What are the coordinates of X′ for the image of △TUX after dilation with center at (0, 0) and scale factor 4, then applying (x, y) ⟶ (x − 3, y + 1), given T(−7, −6), U(−8, 3), X(2, 1)?

Let's use the given information to set up equations to solve for the ages of the family members.

We know that the mean age of the family is 23 years, so we can write:

(sum of ages) / 7 = 23

sum of ages = 161

We also know that the median age is 16 years, which means that the ages of the family members can be arranged in order from smallest to largest, and the middle age (or the average of the two middle ages, if there are an even number of ages) is 16. We can use this information to set up an equation:

(3rd smallest age + 4th smallest age) / 2 = 16

3rd smallest age + 4th smallest age = 32

Next, we know that the range of the ages is 35 years, which means that the difference between the largest age and the smallest age is 35. We can use this information to set up another equation:

largest age - smallest age = 35

Finally, we know that the modes (the most common ages) are 12 years and 45 years. This means that there are two family members whose ages are 12 years and two family members whose ages are 45 years. We can use this information to set up two more equations:

number of 12-year-olds + number of 45-year-olds = 4

12 x number of 12-year-olds + 45 x number of 45-year-olds = sum of ages

We now have five equations and five unknowns (the ages of the seven family members). We can solve for these unknowns using algebra. One possible set of ages that satisfies all of the equations is:

2, 2, 12, 16, 20, 45, 64

(Note that the ages do not have to be integers, but this particular set of ages happens to be integers and satisfies all of the given conditions.)

Answer:

Step-by-step explanation:

2

The solution to the system of equations is given below.

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given is the system of equations as shown in the image.

{ 1 } -

x - 2y = - 7

2x + 5y = 8

We can write -

x = 2y - 7

Now -

2(2y - 7) + 5y = 8

4y - 14 + 5y = 8

9y = 22

{y} = 22/9

x = 44/9 - 7

x = 44/9 - 63/9

{x} = - 19/9

{ 2 } -

5x - 3y = 16

3x + 6y = 18

We can write -

5x - 3y = 16

x + 2y = 9

So -

x = 9 - 2y

5(9 - 2y) - 3y = 16

45 - 10y - 3y = 16

45 - 13y = 16

45 - 16 = 13y

13y = 29

y = 29/13

x = 9 - 58/13

x = 117/13 - 58/13

x = 59/13

Similarly, we can solve the other two system of equations.

Therefore, the solution to the system of equations is given above.

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Answer:

8, 39, 250, 1031

Step-by-step explanation:

(Needing a bit more context but if its sequences then:)

The probability of getting a pair of 10s is 1/26.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Here,

Total number of outcomes = 52

Number of outcomes = 2

So, the probability is 2/52

= 1/26

Therefore, the probability of getting a pair of 10s is 1/26.

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these two events are dependant because the probability of the second event depends on the probability of the first event

follow the order

[tex]\pi /2[/tex] should be in between 0 and [tex]\pi[/tex], therefore it should be right in the middle. every 90 degrees, the circle increases by [tex]\pi /2[/tex] as well.

oh my God cr7 ans messi are running

The number of days that he was in Europe will be 42 days.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since Jordan went to Europe for vacation. He spent 1/3 of his time in Spain.

If he was in Spain for 14 days, the number of days that he was in Europe will be:

1/3 × x = 14

x = (14 × 3)

x = 42 days

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Jordan went to Europe for vacation. He spent 1/3 of his time in Spain. If he was in Spain for 14 days, how long was he in Europe?

Answer:

First, if it's a simple interest problem, convert R percent to r a decimal, r = R/100 = 9%/100 = 0.09 per year, then, solving our equation

I = 4000 × 0.09 × 2

I = 4000 × 0.18

I = $720.00

The simple interest accumulated on a principle of $4,000.00 at a rate of 9% per year for 2 years is $720.00.

Hope this helps. (Compound interest will be added if the equation needs it)

Answer:

El valor obtenido para x es una solución a la ecuación y, por lo tanto, es un punto en la gráfica de la función. Esto significa que el punto (x,y) en la gráfica se encuentra en la recta que representa la ecuación

Step-by-step explanation:

Answer:

x is greater than or equal to 3

Step-by-step explanation:

I'm gonna assume you meant 3x-8

Treat it as an equation

3x-8 =1, 3x=9, x=3

If its x^3 -8

x^3 -8 =1, x^3=9, x is greater than or equal to the cubed root of 9

Number line graph representing the possible heights to ride the kiddie swings is mentioned below.

A number line is a visual representation of the real numbers, arranged in a linear sequence from negative infinity to positive infinity. It is a straight line that is divided into segments or intervals, with each interval representing a specific range of numbers.

The number line is typically drawn with zero in the center, and positive numbers to the right of zero and negative numbers to the left. Each point on the number line corresponds to a specific real number, with the distance between adjacent points representing a unit of one.

Sure, here's a number line graph representing the possible heights to ride the kiddie swings, where the y-axis represents the eligibility to ride and the x-axis represents the height in inches:

   |__________________|__________________|

                      0                                   48

The shaded area on the left side of the number line represents the eligible heights to ride the kiddie swings, which are 48 inches or shorter.

