Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.

The scale factor of the dilation is 1/2.

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Here given that blue figure is the dilated image of the black figure.

Dilation is the reduction.

The bottom left point is (2, 2) and top let point is (2, 4) of blue figure.

Length of the left segment of blue figure = [tex]\sqrt{(2-2)^2+(4-2)^2}[/tex]

                                                                    = 2

The bottom left point is (4, 4) and top let point is (4, 8) of black figure.

Length of the left segment of black figure = [tex]\sqrt{(4-4)^2+(8-4)^2}[/tex]

                                                                      = 4

Scale factor = Ratio of corresponding sides

                    = 2/4

                    = 1/2

This will be the same if we take another corresponding sides.

Hence the scale factor is 1/2.

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Answer:

What is the unit price of each battery in each package?

To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.

For the package of 8 count AA batteries:

Total cost: $6.16

Number of batteries: 8

Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery

For the package of 20 count AA batteries:

Total cost: $15.20

Number of batteries: 20

Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery

Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.

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Step-by-step explanation:

To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.

For the package of 8 count AA batteries:

Total cost: $6.16

Number of batteries: 8

Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery

For the package of 20 count AA batteries:

Total cost: $15.20

Number of batteries: 20

Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery

Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.

Using arithmetic operation, the statement that is true is -

A: The 20-count pack of AA batteries has a lower unit price of $0.78 per battery.

D: The 8-count pack of AA batteries has a lower unit price of S0.77 per battery

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To find the unit price per battery, we divide the cost of each package by the number of batteries in the package.

For the 8-count pack -

Use the arithmetic operation of division.

Unit price per battery = $6.16 / 8 batteries = $0.77 per battery

For the 20-count pack -

Use the arithmetic operation of division.

Unit price per battery = $15.60 / 20 batteries = $0.78 per battery

Therefore, the statements A and D are correct.

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1. The value of the variable 'x' is 10 that is written as x = 10.

2. The equation is ∠3 + ∠4 = 90°. Then angles ∠3 and ∠4 will be complementary angles.

3. The measure of angle ∠2 is 60° which is an acute angle.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

1.  ∠1 = 6x + 45 and ∠3 = 9x + 15

Angle ∠1 and angle ∠3 are opposite angles. Then the equation is given as,

∠1 = ∠3

9x + 15 = 6x + 45

9x - 6x = 45 - 15

3x = 30

x = 30 / 3

x = 10

2.  Angle ∠2, angle ∠3, and angle ∠4 are supplementary angles. Then the equation is given as,

∠2 + ∠3 + ∠4 = 180°

90° + ∠3 + ∠4 = 180°

∠3 + ∠4 = 90°

3.  Angle ∠1 is 120°, then the measure of angle ∠2 is given as,

∠1 + ∠2 = 180°

120° + ∠2 = 180°

∠2 = 60° (acute)

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From the given options, option 1 depicts a decreasing function. Hence, option 1 is the correct answer for the graph.

Calculus uses a function's derivative to determine whether a function is rising or decreasing at various intervals in a specific domain. Given a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

We observe that the function of f approaches to 0 as it moves towards infinity. Thus, it is a decreasing function.

From the given options, option 1 depicts a decreasing function. Hence, option 1 is the correct answer.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{65}~,~\stackrel{y_1}{149})\qquad (\stackrel{x_2}{105}~,~\stackrel{y_2}{221}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{221}-\stackrel{y1}{149}}}{\underset{\textit{\large run}} {\underset{x_2}{105}-\underset{x_1}{65}}} \implies \cfrac{ 72 }{ 40 } \implies \cfrac{ 9 }{ 5 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{149}=\stackrel{m}{ \cfrac{ 9 }{ 5 }}(x-\stackrel{x_1}{65})\implies y-149=\cfrac{ 9 }{ 5 }x-117 \\\\\\ y=\cfrac{ 9 }{ 5 }x-117+149\implies \boxed{y=\cfrac{ 9 }{ 5 }x+32} \\\\\\ \stackrel{\textit{Celsius is 70, so x = 70}}{y=\cfrac{ 9 }{ 5 }(70)+32}\implies \boxed{y = 158}[/tex]

The man's daily wage is given as follows:

$42.

