Points D,B, and E are collinear. Find the value of x so that points A,B, and C are collinear

A. Investment 1: ROI = 20%, Investment 2: ROI = 18%, Investment 3: ROI = 24%. B. Select Investment 3 with the highest ROI of 24% as it generates the most return for the investment amount.

C. Investment 3 is attractive with positive residual income, but from Brown's perspective, the imputed interest charge may reduce overall profitability.

A. To calculate the ROI for each investment, we can use the following formula:

ROI = (Income / Investment) x 100%

For Investment 1: ROI = (50,000 / 250,000) x 100% = 20%

For Investment 2: ROI = (54,000 / 300,000) x 100% = 18%

For Investment 3: ROI = (96,000 / 400,000) x 100% = 24%

B. If the manager's focus is on Glengarry's divisional performance, he would select Investment 3 because it has the highest ROI of 24%. This investment generates the highest return for the amount invested, which is the primary concern for divisional performance.

C. To calculate the residual income for Investment 3, we need to subtract the imputed interest charge from its profit margin traceable to the division:

Residual Income = Profit margin traceable to the division - (Average asset investment x Imputed interest rate)

Residual Income = 96,000 - (400,000 x 22%) = 96,000 - 88,000 = 8,000

From Glengarry's perspective, Investment 3 is attractive because it generates a positive residual income of $8,000. However, from Brown's perspective, it may not be as attractive because the imputed interest charge reduces the overall profitability of the investment.

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Complete question is in the image attached below

Answer:

I hope this helps

y = 5x - 3

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line and in the given situation the slope (m) is -1/4 respectively.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b.

M represents the line's slope.

And b is the b in the point that is the y-intercept (0, b).

For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

So, the slope formula is:

m = y₂-y₁/x₂-x₁

Now, insert values as follows:

m = y₂-y₁/x₂-x₁

m = 4-5/-3-(-7)
m = -1/-3+7

m = -1/4

Therefore, in the given situation the slope (m) is -1/4 respectively.

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Suav would have run approximately [tex]$970$[/tex] miles in [tex]$25$[/tex] weeks, to the nearest whole number.

What are the whole numbers?

Whole numbers are the set of numbers that include all positive integers (1, 2, 3, ...) as well as zero (0). Whole numbers do not include any negative numbers or fractions. Therefore, the set of whole numbers is {0, 1, 2, 3, ...}.

Suav runs [tex]$20$[/tex] miles the first week. Let's use a formula to calculate the number of miles he runs in subsequent weeks. Let [tex]$m$[/tex] be the number of miles he runs in a particular week, and [tex]$w$[/tex] be the number of weeks elapsed since the first week. Then, we have:

[tex]$$m = 20 \cdot 1.05^{w-1}$$[/tex]

This formula takes into account the [tex]$5%$[/tex] increase in miles each week, starting from the initial [tex]$20$[/tex] miles in the first week.

To find the total number of miles Suav runs over [tex]$25$[/tex] weeks, we can sum up the miles he runs in each week using the formula above. That is,

[tex]$$\text{Total miles} = 20 + m_2 + m_3 + \cdots + m_{25}$$[/tex]

where [tex]$m_2, m_3, \ldots, m_{25}$[/tex] are the number of miles he runs in the second to [tex]25$th[/tex] week, respectively.

We can use the formula for [tex]$m$[/tex] to find each of these values. For example, the number of miles he runs in the second week is:

[tex]$$m_2 = 20 \cdot 1.05^{2-1} = 21$$[/tex]

Similarly, we can find the number of miles he runs in each of the other weeks:

[tex]m_3 &= 20 \cdot 1.05^{3-1} = 22.05[/tex]

[tex]m_4 &= 20 \cdot 1.05^{4-1} = 23.103[/tex]

[tex]&\vdots[/tex]

[tex]m_{25} &= 20 \cdot 1.05^{25-1} = 57.597[/tex]

Now, we can substitute these values into the formula for the total miles and simplify:

[tex]\text{Total miles} &= 20 + 21 + 22.05 + \cdots + 57.597 \&\approx 970[/tex]

Therefore, Suav would have run approximately [tex]$970$[/tex] miles in [tex]$25$[/tex] weeks, to the nearest whole number.

