Which type of transformation is described by (x, y)
->
+ (x + 3, y — 2)?

Answers

Answer 1

Answer:

(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.

Step-by-step explanation:

Given the rule of transformation:

(x, y) → (x+3, y-2)

If we move horizontally 3 units to the right, 3 is added to the x-coordinate of any given point, and then 2 units down.

In other words,

(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.

For example,

Let say if we have the point A(4, 5)

Using the translation rule:

(x, y) → (x+3, y-2)

A(4, 5) → A'(4 + 3, 5 - 2) → A'(7, 3)

Therefore, the new position of A(4, 5) after translating 3 units left and 2 units down would be: A'(7, 3)


Related Questions

Sam Bought a shirt for $27 after a discount, He said he bought the shirt at a 10% discount, What was the original selling price of the shirt?

Answers

Answer:$37.00

Step-by-step explanation: hope it helps

Find the length of side X in simple radical form with a rational denominator

Answers

The length of side X in simple radical form with a rational denominator is 25/√3.

What is a 30-60-90 triangle?

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Find the length of side X in simple radical form with a rational denominator

Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?

Answers

Answer

Step by step explantion:

bsf= 26

Eliana:98

SS teacher=203

David=55

Step-by-step explanation:

m= music

bsf: m

eliana:4m-6

David:2m+3

SS teacher: 2(4m-6)+7

m+4m-6+2m+3+8m-12+7

382=15m-7

7+ +7

389=15m

/15m /15m

m=26

multiply 26 to each one of them

Dividing by a Monomial
What is (9x^3-6x^2+15x) ÷ 3x^2?

Answers

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

A rectangle is 4 meters longer than it is wide. Find the dimensions of the rectangle if its area is 165 sq-meters.

Answers

Answer:

width = 11 and length = 15

Step-by-step explanation:

→ Find algebraic length and width

width = x ∴ length = x + 4

→ Find area

x ( x + 4 ) = x² + 4x

→ Equate to area

x² + 4x = 165

→ Solve

x = 11

→ Find length and width

width = 11 and length = 15

the cost of a new car is $32,000 it depreciates at a rate of 15% per year . this means that it loses 15% of each value each year

Answers

The mathematical function describing the cost of car the next year is →

C{n + 1} = C{n} (1 - 3/20).

What is depreciation rate?

The depreciation rate is a rate at which the price of a quantity decreases every year.

Given is that the cost of a new car is $32,000 it depreciates at a rate of 15% per year.

We can understand it as follows.

After one year the cost would be -

{x} = 32000 - {15% of 32000}

{x} = 32000 - 4800

{x} = $27200

After second year the cost would be -

{x} = 27200 - {15% of 27200}

{x} = 27200 - 4080

{x} = $23120

This means that after every year, the value decrease by 15% of what it was a year before. We can write -

C{n + 1} = C{n} - (15/100) C{n}

C{n + 1} = C{n} (1 - 3/20)

Therefore, the mathematical function describing the cost of car the next year is →

C{n + 1} = C{n} (1 - 3/20).

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A number cube numbered 1-6 is rolled 30 times and lands on an even number 18 times.
How does this frequency compare to the expected frequency based on the probability of
the number cube landing on an even number?
The frequency is 15 more than expected.
The frequency is 13 more than expected.
The frequency is 9 more than expected.
The frequency is 3 more than expected.
Done →

Answers

Given statement solution is :- The correct answer is: The frequency is 3 more than expected.

To determine the expected frequency of landing on an even number when rolling a fair six-sided number cube, we need to calculate the probability of landing on an even number and multiply it by the total number of rolls.

The number cube has six possible outcomes: 1, 2, 3, 4, 5, and 6. Of these, three are even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2 or 0.5.

The expected frequency can be found by multiplying the probability by the total number of rolls:

Expected frequency = Probability of landing on an even number × Total number of rolls

Expected frequency = 0.5 × 30 = 15

Now, we can compare the expected frequency (15) to the actual frequency (18) given in the problem statement.

The actual frequency is 18, and it is 3 more than the expected frequency (18 - 15 = 3).

Therefore, the correct answer is: The frequency is 3 more than expected.

