RectangleA′B′C′D′ is the image of rectangleABCD after a dilation.



What is the scale factor of the dilation?


Enter your answer in the box.

Answer: Two 1/6

Step-by-step explanation:

It takes two 1/6 to make the same amount as 1/3 because 1/6 is half of 1/3, so all it takes is two 1/6 to make 1/3.

Answer:

1/3 is equal to 2/6, so it takes 2 sixths to make the same amount as 1/3.

The explicit formula of the geometric sequence is given as follows:

[tex]a_n = 100(4)^{n-1}[/tex]

The recursive formula of the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio (q). In other words, a geometric sequence is a sequence where each term is a fixed multiple of the previous term.

The explicit formula of the sequence is given as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

For the recursive formula, we just take the first term and each consecutive term is the previous term multiplied by the common ratio.

There are 100 views in day one, hence the first term is given as follows:

[tex]a_1 = 100[/tex]

The number of viewers is multiplied by 4 each day, hence the common ratio is given as follows:

q = 4.

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Answer:

To calculate Mr. Dladla's gross profit per day, we first need to calculate his total revenue and total cost per month:

Total revenue per month = Selling price x Expected market share per month

Total revenue per month = R500 x (50% of 4500 customers) = R112,500

Total cost per month = Cost per course x Number of courses per month

Total cost per month = R300 x 20 days = R6,000

Gross profit per month = Total revenue per month - Total cost per month

Gross profit per month = R112,500 - R6,000 = R106,500

To calculate his gross profit per day, we can divide the gross profit per month by the number of days the training company opens per month:

Gross profit per day = Gross profit per month / Number of days per month

Gross profit per day = R106,500 / 20 days = R5,325 per day

Therefore, Mr. Dladla's gross profit per day is R5,325.

Step-by-step explanation:

By answering the above question, we may state that Find any dots that expressions are distant from the other dots to identify outliers. They might be anomalies and need more research.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. .  

You should check for the following data when interpreting a dot plot:

Determine the dot plot's lowest and maximum values by using the range concept.

Shape: Search for any patterns or groups of dots that could point to a certain data distribution.

Central Tendency: Locate the dot plot's centre to ascertain the typical value of the dataset. Finding the data's median or mean can be used to achieve this.

Find any dots that are distant from the other dots to identify outliers. They might be anomalies and need more research.

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Answer:

5 apples

Step-by-step explanation:

Answer:

94.3/C

Step-by-step explanation:

Hope this helps!

Answer:

Two monomials with the quotient 24a2b5 are:

12a b³

48a³ b²

Step-by-step explanation:

The general form of the equation for the given circle centered at O(0, 0) is B. x² + y² - 41 = 0.

A circle is a round, two-dimensional shape with all points on its boundary equidistant from its center.

Since the center of the circle is O(0,0), the equation of the circle will have the form x² + y² + ax + by + c = 0. To find the values of a, b, and c, we can use the fact that point B(4, 5) lies on the circle. Substituting the coordinates of B into the equation and simplifying, we get:

4² + 5² + a4 + b5 + c = 0

16 + 25 + 4a + 5b + c = 0

41 + 4a + 5b + c = 0

We now have one equation with three variables, so we need more information. Since the center of the circle is (0,0), we know that the distance from the center to any point on the circumference is equal to the radius of the circle. The distance between points (0,0) and (4,5) is the length of the line segment joining them, which can be found using the distance formula:

[tex]\sqrt{(4-0)\² + (5-0)\²} = \sqrt{(16+25) }= \sqrt{41}[/tex]

Therefore, the radius of the circle is √(41). We can use this fact to eliminate one of the variables in the equation we derived earlier. Since point (0,0) lies on the circle, we can substitute its coordinates into the equation to get:

41 + 0a + 0b + c = 0

c = -41

Now we can substitute this value of c back into the equation we derived earlier to get:

41 + 4a + 5b - 41 = 0

4a + 5b = 0

Finally, we have two equations with two variables, which we can solve to get:

a = -5/4

b = 4/5

Substituting these values into the equation of the circle, we get:

x² + y² - 5x/4 + 4y/5 - 41 = 0

Multiplying by 20 to eliminate fractions, we get:

20x² + 20y² - 25x + 16y - 820 = 0

Simplifying, we get:

x² + y² - 25/4x + 4/5y - 41 = 0

Which is equivalent to:

x² + y² - 41 = 0

So the answer is B. x²+ y² - 41 = 0.

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Answer:

The answer you're looking for is: (4, -9), (6, -9), (4, -1)

Step-by-step explanation:

When translating an image 90º counterclockwise you go one quadrant to the right and use the scale factor: (x, y) --> (y, -x).