The wages are obtained applying the proportions in the context of the problem.

The woman receives $24 for 8 hours of work, hence her hourly wage is given as follows:

24/8 = $3 per hour.

(Hourly wage = Total wages/total hours).

Their wages per hour are in the ratio 7:5, hence the man's hourly wage is obtained multiplying the woman's hourly wage by 7/5, hence:

7/5 x 3 = 21/5 = $4.2 per hour.

The man works 10 hours a day, hence the daily wage is given as follows, multiplying the hourly wage by 10:

10 x 4.2 = $42.

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Answer:

Step-by-step explanation:

Equate whats inside (arguments) \sin with base period of sine function 2\pi and solve for x to get period,

\pi x=2\pi\implies x=2

So the period of the graph of the given function is precisely 2.

Hope this helps :)

Answer:

A. the graph of the function does not form a straight line.

Step-by-step explanation:

Answer:

Valid

Step-by-step explanation:

This argument is Valid because there could be many other reasons she needs dress altercations, however the most likely one is that she did not have her baby before next week.

Answer:

Step-by-step explanation:

The argument is valid.

We can analyze it using the following symbols:

Let A be the event that Bryony has her baby before next week.

Let B be the event that Bryony needs dress alterations before her sister's wedding next month.

Then the argument can be represented as follows:

If A, then not B.

B.

Therefore, not A.

This is a valid deductive argument form called modus tollens. The conclusion follows logically from the premises. Therefore, the argument is valid.

Handheld consoles are the most at risk of being discontinued compared to other types of consoles.

option A.

Handheld consoles have faced tough competition from the rise of mobile gaming on smartphones and tablets, which has impacted their market share and sales.

For example, Nintendo has faced challenges with their handheld consoles, such as the Nintendo DS and 3DS, which experienced a decline in sales due to the emergence of mobile gaming. As a result, Nintendo shifted its focus to the hybrid console, the Nintendo Switch, which can be used as both a handheld and home console.

That being said, it's important to note that the market for handheld consoles is still significant, and there are still popular handheld devices on the market such as the Nintendo Switch Lite and Sony's PlayStation Vita. The entertainment, interactive, and computer console markets also have their own unique challenges and opportunities, and each type of console has its own risks and benefits.

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Answer:

The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

Step-by-step explanation:

The equation for the function with the described transformations is y(x) = -2f(x+1) + 8.

Starting with the basic function of f(x), we can apply the described transformations in the following order:

Vertical stretching by a factor of 2: We multiply the output of the function by 2. This results in a new function g(x) = 2f(x).

Reflection across the x-axis: We flip the sign of the output of the function. This results in a new function h(x) = -g(x) = -2f(x).

Translation 1 unit left and 8 units up: We shift the graph of the function 1 unit to the left and 8 units up. This can be achieved by replacing x with (x+1) and adding 8 to the output.

This results in a new function y(x) = h(x+1) + 8 = -2f(x+1) + 8.

Putting it all together, the equation for the function with the described transformations is:

y(x) = -2f(x+1) + 8

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The complete question is below:

Write an equation for f(x) when it is vertically stretched by a factor of 2, reflected across the x-axis, then translated 1 unit left and 8 units up.​

The length of the radius and diameter are 10.5 and 21 respectively

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

The area of the sector = tetha/360 × πr²

= 72/360 × 3.14 × r²

= 0.628r²

area of the circle = area of the shaded part + area of sector

3.14r² = 277 + 0.628r²

3.14r²-0.628r² = 277

2.512 r² = 277

r² = 277/2.512

r² = 110.3

r = √ 110.3

r = 10.5

d = 2r

d = 10.5 × 2

= 21

therefore the radius and diameter are 10.5 and 21 respectively

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Answer:

-x.

