abcdefghijklmnopqrstuvwxyz

Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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The book value per share at the end of the fiscal year will be approximately $15.35.

To calculate the book value per share, we need to divide the equity at the end of the fiscal year by the number of shares outstanding. Let's break down the calculation:

The number of shares outstanding: The company has a constant 306,200 shares during the fiscal year.

Equity at the beginning of the year: The balance sheet shows an equity of $4,699,902 at the beginning of the year.

Net income: The income statement indicates a net income of $399,786.

Dividends paid: The company pays out $297,789 in dividends.

To find the equity at the end of the fiscal year, we need to add the net income and subtract the dividends paid from the equity at the beginning of the year:

Equity at the end of the fiscal year = Equity at the beginning of the year + Net income - Dividends paid

= $4,699,902 + $399,786 - $297,789

= $4,801,899

Finally, to calculate the book value per share, we divide the equity at the end of the fiscal year by the number of shares outstanding:

Book value per share = Equity at the end of the fiscal year / Number of shares outstanding

= $4,801,899 / 306,200

≈ $15.65 (rounded to two decimal places)

Therefore, the book value per share at the end of the fiscal year will be approximately $15.35.

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Answer:

(a−5)(a−7)

Step-by-step explanation:

factor a2−12a+35

a2−12a+35

The middle number is -12 and the last number is 35.

Factoring means we want something like

(a+_)(a+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -12

Multiply together to get 35

Can you think of the two numbers?

Try -5 and -7:

-5+-7 = -12

-5*-7 = 35

Fill in the blanks in

(a+_)(a+_)

with -5 and -7 to get...

(a-5)(a-7)

Answer:

AB, CB, AC

Step-by-step explanation:

All the angles in a triangle added up equal 180 degrees

Start by finding the measure of angle A

A + 86 + 27 = 180

A + 113= 180

A = 67 degrees

Now order them

86 is greater than 67 and 27 so B is the greatest

27 is less than 86 and 67 so C is the smallest

67 is less than 86 but greater than 27 so A is in the middle

Now for the sides..

AB is opposite angle C so it's the shortest

CB is opposite angle A so it's in the middle

AC is opposite angle B so it's the longest

I hope this helps!!!

The equation of the ellipse centered at the origin, satisfying the given conditions, is:   \(x^2/25 + y^2/29 = 1.\)

To write an equation of an ellipse centered at the origin, we can use the standard form equation:

\(x^2/a^2 + y^2/b^2 = 1\)

where "a" represents the semi-major axis and "b" represents the semi-minor axis.

Given that the vertex is located at (0, √29), we can determine the value of "b". The distance from the origin to the vertex is equal to the value of "b". In this case, √29 is the value of "b".

Now, we need to determine the value of "a". The co-vertex is located at (-5, 0). The distance from the origin to the co-vertex is equal to the value of "a". In this case, 5 is the value of "a".

Plugging these values into the equation, we get:

\(x^2/5^2 + y^2/√29^2 = 1\)

Simplifying, we have:

\(x^2/25 + y^2/29 = 1\)

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The linear function to show how he earns in weekdays is 12+15=0.3x+0.5y

When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear.When both the dependent variable (often represented by the letter "y") and the independent variable (typically represented by the letter "x") vary by a consistent amount, this is referred to as a linear function.

A linear function is, for instance, the progression in the number of ticks of a clock's second hand through time.

Any function that depicts a straight line on the coordinate plane is said to be linear. Looking at a function's graph is the quickest approach to determine whether it is linear or not. When plotted on a graph, a linear function results in a straight line. Nonlinear functions have some kind of curvature; they don't form a straight line.

The linear function to show how he earns in weekdays is 12+15=0.3x+0.5y

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Answer:

10-20 dollars per hour

The linear equations of the candles are y = 0.5x + 8 and y = 0.4x + 8. And both relationships are the function.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A candle burns down at the rate of 0.5 inches per hour.

The original height of the candle was 8 inches.

Let y be the height of the candle and x be the number of hours.

Then the linear equation will be given as

\(\rm y = mx + c\)

where m is the rate and c is the initial value. Then the linear equation of the candle will be

y = -0.5 x + 8

The function is a linear function.

If the value of m is replaced by 0.4. Then the linear equation will be

y = 0.4x + 8

And this will also be a linear function.