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The equivalent number of inches is given as follows:

The equivalent number of inches is obtained applying the proportions in the context of the problem.

A proportion is applied as the unit conversion rate from feet to inches is given as follows:

1 feet = 12 inches.

Hence the measures are converted from feet to inches multiplying the amounts by 12, as follows:

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Answer: 15 Liters (15L)

Step-by-step explanation:

The constant of proportionality (also known as k), is for every bottle, there are 2.5 liters. (k = y/x)

5 / 2 = 2.5 , 12.5 / 5 = 2.5, 20 / 8 = 2.5, etc.

So, we need to multiply 6 by 2.5, 6 * 2.5 = 15

For 6 bottles, there are 15 liters

Answer:

Let's suppose that Mr. Lee puts "x" apples into each box.

According to the first statement, when he puts an equal number of apples into 8 boxes, he has one apple left. This can be represented by the equation:

8x + 1 = n, where n is the total number of apples Mr. Lee has.

Similarly, the second statement says that when he puts the same number of apples into 5 boxes, he has 7 apples left. This can be represented by the equation:

5x + 7 = n

Now we have two equations with two unknowns (x and n). We can solve for x by setting the two equations equal to each other:

8x + 1 = 5x + 7

Subtracting 5x from both sides, we get:

3x + 1 = 7

Subtracting 1 from both sides, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

So Mr. Lee puts 2 apples into each box. To find the total number of apples he has, we can substitute x = 2 into either of the two equations we started with:

8x + 1 = 8(2) + 1 = 17

So Mr. Lee has 17 apples

To make the profit of $5000, the temperature should be 290 degrees Fahrenheit.

The general equation of a straight line is -

y = mx + c

where -

{m} is the slope of the line.

{c} is the {y} - intercept.

Given is a scatter plot as shown in the image.

We can write the equation of the line of best fit as -

{m} = (400 - 0/(60 - 40)

{m} = 400/20

{m} = 20

We can write the y - intercept as -

y = 20x + c

0 = 800 + c

c = - 800

So, the equation of the line of best fit is -

y = 20x - 800

For {y} = 5000, we can write -

5000 + 800 = 20x

5800 = 20x

x = 5800/20

x = 290

Therefore, to make the profit of $5000, the temperature should be 290 degrees Fahrenheit.

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The principal amount of the loan is $1,200,000.

What is simple interest?

Simple interest is the amount of borrowing-related interest that is computed using only the initial principal and a constant interest rate.

To find the principal amount of a loan, we need to use the formula for simple interest:

I = Prt

Where I is the interest, P is the principal, r is the interest rate as a decimal, and t is the time in years.

In this case, we know that the interest is $3,150 and the interest rate is 10.5%. We also know that the interest is earned quarterly, so the time period is 1/4 of a year, or 0.25 years.

Substituting these values into the formula, we get:

3150 = P * 0.105 * 0.25

Solving for P, we get:

P = 3150 / (0.105 * 0.25) = $1,200,000

Therefore, the principal amount of the loan is $1,200,000.

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The vertex of the parabola is ( 0, -4). The correct option is F.

A vertex of a parabola is the point at which the parabola changes direction. It is the point on the parabola where the curve reaches its minimum or maximum value, depending on whether the parabola opens upward or downward.

A parabola is a type of conic section, a geometric shape formed by the intersection of a plane and a cone. In particular, a parabola is formed when a plane intersects a right circular cone parallel to one of its generating lines.

From the given graph the vertex of the parabola is,

Vertex = ( 0, -4 )

Therefore, the vertex is (0,-4).

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Answer:

pemdas

Step-by-step explanation:

pemdas means Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction

you always want to go left to right

when using pemdas.

example 4^5 • (9-8)

you start from left to right

we would work in parentheses because that is what pemdas said to do.

Answer:45

Step-by-step explanation: see how if you cut off that spike and you plug it in the non-shaded part it fits. Now you’ve got yourself a rectangle so the area is 3+2= 5 x 9= 45

The domain and range of h(n) are the set of whole numbers

The domain and the range of h(n)

Given that

The function h(n), represents the count of houses.

Both n and h(n) can take only whole values.

So, we have the domain and range to be the set of whole numbers

Evaluating h(5) and h(11)

The number of houses is the same as the figure number

This means that

h(5) = 5 and h(11) = 11

The explicit function of h(n)

By the computations above, we have the formula of h(n) to be:

h(n) = n

The values of s(4) and s(7)

Given that

The function s(n), represents the count of segments.

Where the segment is twice the figure number

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

By the statement above, we have the growth pattern to be a proportional equation with a constant rate of change

The explicit function of s(n)

Based on the statements above, we have

s(n) = 2n

Complete the table for f(5) and f(7)

From the table, we can see that

As n increases, the value of f(n) is divided by 2 to get the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

The domain of f(n)

The possible values of n are real numbers

So, we have

Domain: All set of real numbers

The observation of the function

Above, we have

As n increases, the value of f(n) is divided by 2 to get the next term

This means that

As n gets larger and larger, the value of f(n) get halved

The value of g(4)

From the question, we have

First term, a = 9

Common ratio, r = 2

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

Completing the statements

Based on the function definitions, the statements when completed are

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

Divide the equations

g(24)/g(21) = 729

Hence, the value of the ratio is 729

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The logical form of this argument in " If Russia invades the Ukraine, America will impose trade sanctions upon Russia" is c. Hypothetical Syllogism.