Step-by-step explanation:

1) the equation of the line in slope-interception form is: y=slope*x+interception;

2) according to the graph and data in the condition slope=-1, interception=0, then the requred equation is:

y=-x.

The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as,

H² = P² + B²

The height of Triangle ΔABC is given as,

17² = h² + 15²

289 = h² + 225

h² = 289 - 225

h² = 64

h = 8 units

The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.

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Answer:

Step-by-step explanation:

[tex]C=\pi d[/tex]

   [tex]=\pi \times 35[/tex]

   [tex]\approx 109.96 feet[/tex]

Answer:

110. feet approximately

Step-by-step explanation:

circumference means a closed boundary of a curved shape. Mainly known as a circle. To find circumference, use the formula c= π (pie) times diameter.

35 × π ≈ 110

Hope this helps :)

The constant of proportionality between the side length and the perimeter of the equilateral triangle would be = 3.

The constant of proportionality is defined as the constant value that exists between two variables that are in a direct proportional relationship to each other.

For example, the constant of proportionality (k) between the side lengths and the perimeter of the equilateral triangle= y/X= 15/5= 3 or 24/8 = 3 or 27/9 = 3 or 30/10=3.

Therefore, the constant of proportionality which is the constant value existing between the two variables= 3.

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The value of x in the figure and given in the task content is; x = 64.

As evident in the task content; the figure is a triangle with angle measures; 63°, 56° and (x - 3)°.

Since the sum of interior angles of a triangle is; 180°.

Therefore, we have;

63° + 56° + (x - 3 )= 180°

open parenthesis

63 + 56 + x - 3 = 180°

x = 180 + 3 - 63 - 56

x = 64°.

Ultimately, the value of variable, x from the triangle is; 64°.

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1. The fencing and grass for this playground cost $16,360.

2. Springfield's playground can hold approximately 800 kids at a density of 25 square feet per child.

3. We can recommend a rectangular playground measuring approximately 166 yards by 40 yards, with a total area of 6,666.67 square yards. This playground should cost $49,200 for the fencing and grass.

1. To calculate the cost of the fencing and grass, we first need to know the dimensions of the playground. Let's assume that the playground is a rectangular shape measuring 100 feet by 200 feet, for a total area of 20,000 square feet.

To determine the cost of the fence, we need to know how many rolls of fencing are required. Each roll is 50 feet long, so we need four rolls to fence the perimeter of the playground (100 + 100 + 200 + 200 = 600 feet / 50 = 12 rolls, but we can't buy half a roll, so we round up to four rolls). Therefore, the cost of the fence is:

4 rolls x $90/roll = $360

To determine the cost of the grass, we need to know how many square feet of grass we need to cover the playground. Since each roll of grass covers 500 square feet, we need:

20,000 sq ft / 500 sq ft per roll = 40 rolls of grass

Therefore, the cost of the grass is:

40 rolls x $400/roll = $16,000

Adding the cost of the fence and the grass, we get the total cost:

$360 + $16,000 = $16,360

So the fencing and grass for this playground cost $16,360.

2. To calculate how many kids per square yard the playground can hold, we need to know the area of the playground in square yards. There are 9 square feet in a square yard, so the playground measures:

20,000 sq ft / 9 sq ft per sq yd = 2,222.22 sq yds

Assuming that each child requires 25 square feet of space to play, we can calculate how many kids can fit on the playground:

2,222.22 sq yds x (9 sq ft per sq yd / 25 sq ft per child) = 800 kids

Therefore, Springfield's playground can hold approximately 800 kids at a density of 25 square feet per child.

3. To recommend a playground shape and size that would fit Wintermeadow's budget and hold at least 3 times as many kids as Springfield's playground at the same density of kids per square yard, we first need to know Wintermeadow's budget.

Let's assume that Springfield's budget is $50,000, so Wintermeadow's budget is $150,000.