When using this scale factor you switch the x and y coordinates and also make sure that x is the opposite operation, it doesn't always mean it's going to be negative.

In this case points (-9, -4), (-9, -6), and, (-1, -4) were translated to (4, -9), (6, -9), (4, -1) accordingly.

I hope this was helpful!

Answer:

z=89

Step-by-step explanation:

42+z=131

take 42 away from both sides

z= 89

Answer:

z = 89

Step-by-step explanation:

42 + z = 131

z = 131 - 42

z = 89

The line goes through the point and has a slope of 4, a y-intercept of -6, and a slope of 4. (0, 6).

The proportion of the increase in the y-value to the change inside the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) and Q := (4,1) on the line.

A line's slope is how steeply it slopes form LEFT to RIGHT. Divide the rise, or vertically increase, by the run, or horizontally start changing, to get the line's gradient.

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The complete question is:

X in graphs the equation y = 4x - 6.

Select all statements about Xin's graph that are true.

a. The graph is a curved line.

b. The line passes through the origin.

c. The line passes through the point (0, 6).

d. The slope of the line is 4.

e. The y-intercept of the line is -6.

The area of triangle MNL is approximately 10.44 cm².

What is the sine rule?

The sine rule, also known as the law of sines, is a formula used in trigonometry to find the lengths of the sides and the measure of the angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:

[tex]a/sin A = b/sin B = c/sin C[/tex]

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides. The sine rule can be used to find the length of a side of a triangle or the measure of an angle if the other two sides and the included angle are known, or if two sides and the angle opposite one of them are known.

To find the area of triangle MNL, we need to first calculate the length of side NL using the sine rule:

sin(38°) / NL = sin(90°) / 4.8

NL = sin(38°) / sin(90°) * 4.8

NL = sin(38°) * 4.8

NL ≈ 2.9 cm

Now we can find the area of the triangle using the formula:

[tex]Area = (1/2) * base * height[/tex]

[tex]Area = (1/2) * 7.2 * 2.9[/tex]

Area ≈ 10.44 cm²

Therefore, the area of triangle MNL is approximately 10.44 cm².

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27 ÷ 5 = 5.4

∴ 5.4 feet of ribbon goes to each bracelet.

The table that shows proportional relationship is x = 1,3,4,5 and y = 50, 150, 200,250 ( table 1).

The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.

To determine the proportionality the ratio of x toby must be thesame Ina table

in table 1

x/y = 1/50 = 3/150 = 4/200 = 5/250 = 1/50

table 1 show proportional relationship

in table 2

3/1.5 is not equal to 7/3 , therefore table 2 does not show proportional relationship

in table 3

1/1.5 is not equal to 3/6 , therefore table 3 does not show proportional relationship

therefore the table that show proportional relationship is table 1

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The minimum number of streetlights that can be installed along the street is 1641 + 1182 = 2823.

In Euclidean geometry, the distance between two points is defined as the length of the shortest path between them. This is often referred to as the "straight-line distance" or "Euclidean distance." It is calculated using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The total distance between A and C is the sum of the distances AB and BC:

AC = AB + BC = 1625 + 1170 = 2795 m

Since we need to install streetlights at points A, B, and C, there will be two segments of the street with streetlights:

From A to B, which has a distance of 1625 m

From B to C, which has a distance of 1170 m

We want to install streetlights along each segment with equal distance between the lights. Let's call the distance between each pair of adjacent streetlights "d".

For the first segment, there will be "n" streetlights, so the total distance covered by the streetlights will be (n-1)d. Similarly, for the second segment, there will be "m" streetlights, and the total distance covered by the streetlights will be (m-1)d.

The total distance covered by the streetlights should be equal to the distance AC, so we have:

(n-1)d + (m-1)d = AC

Substituting the values we know, we get:

1624d + 1169d = 2795

2793d = 2795

d = 2795/2793

d ≈ 0.999

We can round down to 0.99 to ensure that we don't have more streetlights than necessary.

Therefore, the distance between each pair of adjacent streetlights should be 0.99 m. To find the minimum number of streetlights required, we can divide the distance of each segment by 0.99 and round up to the nearest integer:

For the first segment: ceil(1625/0.99) = 1641

For the second segment: ceil(1170/0.99) = 1182

So the minimum number of streetlights that can be installed along the street is 1641 + 1182 = 2823.

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A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. Thus, option D is correct.

The degree of operating leverage (DOL) formula is:

DOL = Contribution Margin / Net Operating Income

We can calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Now we can calculate the DOL:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Therefore, the company's degree of operating leverage is 4.00.

The answer is (D) 4.00.