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Answer

well if it is 5% each week, then it would be 20 +1. doing this for 25 weeks means it would be 20 + 25 then.

Sorry if wrong. i don't know if u do 5% after each time or from the main number. it doesn't say weather or not.

Step-by-step explanation:

p lz give me brainliest

The height of the pole is 220 centimeters. We can solve it in the following manner.

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

Let h be the height of the pole. Then, we have:

h² + 21² = 221²

Simplifying the right side of the equation, we get:

h² + 441 = 48841

Subtracting 441 from both sides, we get:

h² = 48400

Taking the square root of both sides, we get:

h = 220

Therefore, the height of the pole is 220 cm.

So, the answer is 220 centimeters.

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regular price is 100%, so if we take off 85% from that, that'd be 100% - 85% = 15%, so the sale price is really 15% of the regular price, well, we know regular price is $15.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 15}}{\left( \cfrac{15}{100} \right)15}\implies \text{\LARGE 2.25}[/tex]

The equation in standard form with integer coefficients is -5x + 10y = -6.

A coefficient is a numerical or constant multiplier of a variable, term or expression.

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A is positive. To convert the given equation y = (1/2)x - (3/5) into standard form, we can multiply both sides by the common denominator of 2 and 5, which is 10. This gives:

10y = 5x - 6

Rearranging the terms, we get:

5x - 10y = 6

Multiplying both sides by -1 to get the coefficient of x positive, we get:

-5x + 10y = -6

Therefore, the equation in standard form with integer coefficients is -5x + 10y = -6.

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It takes 105 minutes for the second hose alone to fill the pond.

An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, among others.

Let x be the time it takes for the second hose to fill the pond alone.

The rate at which the first hose fills the pond is 1/42 (ponds/minute).

The rate at which the second hose fills the pond is 1/x (ponds/minute).

The combined rate at which the two hoses fill the pond is 1/30 (ponds/minute).

Since they are filling the same pond, we can add their rates to get the combined rate:

⇒ 1/42 + 1/x = 1/30

To solve for x, we can simplify this equation;

⇒ 30x + 1260 = 42x

Subtracting 30x from both sides gives:

⇒ 1260 = 12x

⇒ x = 105

Therefore, it takes the second hose alone 105 minutes to fill the pond.

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Joshua scored 65, 80, 85, and 100 on his math tests. 90 score Joshua has to earn on his fifth test to have a mean score of 85

       To calculate the mean score, add up all of the scores and divide by the total number of tests.

       To figure out what score Joshua needs to get on the fifth test, use the formula:

            Total score = mean score × total number of tests

            Total score = 85 × 5

            Total score = 425

  Joshua's total score on all five tests must be 425. He has already earned 330 points from his first four tests (65 + 80 + 85 + 100).

  Therefore, Joshua must earn 95 points on his fifth test (425 - 330 = 95) to achieve a mean score of 85.

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The ship sailing in a straight line from the Isle of Strutay to Emerald Cay should travel on a bearing of approximately 72.6°.

We can use the Law of Cosines to find this angle. Let's call this angle θ.

cos θ = (a² + b² - c²) / (2ab)

where a is the distance between the Isle of Strutay and Crook Island (25 km), b is the distance between Crook Island and Emerald Cay (40 km), and c is the distance between the Isle of Strutay and Emerald Cay (65 km).

cos θ = (25² + 40² - 65²) / (2 x 25 x 40)

cos θ = 0.275

θ = cos⁻¹(0.275)

θ ≈ 72.6°

Therefore, the ship sailing in a straight line from the Isle of Strutay to Emerald Cay should travel on a bearing of approximately 72.6° (east of north).

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Exponential smoothing, simple moving averages, autoregressive models, and regression-based models are all commonly used methods for analyzing and forecasting seasonal data.

Regression-based models are statistical models that use the relationship between a dependent variable and one or more independent variables to predict or explain the behavior of the dependent variable. These models estimate the strength and direction of the relationships between the variables by fitting a regression line or curve to the observed data. They can be used for both descriptive and predictive purposes and are widely used in various fields, including economics, finance, marketing, and social sciences. Examples of regression-based models include linear regression, logistic regression, and time-series regression.