To determine the size of the new playground, we can start by calculating the cost of the fencing and grass for Springfield's playground per square yard:

$16,360 / 2,222.22 sq yds = $7.38 per sq yd

We can then use this cost to estimate the size of the new playground. Let's assume that the new playground will also be rectangular, and that we want it to hold at least 3 times as many kids as Springfield's playground, or 2,400 kids. Using the same density of 25 square feet per child, we need:

2,400 kids x 25 sq ft per child = 60,000 sq ft

Since there are 9 square feet in a square yard, this is:

60,000 sq ft / 9 sq ft per sq yd = 6,666.67 sq yds

Multiplying this area by the cost per square yard, we get the cost of the fencing and grass for the new playground:

6,666.67 sq yds x $7.38 per sq yd = $49,200

Therefore, we can recommend a rectangular playground measuring approximately 166 yards by 40 yards, with a total area of 6,666.67 square yards. This playground should cost $49,200 for the fencing and grass.

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Answer:

0.0166666666666666666666666666666666666666666667

Step-by-step explanation:

USE CALCULATORRRRRR

Answer:

[tex](r \;\circ\;q)(4) = \boxed{5}\\\\(q \;\circ\;r)(4) = \boxed{13}\\[/tex]

Step-by-step explanation:

We have the following functions

[tex]q(x) = x^2+4\\\\and\\\\r(x) = \sqrt{x+5}\\\\[/tex]

1. To find
[tex](r \;\circ \;q)(4) = r(\;q(4)\;)[/tex]

First find
[tex]q(4) = 4^2 + 4 = 16 + 4 = 20[/tex]

Substitute this value for x in r(x)

[tex]r(20) = \sqrt{20 + 5} = \sqrt{25} = 5[/tex]

So
[tex]\bold{(r \;\circ \;q)(4) = 5}[/tex]

2. To find
[tex](q \;\circ\;r)(4) = q(\;r(4)\;)[/tex]

First find
[tex]r(4) = \sqrt{4 + 5} = \sqrt{9} = 3\\\\[/tex]

Substitute this value for x in q(x)

[tex]q(3) = 3^2 + 4 = 9 + 4 = 13\\\\\bold{(q \;\circ\;r)(4) = 13}[/tex]

The compositions of functions are:

Here we have the two functions:

q(x) = x² + 4

r(x)=  √(x + 5)

We want to find the two compositions:

(r o q)(4) = r(q(4))

First let's find:

q(4) = 4² + 4 = 16 + 4 = 20

Then:

r(q(4)) = r(20) =  √(20 + 5) = 5

And the other composition is:

(q o r)(4) = q(r(4))

First, r(4) = √(4 + 5) = 3

Then:

q(r(4)) = q(3) = 3² + 4 = 9 + 4 = 13

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Answer:333

Step-by-step explanation:53533535

The solution to the system of inequalities is:

{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.

A linear inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

First, let's graph the line x = -2, which is a vertical line passing through -2 on the x-axis.

Next, let's graph the line x - y = 1, which can be rewritten as y = x - 1. This is a line with a slope of 1 (meaning it goes up 1 unit for every 1 unit it goes to the right) and a y-intercept of -1 (meaning it passes through -1 on the y-axis).

Now, we need to shade in the region that satisfies both inequalities. We know that x has to be greater than or equal to -2, so we shade to the right of the vertical line x = -2. We also know that x - y has to be greater than or equal to 1, so we shade above the line y = x - 1.

The shaded region is the overlapping region that satisfies both inequalities. It is the region above the line y = x - 1 and to the right of the vertical line x = -2.

Therefore, the solution to the system of inequalities is:

{x | x ≥ -2, x - y ≥ 1} or in set-builder notation: {(x,y) | x ≥ -2, y ≤ x - 1}.

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The complete question is as follows:

What is the solution to the system of inequalities?

x ≥ -2

x - y ≥ 1

The measure of angle x in the hexagon is 140 degree.

