]

Dividing the third row by 5 to get a leading 1:

[ 1  -1    2              |  400           ]

[ 0   1 -199/901         | -403/901        ]

[ 0   0   1  - (2*199/901) | -496/901 * (1/5) ]

Subtracting 2 times the third row from the second row:

[ 1  -1     2                |  400                 ]

[ 0   1     0.12985349611    | -1.45323773515        ]

[ 0   0     1 - (2*199/901)  | -0.21964542252517706 ]

Subtracting 2 times the third row from the first row:

[ 1  -1     0.640177312      |  1.82816635434407        ]

[ 0   1     0.12985349611    | -1.45323773515            ]

[ 0   0     1 - (2*199/901)  | -0.21964542252517706       ]

This is now in row echelon form with 1's on the diagonal. Therefore, the echelon form of the given augmented matrix is:

[ 1  -1     0.640177312      |  1.82816635434407        ]

[ 0   1     0.12985349611    | -1.45323773515            ]

[ 0   0     1 - (2*199/901)  | -0.21964542252517706      ]

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The required value of  "regression constant" is 7.

Y = a + b X + e is the formula for the regression equation. The dependent variable (Y), which is being predicted or explained, has a value of Y. a, or Alpha, is a constant; it equals the value of Y when the value of X is 0, and b, or Beta, is a coefficient of X; it determines how much Y varies for each unit change in X and determines the slope of the regression line.

In a linear regression equation, the regression constant (also called the intercept) represents the predicted score when the predictor variable has a value of 0. In this scenario, the predicted score for a person with a predictor variable score of 0 is 7.

Therefore, the regression constant is 7.

The regression constant is usually combined with the regression coefficient of the predictor variable to form the complete regression equation, which is used to predict scores for individuals with different values of the predictor variable.

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