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The 4th vertex of the rectangle is given by D ( 4 , -1 ) and the graph is plotted

The product of the rectangle's length and its breadth determines the area of the rectangle.

Rectangle area equals length times width

Given data ,

Let the area of the rectangle be represented as S

Let the rectangle be represented as ABCD

The coordinates of A = A ( -1 , -1 )

The coordinates of B + B ( -1 , 1 )

The coordinates of C = C ( 4 , 1 )

So , the length of the rectangle = 4 units

The width of the rectangle = 2 units

So , the area of the rectangle S = 4 x 2 = 8 units

And , the 4th vertex of rectangle D = D ( 4 , -1 )

Hence , the coordinate D of rectangle is D ( 4, -1 )

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The only price at which consumer and producer plans are in agreement is the equilibrium price, which is reached when the quantities of a good that consumers want to buy and a good that producers want to sell are equal.

The equilibrium price, which is obtained when the quantity of a good that consumers want to buy (quantity requested) and the quantity of a good that producers want to sell (quantity provided) are equal, is the only price at which consumer and producer plans are in sync. This common quantity is referred to as the "equilibrium quantity".

If supply and demand are balanced in an economy, the equilibrium price will be reached. Thus, the manufacturer can create the same quantity of a good (supply) that consumers can purchase at this price (demand). As a result, supply and demand are met. Additionally, at this time, both buyers and sellers win. In addition, the equilibrium price contrasts with the idea of disequilibrium, in which supply and demand are not equal.

Supply and demand for a good are in equilibrium when the quantity is the same. In order to create economic equilibrium and equilibrium quantity, the supply and demand curves finally cross. This is hypothetically the most effective state the market can achieve and the state to which it naturally tends.

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0.156 is the  unit rate games per loss.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Plug in the values from the table to the above formula.

Slope is nothing but rate of change.

m=17-12/68-36

m=5/32

m=0.156

Hence, 0.156 is the unit rate games per loss.

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The acceleration needs to for a 5kg hammer to create a force of 10N is 2 m / s².

Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.

Given that the weight is 5 kg and the force applied is 10N. The acceleration will be calculated as below,

Force =  Mass x Acceleration

Acceleration = Force / Mass

Acceleration = 10 / 5

Acceleration = 2 m/ s²

Therefore, the acceleration will be 2 m/ s².

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Answer:

5×5=25-10=15&$%#%$%%^/<=^$^$

the equation of the line tangent to the curve y at x = 3 is y = 36x - 102.  The slope of the tangent line to the curve y at x = 3 is 36.

The equation of the line tangent to the curve y at x = 3 can be written using the point-slope form of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and m and (x1, y1) are known. In this case, m = 36 and (x1, y1) = (3, y). Substituting these values into the equation above, we get:

y - y = 36(x - 3)

y = 36x - 102

So the equation of the line tangent to the curve y at x = 3 is

y = 36x - 102.

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Answer:

See below

Step-by-step explanation:

The value of x, y, and z for the train and number of passengers are 0, -32, and 32 respectively.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The total number of trains are 20. This is represented as:

x + y + z = 0  

The accommodation of passengers is represented as:

2x + 3y + 5z = 64......(2)

During market day the train used is:

3x + 2y + 4z = 64.......(3)

Multiply the equation 2 with 3 and equation 3 with 2:

6x + 9y + 15z = 192

6x + 4y + 8z = 128

Subtract the two equations:

5y + 7z = 64..........(4)

Multiply the first equation by 2:

2x + 2y + 2z = 0

2x + 3y + 5z = 64.

Subtract the two equations:

-y - 3z = -64

y + 3z = 64..........(5)

Multiply the equation 5 by 5.

5y + 15z = 320

5y + 7z = 64

Subtract the two equations:

8z = 256

z = 32

Substitute the value of z in equation 5:

y + 3z = 64.

y + 3(32) = 64

y + 96 = 64

y = - 32

Using equation 1:

x + y + z = 0

x - 32 + 32 = 0

x = 0

Hence, the value of x, y, and z are 0, -32, and 32 respectively.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{w - 0.2 = 0.8}\\\\\large\text{ADD 0.2 to both sides:}\\\\\mathsf{w - 0.2 + 0.2 = 0.8 + 0.2}\\\\\large\text{SIMPLIFY it:}\\\\\mathsf{w = 0.8 + 0.2}\\\\\mathsf{w = 1}\\\\\\\\\huge\text{Therefore, your answer should be:}\\\\\huge\boxed{\mathsf{w = 1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex] \sf \: W = 1 [/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of W.

The equation is,

→ W - 0.2 = 0.8

Then the value of W will be,

→ W - 0.2 = 0.8

→ W = 0.8 + 0.2

→ [ W = 1 ]

Hence, the value of W is 1.

Answer:

  (B) The price is 150% of the price before

  (E) The price is now 1.5 of what it was before

Step-by-step explanation:

You want to identify statements equivalent to "price increased by 1/2 of what it was before".

For some initial price of p, the new price is ...

  p + 1/2p . . . . price increased by 1/2 of what it was before

This can be simplified to ...

  p(1 +1/2) = p(1.50) . . . . price is now 1.5 of what it was

Expressed as a percentage, the multiplier is ...

  p(1.50 × 100%) = p(150%) . . . . price is 150% of the price before

The correct choices are ...

  (B) The price is 150% of the price before

  (E) The price is now 1.5 of what it was before

<95141404393>

ax+b-(cx+d)=

ax+b-cx+d=

x(a-c)+b-d

Part (a)

Reason:

The car loses 15% of its value in one year. It keeps the remaining 85% (since 100-15 = 85).