The formula for calculating the sum of interior angles of a polygon is ( n − 2 ) × 180 degree.

where is the number of sides

Since the number of sides of the polygon in the diagram is 6, we can find the sum of the interior angle.

Sum of interior angle = ( n − 2 ) × 180

Plug in n = 6

Sum of interior angle = ( 6 − 2 ) × 180

Sum of interior angle = ( 4 ) × 180

Sum of interior angle = 720°

Next, we sum up the interior angles given in the diagram equate to 720 degree and solve for x.

108 + 155 + 123 + 104 + 90 + x = 720

Collect and add like terms

580 + x = 720

Subtract 580 from both sides

580 - 580 + x = 720 - 580

x = 720 - 580

x = 140°

Therefore, the value of x is 140 degree.

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John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. $75 = $15p + A

What is the total of the cost?

Whole cost is the sum of all expenditures made to generate a certain level of production; when this total cost is divided by the amount produced, average or unit cost is discovered.

Let the number of people on John's family plan be represented by p.

According to the problem, the family plan cost is $68, and there is an additional cost of $15 for each person on the plan. Therefore, the total cost C of the plan with p people is:

C = $68 + $15p

We know that John's family phone bill is $143, which represents the total cost of the family plan plus any additional charges. Therefore, we can write:

$143 = C + A

where A represents any additional charges.

Substituting C into this equation, we get:

$143 = ($68 + $15p) + A

Simplifying, we can write:

$75 = $15p + A

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This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

Product is an item or service that is created by a business or organization to meet the needs of their customers. It is anything that is offered to a market for sale or trade. Products can be tangible, such as physical goods or intangible, such as services, ideas, or experiences. Companies need to create products that offer value to their customers. This includes making sure that the product meets the customer's needs, is of good quality, and is priced appropriately.

An empty product is a mathematical term that is used to describe a product of two or more numbers, where the result is equal to the product of just one of the numbers. This is because when you multiply any number by zero, the result is zero. Therefore, if a product contains a zero, then the result will be the same as if you only multiplied one of the numbers in the product. For example, if we take the product of 5 and 0, then the result is 0. This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

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Answer:

The researcher used a ratio scale of measurement for the number of people using their cell phone.

Mean: (3+4+4+5+6+8)/6 = 30/6 = 5

Median: arrange the data in ascending order: 3, 4, 4, 5, 6, 8. The median is the middle value which is 5.

Mode: there is no mode as no value occurs more than once.

Range: 8-3 = 5

Variance:

s^2 = Σ(x-ȳ)^2 / (n-1)

s^2 = [(3-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (6-5)^2 + (8-5)^2] / (6-1)

s^2 = 5.6

Standard deviation: s = sqrt(s^2) = sqrt(5.6) ≈ 2.37

To find the number of people using their cell phone associated with +1 SD, we add one standard deviation to the mean:

Mean + 1 SD = 5 + 2.37 ≈ 7.37

Therefore, approximately 7 people using their cell phone are associated with +1 SD.

To find the number of people using their cell phone that reflects 96% of the sample, we need to find the z-score that corresponds to the 96th percentile. From a standard normal distribution table, we find that the z-score is approximately 1.75. We can use this z-score to find the corresponding value in our data set using the formula:

z = (x - ȳ) / s

Rearranging, we get:

x = z * s + ȳ

x = 1.75 * 2.37 + 5

x ≈ 9.3

Therefore, approximately 9 people using their cell phone reflect 96% of the sample.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use the conditional probability formula to find the probability of a student taking a calculus class given that the student takes a statistics class:

P(calculus | statistics) = P(calculus and statistics) / P(statistics)

We are given that P(statistics) = 0.83 and P(calculus and statistics) = 0.66.

Substituting the values we have:

P(calculus | statistics) = 0.66 / 0.83

Simplifying the fraction:

P(calculus | statistics) = 0.795

Therefore, the probability of a student taking a calculus class given that the student takes a statistics class is 0.795. Rounded to three decimal places, the answer is 0.795.