Here,

Seasonal data refers to data that exhibits regular patterns that repeat over a fixed time period, such as weekly, monthly, or yearly. The methods that are best for dealing with seasonal data are those that take into account the regular patterns and fluctuations in the data over time. Methods that are best when you are dealing with seasonal data:

a. Exponential smoothing

c. Simple moving averages

d. Autoregressive models

e. Regression based models

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Answer:

Katelyn needs to mow 3 lawns to have enough money to buy the skateboard.

What are inequalities and their types?

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let, 'x' be the no. of lawns she has to mow.

Given, Katelyn wants to buy a $75.00 skateboard and she has $25.00 saved and she mows lawns to make extra money and earns $20.00 for each lawn he mows.

Therefore the inequality that represents this context is,

20x + 25 ≥ 75.

20x ≥ 75 - 20.

20x ≥ 55.

x ≥ 55/20.

x ≥ 2.75, But she has to mow a lawn completely to get paid so she must mow 3 lawns.

Apples make up one-third of the dozen fruits in a fruit vendor cart. If bananas make up the remaining fruit and oranges make up 1/4 of the total fruit, there are 2.5 dozen bananas in the fruit vendor's cart.

First, let's calculate how many apples are in the cart:

1/3 of 6 dozen fruits = 2 dozen fruits are apples

Next, let's calculate what proportion of the fruits are oranges:

1/4 of all fruits = (1/4) x 6 dozen = 1.5 dozen fruits are oranges

To find the number of dozen bananas, we can subtract the number of dozen apples and oranges from the total number of dozen fruits in the cart:

Total number of dozen fruits = 6 dozen

Number of dozen apples = 2 dozen

Number of dozen oranges = 1.5 dozen

Number of dozen bananas = 6 dozen - 2 dozen - 1.5 dozen

Number of dozen bananas = 2.5 dozen

Therefore, there are 2.5 dozen bananas in the fruit seller's cart.

The complete question is:-

1/3 of the 6 dozen fruits in a fruit seller cart are apple. If 1/4 of all the fruits are oranges and the rest of the fruits are bananas, find how many dozen bananas are there in the fruits sellers cart

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The product of the matrices ( 5 6 ) and ( 1 7 ) is equal to 47.

The number of columns in the first matrix must equal the number of rows in the second matrix in order for two matrices to be multiplied. In this instance, the 1x2 multiplied by 2x1 matrix satisfies this requirement.

In many disciplines, such as computer graphics, physics, and engineering, matrix multiplication is a key idea in linear algebra. It can be used to transform data, determine eigenvalues and eigenvectors, and solve systems of linear equations.

To get the product of two matrices, we need to perform the dot product of each row in the first matrix with each column in the second matrix.

Given the matrices ( 5 6 ) and ( 1 7 ), we can perform the dot product as follows:

( 5 6 ) ( 1 7 ) = ( (5)(1) + (6)(7) )

= (5 + 42)

= 47

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The length of line segment AC is equal to 34 units.

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to this circle, we have the following:

DC² = AB × BC

15² = (3x + 1) × 9

225 = 27x + 9

27x = 225 - 9

27x = 216

x = 216/27

x = 8

Now, we can determine the length of AC;

AC = AB + BC

AC = 3x + 1 + 9

AC = 3(8) + 1 + 9

AC = 34 units.

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After solving the given equations the value of x and y are -2 and 5 respectively.

An equation is a mathematical statement consisting of two expressions joined by an equal sign.

For example, 3x – 5 = 16 is an equation.

Solving this equation gives the value of the variable x as x = 7.

So, the equations are:

7x+10y = 36 ...(1)

y = 2x +9  ...(2)

Now, insert 2x+9 in equation (1):

7x+10y = 36

7x+10(2x +9) = 36

7x+20x+90 = 36

27x = -54

x = -54/27

x = -2

Then, the value of y:

y = 2x +9

y = 2(-2) +9

y = -4+9

y = 5

Therefore, after solving the given equations the value of x and y are -2 and 5 respectively.