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which propertied belong to all isosceles triangles? check all that apply

Answers

Answer:

Step-by-step explanation:

At least two sides have the same length.

At least two angles have the same measure.

The base angles (angles opposite the equal sides) have the same measure.

The altitude (perpendicular segment from the base to the vertex) bisects the base and the corresponding base angle.

The median (segment connecting the vertex to the midpoint of the base) is also an altitude, angle bisector, and perpendicular bisector of the base.

Based on these characteristics, the properties that belong to all isosceles triangles are:

At least two sides have the same length.

At least two angles have the same measure.

The base angles have the same measure.

Therefore, the correct options are:

At least two sides have the same length.

At least two angles have the same measure.

The base angles have the same measure.

Which graph represents the following piecewise defined function?

Which graph represents the following piecewise defined function?

Answers

The graph that represents the given piecewise function has a range of

R: (-∞, 0) ∪ (0,2] ∪ (4, ∞).

What is a piecewise function?

A piecewise function is a combination of subfunctions that are defined with different intervals in the domain.

The range of the piecewise function is the union of all the ranges of the subfunctions.

Calculation:

The given piecewise function is

g(x) = x², x < 0

      = 1/2 x, 0 < x ≤ 4

      = x, x > 4

The domain and range for the subfunctions in the given piecewise function are:

for g(x) = x²; Domain is {x < 0} and Range is (-∞, 0)

for g(x) = 1/2 x; Domain is {0 < x ≤ 4} and Range is (0, 2]

for g(x) = x; Domain is {x > 4} and Range is (4, ∞)

Then, the range of the given piecewise function is

Range: (-∞, 0) ∪ (0, 2] ∪ (4, ∞)

Thus, the graph shown in the question is the correct one.

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Which graph represents the following piecewise defined function?

Answer: c, its da 3rd graph

Step-by-step explanation:

Which graph represents the following piecewise defined function?
Which graph represents the following piecewise defined function?

OSTATISTICS
Choosing the best measure to describe data
Answer the questions below.
(a) The 10 members of the swim team completed the following numbers of laps at today's practice:
76, 77, 78, 79, 82, 83, 86, 87, 89, 91.
Which measure should be used to summarize the data?
Mean
O Median
O Mode
(b) Lucy has recorded the number of miles she has driven for each of the last 9 weeks:
126, 380, 383, 385, 386, 396, 398, 404, 419.
Which measure should be used to summarize the data?
Mean
Median
O Mode
(c) A reporter has recorded the rating (G, PG, PG-13, or R) of each movie played in a theater over the
past year.
Which measure gives the most common rating?
O Mean
Median
O Mode
S

OSTATISTICSChoosing the best measure to describe dataAnswer the questions below.(a) The 10 members of

Answers

Answer:

a) Mean

b) Median

c) Mode

Step-by-step explanation:

a) The data set has no outliers, therefore taking the average (mean) would be the best.

b) The data has outliers which would skew a mean. None of the numbers repeat, therefore mode would not work, so by process of elimination, one can find that Median is the best.

c) This data set does not have numbers, therefore mean does not make sense. The most common rating would be the rating that occurs most often, which would be mode.

Please? I really need this answer if you can

Please? I really need this answer if you can

Answers

From two to three there are 8 gaps and it is up to 7 so
Third answer 2 7/8

the sum of (n + 8) + (n − 12)

Answers

Answer:

n+8+n-12=

simplyfiy=2n+20

Step-by-step explanation:

Ya'll just have to simplify the expression and add the like terms together. hope I helped

The container that holds the water for the football team is 1/5 full. After pouring in 7 gallons of water, it is 7/10 full. How many gallons can the container hold?

Answers

14 gallons I believe
Let me know if this helped!

Aaron wants to draw the development of a cylinder. Which method of development should he use?

A.
parallel line
B.
approximate
C.
triangulation
D.
radial line
E.
non-curved to non-curved triangulation

Answers

Answer:

The correct option is A. Parallel line.