Step-by-step explanation:

Identify the relevant values from the problem statement:

Net operating income = $30,000

Fixed expenses = $90,000

Sales = $200,000

CM ratio = 60%

Calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Use the contribution margin and net operating income to calculate the degree of operating leverage:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Interpret the result:

A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. This indicates that the company has a high degree of operating leverage, which means that it is more sensitive to changes in sales volume. In other words, small changes in sales can have a big impact on the company's profitability.

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A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. Thus, option D is correct.

The degree of operating leverage (DOL) formula is:

DOL = Contribution Margin / Net Operating Income

We can calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Now we can calculate the DOL:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Therefore, the company's degree of operating leverage is 4.00.

The answer is (D) 4.00.

Identify the relevant values from the problem statement:

Net operating income = $30,000

Fixed expenses = $90,000

Sales = $200,000

CM ratio = 60%

Calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Use the contribution margin and net operating income to calculate the degree of operating leverage:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Interpret the result:

A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. This indicates that the company has a high degree of operating leverage, which means that it is more sensitive to changes in sales volume. In other words, small changes in sales can have a big impact on the company's profitability.

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Answer: [tex]\sqrt{\text{x}-7}-10[/tex]

Work Shown:

[tex]f(\text{x}) = \sqrt{\text{x}-6}-10\\\\f(\text{x}-1) = \sqrt{\text{x}-1-6}-10\\\\f(\text{x}-1) = \sqrt{\text{x}-7}-10[/tex]

Explanation:

I replaced each copy of x with x-1. Then I combined like terms. Doing this will shift the graph 1 unit to the right.

Answer: -7

Step-by-step explanation:

-2x+5=19

-5 |-5

-2x=14

-2x/-2 = 14/-2

x = -7

An equation to represent one way you can find how many miles Emily’s plane flew each hour is y = 182x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Assuming the variable m represent the miles flown each hour, an equation for the number of miles Emily’s plane flew each hour can be calculated as follows;

y = kx

y = (2184/12)x

y = 182x

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Complete Question:

Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.

Use this to help you:

Air travel time: 12 hours

Destination: 2,184 miles​

Answer:??? Bio?

Step-by-step explanation:give a good expample

Answer:

False

Step-by-step explanation:

The absolute value of a number is defined as its distance from zero on the number line. Distance is always a non-negative quantity, so the absolute value of a number can never be negative.

Therefore, the absolute value of any number, whether positive or negative, is always a non-negative value.

Answer:

x = 20

Step-by-step explanation:

x² − 1 = 399

x² = 400

x = 20

We can write the quadratic equation as -

y = - (x - 25)² + 625

The general form of a quadratic equation is -

y = ax² + bx + c

where -

a, b and c are constants.

Given is that Sameen wants to build a fence around a rectangular area of her yard. The graph shows the area {y} in square feet that she can surround with the fencing that she has, where the breadth is width {x} in feet of the rectangle.

The given coordinates on the parabola are -

(8, 336)

(42, 336)

(25, 625)

Here, the point (25, 625) represents the vertex (h, k) of the parabola.

We can write the equation of parabola as -

y = a(x - h)² + k

y = a(x - 25)² + 625

For the point (8, 336), we can write -

336 = a(8 - 25)² + 625

336 - 625 = a(8 - 25)²

a(8 - 25)² = - 289

a(- 17)² = -289

a = -289/289

a = -1

So, we can write the quadratic equation as -

y = - (x - 25)² + 625

Therefore, we can write the quadratic equation as -

y = - (x - 25)² + 625

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NO || PR using the converse of the Triangle Proportionality Theorem are not parallel.

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Conversely, if a line divides two sides of a triangle proportionally, then it is parallel to the third side.

In this problem, we are given a right triangle NQM, where line PR intersects the sides NM and QM at points P and R, respectively. We are also given that NM = 16, PM = 12, RM = 6, and QR = 8. We want to verify that NO || PR.

To do this, we will use the converse of the Triangle Proportionality Theorem. We know that PR divides NM proportionally, so we need to show that it also divides QM proportionally.

Using the ratios of corresponding side lengths of similar triangles, we can write:

PM / RM = PN / RN

Substituting the given values, we get:

12 / 6 = PN / (16 - 6)

2 = PN / 10

PN = 20

Similarly, we can write:

QR / RM = QN / RN

Substituting the given values, we get:

8 / 6 = QN / (16 - 6)

4 / 3 = QN / 10

QN = 40 / 3

Now we can check if PR divides QM proportionally:

PM / QN = 12 / (40 / 3) = 9 / 5

PN / RM = 20 / 6 = 10 / 3

Since these ratios are not equal, we can conclude that PR does not divide QM proportionally.

Therefore, by the converse of the Triangle Proportionality Theorem, we can conclude that NO is not parallel to PR.