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The fraction that is most often used to approximate pi is 22/7

The fraction 22/7 is often used to approximate pi. This is because 22/7 is a common fraction that is close to the decimal approximation of pi, which is 3.14159265359...

While pi is an irrational number that cannot be expressed as a finite decimal or fraction, 22/7 is a commonly used approximation that is easy to remember and gives a reasonable estimate of pi to two decimal places.

However, it is important to note that there are other fractions that can be used to approximate pi with greater accuracy, such as 355/113, which is accurate to six decimal places.

Nonetheless, 22/7 remains a popular approximation of pi in various contexts, from mathematics and engineering to everyday life.

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Answer: The second piece-wise function, f(x), will produce the graph given.

The value of x is 41

When three line segments cross each other at three non-collinear points, a triangle is formed. A triangle is a three-sided polygon with three sides and three angles.

Using the Angle Bisector Theorem and assuming ED is an angle bisector

⇒ EG/EH = DG/HD

⇒ 49 / 58.8 = 35 / (x + 1)

⇒ 49 (x+1) = 58.8×35 ⇒ 2058

⇒ x + 1 = 2058 /49

⇒ x + 1 = 42

⇒ x = 41

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Complete question-

Assuming ED is an angle bisector and applying the Angle Bisector Theorem.

The value of x is 41

A polygon with three sides and three vertices is called a triangle. It belongs to the basic geometric shapes. A triangle with the parts A, B, and C is referred to as triangle ABC. Any three points that are not collinear in Euclidean geometry result in a separate triangle and a distinct plane. When three line lengths cross each other at three non-collinear points, a triangle is formed. A triangle is a three-sided polygon because it has three sides and three angles.

Assuming ED is an angle bisector and applying the Angle Bisector Theorem

[tex]\frac{EG}{EH} =\frac{DG}{HD} \\\\\frac{49}{58.8} =\frac{35}{(x+1)}[/tex]

49 (x+1) = 58.8×35 ⇒ 2058

x + 1 = 2058 /49

x + 1 = 42

x = 41

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The complete question is,

In right angle triangle ΔXYZ  in which ∠XYZ = 90° and ∠XZY i= 25°.

YZ =  33 inch, the length of XZ to the nearest hundredth is approximately 13.99 inches.

A trigonometric function is a mathematical function that relates the angles of a right triangle to the ratios of its sides. Three basic trigonometric functions are sine (sin), cosine (cos), and tangent (tan).

In a right triangle, if one angle is θ (where θ is not the right angle), then we can define the following trigonometric functions:

sine of θ (sin θ): the ratio of the length of the side opposite θ to the length of the hypotenuse

cosine of θ (cos θ): the ratio of the length of the adjacent side to the length of the hypotenuse

tangent of θ (tan θ): the ratio of the length of the side opposite θ to the length of the adjacent side

We can use the trigonometric function sine to relate the lengths of the sides in the right triangle XYZ. In particular, we know that:

sin(25°) = XZ / 33

To solve for XZ, we can multiply both sides by 33 and simplify:

XZ = 33 sin(25°)

XZ ≈ 13.99 (rounded to the nearest hundredth)

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Answer: I really don't know the answer , and im really good at this math problem but i forgot how to do this

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Step-by-step explanation:

Equation of a circle

(x-h)^2  + (y-k)^2 = r^2

 so the given circle has center at  (h,k) = (5,-10)

    new circle center will be at x = 1 left of 5 = 4    y = 2 down from -10 = -12

            (4,-12)              

Equation then becomes     (x-4)^2 + ( y+ 12)^2 = 64                

The classification of the angles are:

20° and 70°: complementary angles.

20° and 160°: supplementary angles

20° and 20°: vertical angles

Congruent angles are defined as two or more angles that are identical to each other. Thus, the measure of these angles are equal to each other. These type of angles do not make any difference in the congruence of angles, which tells us that they can be acute, obtuse, exterior, or interior angles.

Complementary angles are defined as two angle that sum up to 90 degrees. Thus: 20° and 70° are complementary angles.