A gas stove that normally sells for $749 is on sale at a 30% discount. What is the sale price of the gas stove?
A
$224.70
B
$524.30
C
$719

Answers

Answer:

b. 524.30

Step-by-step explanation:

a good method to finding percentages of numbers is to multiply both numbers which here would be 749 and 30 together then divide by 100 edit: to finish the answer you need to subtract the product of the two numbers which is 224.7 by the price beforehand to receive the total amount of 524.30

Answer: $524.30 (choice B)

========================================================

Explanation:

If you save 30%, then you pay the remaining 70% which converts to the decimal form 0.70

70% of $749 = 0.70*749 = 524.30

----------

Or another way to look at it is to calculate how much you save

30% of 749 = 0.30*749 = 224.70

You save $224.70 and the final price is 749 - 224.70 = 524.30

. Suppose a government agency has a monopoly in the provision of internet connections.
The marginal cost of providing internet connections is 1
2
, whereas the inverse demand
function is given by: p = 1

Answers

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Can someone please help and thank you:)

Can someone please help and thank you:)

Answers

the answer is letter F :)

Answer:

F.

Step-by-step explanation:

x - dependent (-2)

y - independent (4)

A sack of rice wieghs 50 kilos. What is the weight of 85 sacks of rice?

Answers

Answer:

4250 kilos

Step-by-step explanation:

what are the coordinate of point A​

Answers

I need a picture to answer your question.

Select the statement that is true. Group of answer choices There are integers s and t such that 2=102⋅s+72⋅t . here are integers s and t such that 8=102⋅s+72⋅t . There are integers s and t such that 1=102⋅s+72⋅t . There are integers s and t such that 6=102⋅s+72⋅t .

Answers

Answer:

Step-by-step explanation: true

valuate the
expression
12 - 3y
2
+
√²v=4] for y = 3.
2y -

Answers

The result of the formula  \(12 - 3y2 + (v=4) / (2y - 2)\) for y = 3 is  \(-29/2\)  .

What are the ways to analyse an algebraic expression?

When \(y = 3\) is used, the value of the expression \(12 - 3y2 + (v=4) / (2y - 2)\)  has a value of  \(-29/2\) .

To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.

If  \(y = 3\) , we can insert it into the expression & simplify as follows to evaluate   \(12 - 3y2 + (v=4) / (2y - 2)\) for  \(y = 3\)  .

\(12 - 3(3)^2 + (√4) / (2(3) - 2)\) (y = 3 replacement)

\(12 - 27 + 2 / 4\s-15 + 1/2\s-29/2\)

Therefore, The result of the formula  \(12 - 3y2 + (v=4) / (2y - 2)\) for y = 3 is  \(-29/2\)  .

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Sorting algorithms no unread replies.no replies. we are using and interacting with sorting algorithms in every day life. in your chapter reading this week, you reviewed many sorting algorithms. find an example of a place in real, everyday life where you interact with, implement or use one of the sorting algorithms covered in chapter 3. for example, while playing cards you may have found yourself implementing the insertion sort algorithm (without knowing it). for this peer interaction, post your example of a place in real, everyday life where you interact with, implement or use one of the sorting algorithms. be sure to provide your us with enough information so that we will thoroughly understand your example and use of a sorting algorithm. once you have made your post, please respond to at least two of your classmates interacting and communicating on the sorting algorithm use in real world context.

Answers

A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.

A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.

1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."

2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.

3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).

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Sorting algorithms no unread replies.no replies. we are using and interacting with sorting algorithms

HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.

HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.

Answers

Answer:

C. x=2 ± √13

Explanation:

Please find the volume of the figure

Please find the volume of the figure

Answers

The volume of the pyramid is 576 cubic inches.

To find the volume of a square base pyramid, you can use the formula:

Volume = (1/3) x base area x height

In this case, the side of the square base is given as 12 inches, and the height is given as 12.5 inches.

First, calculate the base area of the pyramid:

Base area = side²

= 12²

= 144 square inches

Now, substitute the values into the volume formula:

Volume = (1/3) x 144 x 12.5

Volume = 576 cubic inches

Therefore, the volume of the pyramid is 576 cubic inches.