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Step-by-step explanation:

we know,

angle ABD = 90° so,

Angel ABC + angle CBD = angle ABD

→ 4x + 5x = 90

→ 9x = 90

→ x = 90/9 = 10

therefore, option c 10 is correct.

hope this answer helps you dear...take care and may u have a great day ahead!

The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)

Given data ,

To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.

The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:

Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>

Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)

= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))

= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)

= 40 / √(33)

To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:

Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)

= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)

= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))

= (-160/9√(33), -40/9√(33), 340/9√(33))

Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)

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The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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Answer:

B

Step-by-step explanation:

x > 1

Answer:

3 M= 3 B=-7

Step-by-step explanation:

Answer:

Answer is 3

3 M= 3 B= -7

The time complexity of finding a source in a directed graph or determining such a source does not exist if the graph is represented by its adjacency matrix is V².

If a directed graph is represented by an adjacency matrix, the following approach may be used to either discover a source inside the network or establish that there isn't one:

This approach has an O(V²) time complexity, where V is the number of graph vertices. This is due to the fact that it takes O(V²) time to traverse the whole adjacency matrix in order to determine each vertex's in-degree. The next step requires traversing the inDegree array in O(V) time in order to discover a vertex with in-degree 0. In the worst scenario, it takes O(V²) time to determine if there is a path connecting this vertex to every other vertex.

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The most general real-valued solution to the linear system of differential equations,\(\( \overrightarrow{\boldsymbol{x}}^{\prime}=\left[\begin{array}{rr}-4 & -9 \\ 1 & -4\end{array}\right] \overrightarrow{\boldsymbol{x}} \),\) can be found by diagonalizing the coefficient matrix and using the exponential of the diagonal matrix.

To find the most general real-valued solution to the given linear system of differential equations, we start by finding the eigenvalues and eigenvectors of the coefficient matrix \(\(\left[\begin{array}{rr}-4 & -9 \\ 1 & -4\end{array}\right]\).\)

Solving for the eigenvalues, we get:

\(\((-4-\lambda)(-4-\lambda) - (-9)(1) = 0\)\(\lambda^2 + 8\lambda + 7 = 0\)\((\lambda + 7)(\lambda + 1) = 0\)\(\lambda_1 = -7\) and \(\lambda_2 = -1\)\)

Next, we find the corresponding eigenvectors:

For \(\(\lambda_1 = -7\):\)

\(\(\left[\begin{array}{rr}-4 & -9 \\ 1 & -4\end{array}\right]\left[\begin{array}{r}x_1 \\ x_2\end{array}\right] = -7\left[\begin{array}{r}x_1 \\ x_2\end{array}\right]\)\)

This leads to the equation:\(\(-4x_1 - 9x_2 = -7x_1\)\), which simplifies to \(\(3x_1 + 9x_2 = 0\)\). Choosing\(\(x_2 = 1\),\) we get the eigenvector \(\(\mathbf{v}_1 = \left[\begin{array}{r}3 \\ 1\end{array}\right]\).\)

For\(\(\lambda_2 = -1\):\(\left[\begin{array}{rr}-4 & -9 \\ 1 & -4\end{array}\right]\left[\begin{array}{r}x_1 \\ x_2\end{array}\right] = -1\left[\begin{array}{r}x_1 \\ x_2\end{array}\right]\)\)

This gives the equation:\(\(-4x_1 - 9x_2 = -x_1\),\) which simplifies to\(\(3x_1 + 9x_2 = 0\).\) Choosing \(\(x_2 = -1\)\), we obtain the eigenvector \(\(\mathbf{v}_2 = \left[\begin{array}{r}-3 \\ 1\end{array}\right]\).\)

Now, using the diagonalization formula, the general solution can be expressed as:

\(\(\overrightarrow{\boldsymbol{x}} = c_1e^{\lambda_1 t}\mathbf{v}_1 + c_2e^{\lambda_2 t}\mathbf{v}_2\)\(\overrightarrow{\boldsymbol{x}} = c_1e^{-7t}\left[\begin{array}{r}3 \\ 1\end{array}\right] + c_2e^{-t}\left[\begin{array}{r}-3 \\ 1\end{array}\right]\),\)

where\(\(c_1\) and \(c_2\)\) are constants.