Supplementary angles are defined as two angles that sum up to 180°. Thus: 20° and 160° are supplementary angles

Vertical angles are defined as angles that are opposite of each other when two lines cross. Thus they are congruent. Thus:

20° and 20° are vertical angles

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A line plot can be a useful tool for the students to analyze their results because it allows them to easily see the distribution of heights among the 20 students. By plotting each student's height as a dot above a number line, the students can quickly see how many students fall into each height range and identify any outliers or patterns in the data.

For example, if most of the dots fall within a small range of heights, the students can see that there is a cluster of heights in that range. Conversely, if there are only a few dots in a particular height range, the students can see that there is less variation in that range.

The line plot can also help the students to identify the mode, which is the most common height among the students, and the median, which is the middle height when the heights are ordered from smallest to largest. These measures of central tendency can help the students to understand the typical height of their classmates and how much variation there is in the data.

Overall, a line plot is a simple and effective way for the students to visualize and analyze their height data, and it can help them to draw meaningful conclusions about the distribution of heights among the 20 students.

Entertainment will comprise 90% of Ryan's total budget. The amount budgeted towards entertainment each month will be 90% of his take-home pay.

The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.

Let's assume Ryan's take-home pay is P dollars.

Given that Ryan saves 10% of his take-home pay for retirement, he will save 0.10P dollars.

The remainder of his take-home pay after saving for retirement will be 90% of his take-home pay, which is 0.90P dollars.

Now, if Ryan allocates the remainder of his take-home pay to entertainment, the percentage of his total budget that entertainment will comprise can be calculated as:

Percentage of entertainment budget = (Entertainment budget / Total budget) * 100

Since the entertainment budget is 0.90P dollars and the total budget is P dollars, the percentage of his total budget that entertainment will comprise is:

Percentage of entertainment budget = (0.90P / P) * 100

Percentage of entertainment budget = 90%

So, entertainment will comprise 90% of Ryan's total budget.

The amount of money budgeted towards entertainment each month will be 0.90P dollars, which is 90% of his take-home pay.

Therefore, Entertainment will comprise 90% of Ryan's total budget. The amount budgeted towards entertainment each month will be 90% of his take-home pay.

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The exact value of the volume of the sphere is V = 20.833π cm³ and the exact value is V = 64.45 cm³

A sphere is defined as symmetrical and round in shape. It is also referred to as a three dimensional solid, that has all its surface points at equal distances from the center.

The formula for the volume of a sphere is:

V = ⁴/₃πr³

where:

V = volume

r = radius

The radius of a sphere is half its diameter.

We are given diameter = 5cm

Thus: r = 5/2 = 2.5 cm

V = ⁴/₃π * 2.5³

V = 20.833π cm³

V = 64.45 cm³

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Answer:

Ignore this my answer is wrong

Answer:

80:3

Step-by-step explanation:

8m = 800cm, so the ratio is 800cm:30cm

This can be divided by 10cm on both sides to get 80:3

Answer:

kilometers she has walked his year is 1199.814 km

i hope it helps

have a nice day

Step-by-step explanation:

Answer:

≈38.57 units.

Step-by-step explanation:

To find the perimeter of a rectangle, we need to add up the lengths of all its sides.

First, gather the coordinates:

R - (4, 5)

U - (8, -3)

F - (-6, 0)

O - (-2, -8)

Using the coordinates given, we can calculate the lengths of the sides of the rectangle using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

So, for the rectangle with vertices R, U, F, and O, we have:

Side RU: d = √((8 - 4)^2 + (-3 - 5)^2) = √(16 + 64) = √80

Side UF: d = √((-6 - 8)^2 + (0 - (-3))^2) = √(196 + 9) = √205

Side FO: d = √((-6 - (-2))^2 + (0 - (-8))^2) = √(16 + 64) = √80

Side OR: d = √((-2 - 4)^2 + (-8 - 5)^2) = √(36 + 169) = √205

Since opposite sides of a rectangle are congruent, we have RU = FO and UF = OR. Therefore, the perimeter of the rectangle is:

Perimeter = RU + UF + FO + OR

Perimeter = √80 + √205 + √80 + √205

Perimeter ≈ 38.57

Therefore, the perimeter of the rectangle is approximately 38.57 units.