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In parallelogram WXYZ,diagonals Wy and XZ intersect at Point A.Give WA=x2-48 and AY= x2-6x.What is WY?Show your work

Answers

The diagonals of a parallelogram are congruent

The length WY is 32

How to determine the length WY

Given that:

\(WA = x^2 - 48\) and

\(AY = x^2 - 6x\)

Then, we have:

\(x^2 - 48 = x^2 - 6x\) -- the bisector of a diagonal

Subtract x^2 from both sides

\(- 48 =- 6x\)

Divide both sides by -6

\(x = 8\)

The length WY is calculated as:

\(WY=2 * WA\)

So, we have:

\(WY=2 * [x^2 - 48]\)

Substitute 8 for x

\(WY=2 * [8^2 - 48]\)

Simplify

\(WY=32\)

Hence, the length WY is 32

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Bao walked 15 miles in 6 hours. What was her walking rate in miles per hour?
Group of answer choices

2.5 miles per hour

2 miles per hour

1 mile per hour

1.5 miles per hour

Answers

The solution is,  2.5 miles per hour was her walking rate in miles per hour.

We know that,

Speed is measured as distance moved over time.

The formula for speed is speed = distance ÷ time.

To work out what the units are for speed, you need to know the units for distance and time.

In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

Here, given that,

Bao walked 15 miles in 6 hours.

so, we get,

in 6 hours = 15 miles

so, in 1 hour = 15 / 6 miles

                    =2.5 miles

Hence, The solution is,  2.5 miles per hour was her walking rate in miles per hour.

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A fishing shop charges $8 to rent fishing gear and $35 per hour to rent a boat Write a function to model the cost, y, to rent fishing gear and a boat for x hours.​

Answers

Answer:

y= 35x + 8

Step-by-step explanation:

the $35 is an hourly charge so it goes with x and the $8 is a one time charge so it just gets added on

The required function is y = 35x + 8 to model the cost, y, to rent fishing gear and a boat for x hours.​

What is the function?

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

We have been given that a fishing shop charges $8 to rent fishing gear and $35 per hour to rent a boat.

According to the given situation, we can write the function as:

⇒  y = 35x + 8

Here the $35 is an hourly rate, so it corresponds to x, and the $8 is a one-time charge, so it is simply put on.

Therefore, the required function is y = 35x + 8 to model the cost, y, to rent fishing gear and a boat for x hours.​

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The perimeter of a pool is 150 m. the rectangle at the right is a scale drawing of the pool. The length of each square on the grid represents 1 cm. draw another scale drawing of the pool using the scale 25 m to 2 cm. Explain why your drawing is accurate.

The perimeter of a pool is 150 m. the rectangle at the right is a scale drawing of the pool. The length

Answers

Answer:

Step-by-step explanation:

From the given rectangle,

Length of the rectangle = 5 cm

Width of the rectangle = 10 cm

Ratio of length : width = 1 : 2

Perimeter of the rectangle = 2(l + b)= 150 cm

l + b = 75 -----(1)

Since, l : b = 1 : 2

\(\frac{l}{b}= \frac{1}{2}\)

b = 2l ------(2)

From equations (1) and (2),

l + 2l = 75

3l = 75

l = 25 m

Width 'b' = 2(25) = 50 m

Now we have to draw a rectangle with a scale = 25 : 2

Therefore, Scale factor = \(\frac{25}{l}=\frac{25}{2}\)

l = 2 cm

Similarly,

\(\frac{50}{w}=\frac{25}{2}\)

w = 4 cm

Now we can draw a rectangle with length = 2 cm and width = 4 cm.

The perimeter of a pool is 150 m. the rectangle at the right is a scale drawing of the pool. The length

determine whether the statement describes a population or a sample. the number of times the students on your floor order fast food in a week.

Answers

The number of times the students on your floor order pizza in a week, population.

A population is a complete set of individuals or objects that share common characteristics. It is an entire group of people, animals, plants, or objects that can be studied. A population can also be a group of people living in a certain geographical area.

A sample is a subset of a population. It is a smaller group of individuals or objects drawn from the population that are used to make inferences about the population as a whole.

A sample is used in statistical analysis to estimate population characteristics, such as mean, median, and variance. The accuracy of the estimates depends on the size and representativeness of the sample.