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The requried (a) median for the chocolate candy and nonchocolate candy sales are $3040 and $1566.5 respectively. (b) The range for the chocolate candy sales, the range is ($1941, $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).

A histogram is a graphical representation of the distribution of a set of numerical data. It consists of a set of rectangles, where the area of each rectangle is proportional to the frequency (or count) of the observations falling within a particular interval, called a bin.

Here,
A. The interval for the median for each data set can be found by arranging the data in ascending order and finding the middle value. For the chocolate candy sales, the median falls in the interval of 2800-3,099 dollars. While for the Nonchocolate candy, it falls under 1300 -1599

The median for the chocolate candy sales  = $3040
The median for the Nonchocolate candy sales  = $1566.5

B. The range for each data set can be found by subtracting the minimum value from the maximum value. For the chocolate candy sales, the range is ($1941, to $3454). For the non-chocolate candy sales, the range is (from 1,096 dollars to 2,892 dollars).

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The equivalent expressions are A3, B2, C3, D4 and E5.

Expression in math is a combination of numbers, symbols, and operations that represent a value or a relationship between values. Expressions are used to represent relationships between numbers, variables, and other mathematical objects. Expressions are the basic building blocks of algebra and calculus, and allow us to solve problems and describe relationships between different quantities. Expressions help us to understand math better, as they allow us to express complex ideas in concise, clear, and concise form.

Once the wires are connected by matching the equivalent expressions, the code word is 8+7+(-3).

This is happening because in order to unlock the communication system, you need to match the equivalent expressions in order to find the code word. By evaluating each expression, you can determine which of the expressions are equivalent and then connect the wires accordingly. By connecting the wires, you can then find the code word which will unlock the communication.

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Answer:

t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32

Step-by-step explanation:

Solve for t:

16 t^2 - 23 t + 18 = 0

Divide both sides by 16:

t^2 - (23 t)/16 + 9/8 = 0

Subtract 9/8 from both sides:

t^2 - (23 t)/16 = -9/8

Add 529/1024 to both sides:

t^2 - (23 t)/16 + 529/1024 = -623/1024

Write the left hand side as a square:

(t - 23/32)^2 = -623/1024

Take the square root of both sides:

t - 23/32 = (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32

Add 23/32 to both sides:

t = 23/32 + (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32

Add 23/32 to both sides:

Answer: t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32

The value of the double integral of y over D is 160.

The region D is defined as the image of the rectangle R under the transformation Φ(u,v) = (u², u+v). To find the integral of y over D, we need to express y as a function of u and v, and then compute the double integral in terms of u and v.

From the definition of Φ, we have:

u² = x

u + v = y

Solving for v in terms of u and y, we get:

v = y - u

Substituting this expression for v into the second equation, we get:

y = u + (y - u) = y

Therefore, y does not depend on u, and we can write:

y = f(v) = v + u

The integral of y over D can then be written as:

∫∫D y dA = ∫∫R f(v) |J| dA

where J is the Jacobian of the transformation Φ.

The Jacobian of Φ is given by:

J = ∂(x,y)/∂(u,v) =

| 2u 1 |

| 1 1 |

The determinant of J is:

|J| = 2u - 1

Substituting this expression for |J| and the expression for f(v) into the integral, we get:

∫∫D y dA = ∫∫R (v + u)(2u - 1) dudv

To evaluate this integral, we can integrate first with respect to u and then with respect to v:

∫∫D y dA = ∫[0,5]∫[1,9] (v + u)(2u - 1) dudv

= ∫[0,5] [(v+9)³/3 - (v+1)³/3] dv

= [(5+9)⁴/12 - (1+9)⁴/12]

= 480/3

= 160

Therefore, the value of the double integral of y over D is 160.

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Complete question:

Let D= Ф(R), where Φ(u,v)= (u², u+v) and R= [1,9] × [0,5].

Calculate [tex]\mathrm{\int \: \int \: _D ydA}[/tex]

There are 509 tourists only visited the LEGOLAND (of these three).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, To find the number of tourists who only visited LEGOLAND, we need to subtract the tourists who visited LEGOLAND and another theme park from the total number of tourists who visited LEGOLAND.

Calculation:

First, we can find the total number of tourists who visited LEGOLAND:

Total = Tourists who visited only LEGOLAND + Tourists who visited LEGOLAND and another park

Hence, Total = (Total visitors to LEGOLAND) - (Tourists who did not visit any of the parks)

Total = 1,033 - (256 + 267 + 75 + 93 - 52 - 82 - 33)

Total = 1033 - 260

Total = 509

Hence, There are 509 tourists only visited the LEGOLAND (of these three).

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