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Find the most general real-valued solution to the linear system of differential equations\(\( \overrightarrow{\boldsymbol{x}}^{\prime}=\left[\begin{array}{rr}-4 & -9 \\ 1 & -4\end{array}\right] \ove\)

Answer:

We first ALWAYS have to split the figure apart from each other,

lets split it into a triangle and a square!

Let's find the area of the triangle:

20(height) x 20(base) = 400!

400 x 1/2 (just dividing by 2) = 200!

*Remember* Formula of a triangle is:

B(base) x H(height) x 1/2 (basically dividing by 2)

Now time to find the area of the square!

20 x 20 = 400!

Now let's add both their areas:

400 + 200 = 600!

Step-by-step explanation:

600cm2 is your answer.

The figure has an area of 600 square centimeters.

In this question we need to determine the area of the entire figure, this area is the sum of the areas of a square and two symmetric right triangles, defined by respective formulas, that is:

\(A = A_{s} + 2\cdot A_{t}\) (1)

Where:

By applying area formulas for squares and triangles, we expand (1):

\(A = x^{2} + \frac{1}{2}\cdot x\cdot y\) (2)

Where:

If we know that \(x = 20\,cm\) and \(y = 20\,cm\), then the area of the figure is:

\(A = \frac{3}{2}\cdot (20\,cm)^{2}\)

\(A = 600\,cm^{2}\)

The figure has an area of 600 square centimeters.

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Final Answer: \(t = 9\)

Steps/Reasons/Explanation:

Question: Solve for \(t\). \(-t=9(t-10)\).

Step 1: Expand.

\(-t = 9t - 90\)

Step 2: Subtract \(9t\) from both sides.

\(-t - 9t = -90\)

Step 3: Simplify \(-t - 9t\) to \(-10t\).

\(-10t = -90\)

Step 4: Divide both sides by \(-10\).

\(t = \frac{-90}{-10}\)

Step 5: Two negatives make a positive.

\(t = \frac{90}{10}\)

Step 6: Simplify \(\frac{90}{10}\) to \(9\).

\(t = 9\)

~I hope I helped you :)~

Answer:

56

Step-by-step explanation:

Solution for 2.8 is what percent of 5:

2.8:5*100 =

(2.8*100):5 =

280:5 = 56

Answer: 160%

Step-by-step explanation:

By convention, we use a bar graph when the groups on the x-axis (horizontal axis) are represented on a categorical or discrete scale; we use a line graph when the groups on the x-axis are represented on a continuous or numerical scale.

A bar graph is commonly used to display categorical or discrete data, where the groups or categories on the x-axis are distinct and separate from each other.

For example, the x-axis could represent different types of fruits or months of the year. Each category is represented by a separate bar, and the height of each bar corresponds to the frequency, count, or value associated with that category.

On the other hand, a line graph is typically used to represent data on a continuous or numerical scale. The x-axis represents a continuous range of values, such as time, temperature, or distance.

Each data point is plotted as a dot or marker on the graph, and the points are connected by lines. This type of graph is useful for showing trends, patterns, or changes over time or across a continuous range.

The choice of using a bar graph or a line graph depends on the nature of the data and the purpose of the visualization. Categorical data is best represented using a bar graph to emphasize the distinct categories, while numerical or continuous data is better suited for a line graph to visualize trends and relationships.

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Answer:

Step-by-step explanation:

The simple explanation is that the hypotenuse and sides of a right triangle are always shorter than one another. Therefore, any side's to any hypotenuse's ratio will never be greater than 1. The figure is no longer a triangle when the angle is 0 or 90 degrees because one of the sides vanishes and the other side lines up with the hypotenuse. For this reason, sin and cosine have values of 0 or 1 in these extreme situations.

Answer:

Arithmetic, -4

Step-by-step explanation:

Yes.  

This is an arithmetic sequence, the common difference is -4. :)

Answer:

Step-by-step explanation:

Arithmetic, -4

Step-by-step explanation:

Yes.  

This is an arithmetic sequence, the common difference is -4. :)

Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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±

hello that is the soulution

Answer:

9179.84

Step-by-step explanation:

150 grams to milligrams is 9179.84

Answer:

I'm not sure tbh, sorry .

Answer: 8x +29

Step-by-step explanation:

5+8(3+x)

5+8(x+3)

__________

5 + 8(x+3)

5+ 8x +25

_________

5+8x+ 24

29+8x

____

8x+29