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The complete question is:

Determine whether the statement describes a population or a sample. The number of times the students on your floor order pizza in a week, ___.

Please help. Thank you

Please help. Thank you

Answers

Answer:

0.008 or 8/1000

Step-by-step explanation:

1/5 = 0.2

0.2 x 0.2 x 0.2 = 0.08

0.08 = 8/1000

Answer:

0.008

Step-by-step explanation:

just divide it (1÷5) and cube the answer and calculate it

Other Questions
Does lemon juice rust metal? Toss a fair coin repeatedly. On each toss, you are paid 1 dollar when you get a tail and Odollar when you get a head. You must stop coin tossing once you have two consecutive heads.Let X be the total amount you get paid. Find E(X). What is the image of (0,8) after a reflection over the line y = 2? 11 3 =______ PLEASE HELP A bag contains 15 marbles. The probability of randomly selecting a green marble is 1/5. The probability of randomlyselecting a green marble, replacing it, and then randomly selecting a blue marble is 2/25. How many blue marbles are inthe bag?2356 A firm had beginning finished goods inventory of RM15,000, ending finished goods inventory of RM20,000 and cost of goods sold of RM80,000. What wasthe cost of goods manufactured? Suppose two countries produce the same two goods and have identical production possibilities frontiers. you would expect these countries:_____ Evaluate the following expression. 5^-1/5^0 Based on the Punnett square above, what is the probability that an offspring from this cross will have a completely heterozygous genotype for both traits ?A. 50%B. 25% C. 12.5%D. 6.25% The table comparesthe frequency of some unknown electromagnetic waves.Comparison of FrequencyElectromagnetic Wave Frequency (hertz)W1014 Hz1010 Hz1020 HzZ106 HzWhich electromagnetic wave has the longest wavelength?Wave WWave XWave YWave Z what is the order of steps in the synthesis of silver nanoparticles? Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Find CG. eory.According to cell theory, which of the following aremade of cells? Check all that apply.O flowersrocksbloodwaterbacteriasugarskinRETRY Determine whether each of the equations in Problems 1 through 8 is exact. If it is exact, find the solution. 1. (2x + 3) + (2y - 2)y' = 0 2. (2x + 4y) + (2x - 2y)y' = 0 3. (3x2 - 2xy + 2) + (6y2 - x2 + 3) y' = 0 dy ax + by 4. dx bx + cy dy ax - by 5. dx 6. (ye"y cos(2x) -2e* sin(2x)+2x)+(xey cos(2x) -3) y'=0 7. (y/x+6x) +(In x - 2)y' = 0, > 0 8. dy + 0 (x2 + y2)3/2 (x2 + y2)3/2 dx bx - cy x Why did businesses move their factories to the South after 1960?A. The cool weather was better for machinery.B. The South had a strong union presence.C. The land could be purchased for less.D. The region was known as the Rust Belt. What does the underlined word mean in the following sentence? Patrick n'aime pas sortir la poubelle.to shaveto put make-up onto take out the garbageto brush one's teeth (1) An american who perfectly matches the statistical average receives additional income amounting to $5,000. she spends $4,500 of it. what must be her marginal propensity to save? (2) Based on the information in part (a), calculate the tax multiplier in this economy. (3) Which component of aggregate demand will be most directly impacted by a change in the income tax rates? explain. (4) Assume the government increases the income tax revenues by $100 billion. based on the information in part (a), what will be the total possible change in aggregate demand, ceteris paribus? (5) Assume the government increases government spending by $200 billion. based on the information in part (a) What will be the total possible change in aggregate demand, ceteris paribus? (6) What is the autonomous spending in the scenario from part (e)? (7) Assuming all impacts were explained directly through the multipliers, and based on the information from part (b), what would be the change in gdp that would result from the government decreasing spending by $18 billion at the same time that it decreases corporate taxes by $20 billion? what should i do if my earbuds keep dying and not charge fully to where i get 2 minutes out of them why database systems support data manipulation using a declarative query language such as sql, instead of just providing a library of c or c functions to carry out data manipulation. Which phrase best completes the list?