A hypothetical syllogism is a logical argument that uses two conditional statements, or "if-then" statements, to draw a conclusion. The general form of a hypothetical syllogism is:

If A is true, then B is true.

If B is true, then C is true.

Therefore, if A is true, then C is true.

Here's an example of a hypothetical syllogism:

If it rains, then the ground is wet.

If the ground is wet, then the grass is slippery.

Therefore, if it rains, then the grass is slippery.

Therefore, option C is correct.

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The value of the speed(v) is 5.14 km/hr

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector. Speed is measured in m/s and km/hr

speed = distance / time

distance = 3km

converting the time in seconds to hour,

time = 35 mins = 35/60 = 7/12 hr

speed = 3 ÷ 7/12

= 3× 12/7

= 36/7

= 5.14 km/hr

therefore the speed of the boy is 5.14 km/hr

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Answer:

Hannah drinks 64 fluid ounces of water per day, which is equivalent to 0.5 gallons.

We are given the following system of equations:

y = (1/2)x + 4 ---(1)

x - y = 8 ---(2)

We can solve this system of equations by substitution method.

From equation (2), we have:

x - y = 8

Solving for x, we get:

x = y + 8

Substitute this value of x in equation (1):

y = (1/2)(y+8) + 4

Simplifying and solving for y, we get:

y = 2

Now, substitute this value of y back in equation (2) to find the value of x:

x - 2 = 8

x = 10

Therefore, the solution of the given system of equations is (x, y) = (10, 2).

The figure is a composite figure compromising of a rectangle OHKN, two triangles ∆LMN and ∆HJK, and a semicircle of arc HP, hence the total area will be derived by the sum of area for each basic shapes.

We can observe from the figure that the lines OL and HK are parallel, likewise the lines OH and NK, so OHKN is a rectangle and its area can be simply derived by multiplying its length by the width.

LMN and HJK are two different triangles and their area can be derived by half of the multiple of their base and height.

we will be left with a semicircle of arc HP and the area is derived using the formula πr²/2, where r is the radius.

In conclusion, the area of the figure will derived by the sum of area for each basic shapes(rectangle OHKN, triangles ∆LMN and ∆HJK, and semicircle of arc HP).

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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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The equation and solution for given situations are

Situation 1: 1.45x + 3.25 = 9.05; 4 pounds

Situation 2: 850 - 15a = 805; 3 days

Situation 3: 12.50 + 1.50r = 39.50; 18 times

Situation 4: 29.95x + 5.95 = 185.65; 6

Situation 5:  y = x - 5; 37 inches

The linear equation is a mathematical statement that is used to find an unknown quantity or number in a given situation. In this, we used different types of variables to represent the unknown value.

To solve the following situations use different variables and solve them for the value of variables.

Here we have

Situation 1:

A freight company charges $ 1.45 per pound plus a handling fee of $ 3.25. A customer was charged $ 9.05 to ship a package  

Let 'x' be the weight of the package

=> 1.45x + 3.25 = 9.05

=> 1.45x = 5.8

=> x = 4

∴ weight of the package is 4 pounds

Situation 2

A tenant is charged $ 850 for rent on the 5th of the month. For every day they are early, they can deduct $ 15 from the rent. The tenant pays $ 805

Let the tenant pay the rent 'a' number of days early

=> 850 - 15a = 805

=> 15a = 45

=>  a = 3

∴ The tenant paid 3 days early.

Situation 3

Jordan pays $ 12.50 for a city bus pass lowering his bus fare to $ 1.50 per ride. In March, Jordan spent $ 39.50 to ride the city How many times did he ride the bus

Let Jordan ride for 'r' time

=> 12.50 + 1.50r = 39.50

=> 1.5r = 27

=> r = 18

∴  Jordan ride the bus 18 times

Situation 4

Jung purchased several video games priced at $ 29.95 and the shipping cost is $ 5.95. His total purchase is $ 185.65

Let Jung buy 'y' number of games

=> 29.95x + 5.95 = 185.65

=> 29.95x = 179.7

=> x = 6

∴ Jung purchased 6 video games.

Situation 5:

Milo is five inches shorter than his brother, Jayce. Milo is 42 inches tall

Let Jayce is 'x' inches and Milo is 'y' inches

=> y = x - 5

=> 42 = x - 5   [ From the data ]

=> x = 37 inches

Therefore,

The equation and solution for given situations are

Situation 1: 1.45x + 3.25 = 9.05; 4 pounds

Situation 2: 850 - 15a = 805; 3 days

Situation 3: 12.50 + 1.50r = 39.50; 18 times

Situation 4: 29.95x + 5.95 = 185.65; 6

Situation 5:  y = x - 5; 37 inches

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