The 85% then converts to the decimal form 0.85

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

Part (b)

Reason:

The exponential equation shown in bold above is of the form

y = a*b^x

where,

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

Part (c)

Work Shown:

y = 25000*(0.85)^x

y = 25000*(0.85)^10

y = 25000*0.19687440434072

y = 4921.86010851808

y = 4921.86

The linear relation of the given Rate of Change and Initial Value is y = 2/3x + 10

Suppose that we have to measure the rate of change of y as x changes, then we have:

[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]

Note that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

We are given the parameters as;

Constant Rate of Change: 2/3

Initial Value:10

Since we know that linear relation between x and y is y = m x + b, where

m is the rate of change

b is the initial value

Therefore,

y = 2/3x + 10

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The percentage of the second is greater than the first and the first number is less than the second will be 10% and 9.09%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolised by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Each pair of numbers determines by what percentage the second is greater than the first. Then we have

P = [(110 - 100) / 100] x 100

P = (10/100) x 100

P = 0.10 x 100

P = 10%

The percentage of the first number is less than the second is given as,

P = [(110 - 100) / 110] x 100

P = (10 / 110) x 100

P = 0.0909 x 100

P = 9.09%

The percentage of the second is greater than the first and the first number is less than the second will be 10% and 9.09%.

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Answer:

see explanation

Step-by-step explanation:

the equation for direct variation is

y = kx ← k is the constant of variation

divide both sides by x , then

k = [tex]\frac{y}{x}[/tex]

calculate k for each ordered pair from the table

k = [tex]\frac{2}{-4}[/tex] = - [tex]\frac{1}{2}[/tex]

k = [tex]\frac{1}{-2}[/tex] = - [tex]\frac{1}{2}[/tex]

k = [tex]\frac{-4}{8}[/tex] = - [tex]\frac{1}{2}[/tex]

since k is constant for all ordered pairs

then the table shows a direct variation with equation

y = - [tex]\frac{1}{2}[/tex] x

---------------------------------------------------------------------------------

similarly for the second table

k = [tex]\frac{5}{2}[/tex]

k = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]

k = [tex]\frac{21}{6}[/tex] = [tex]\frac{7}{2}[/tex]

since k is not constant for all ordered pairs then NOT direct variation

Answer:

The probability of selecting a peach is 8/14, or approximately 0.57.

The probability of not selecting a peach is 6/14, or approximately 0.43.

The total of these two probabilities is 1, because any given selection must either be a peach or not a peach.

The probability of selecting a plum cannot be determined because the number of plums in the bowl is not specified.

The sum of the probabilities of selecting a peach and a plum cannot be determined for the same reason as in 4.

Step-by-step explanation:

Answer:

To calculate the percentage change when a price of £40 is increased to £70, we can use the following formula:

Percentage Change = (New Value - Old Value) / Old Value * 100

Plugging in the numbers:

Percentage Change = (£70 - £40) / £40 * 100 = £30 / £40 * 100 = 75%

So the price has increased by 75%.

The mall should not prohibit loud and annoying rock music in the food court.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given that surveyed 850 teenagers to find out their favorite type of music she found that 32% of teenagers to Vader like hard rock

The survryed was on 850 teenagers

Therefore, Number of teenage that evade light hard rock = 32% of 850

=32/100 x850

=272

Hence, we can conclude that the mall should not prohibit loud and annoying rock music in the food court.

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The rate of interest that Gordon paid using the ordinary interest method is 9.63%.

The ordinary interest method is based on 360 days instead of 365 days.

The rate of interest based on the ordinary interest method uses the same formula as the rate of interest based on the 365 days calendar method.

Principal amount of loan = $600

Interest for 90 days = $14.25

Rate of interest = R

R = (Interest x 100)/(Principal x Time)

= $14.25 x 100 x 360/($600 x 90

= $513,000/$54,000

= 9.5%

Thus, the rate of interest paid by Gordon for borrowing $600 from the bank and paying $14.25 for 90 days is 9.5%.

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The initial value problem (2x - y) + (2y - x)y' = 0, y(1) = 3 has the particular solution y = -x²/2 + 2x + 1/2, and is valid for all x except for x = 2y.

An initial value problem is a differential equation that is given with an initial condition, which is a specific value for the solution of the equation at a particular point.

Problem 9 and 10 involve solving the same initial value problem: (2x - y) + (2y - x)y' = 0, y(1) = 3. To solve this initial value problem, we must find the general solution to the differential equation and then use the initial condition to determine the particular solution.

First, we must find the general solution to the differential equation (2x - y) + (2y - x)y' = 0. We can rearrange the equation to get (2y - x)y' + (2x - y) = 0. This is a separable differential equation, so we can separate the variables and integrate both sides to get:

y' = -(2x - y)/(2y - x)

∫(y')dy = -∫(2x - y)/(2y - x)dx

y = -x²/2 + 2x + C

Where C is an arbitrary constant of integration. To find the particular solution, we can use the initial condition y(1) = 3. We can substitute this into the general solution to find the value of C:

3 = -1/2 + 2 + C

C = 3 + 1/2 - 2 = 1/2

So the particular solution is y = -x²/2 + 2x + 1/2. This solution is valid for all values of x such that 2y - x ≠ 0, which means that the solution cannot be evaluated for x = 2y. This is because the denominator in the differential equation would be zero, which would make the equation undefined.

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Answer:  21.98

Step-by-step explanation:

The formula for circumference is r times 2 times pi

so, the circumference is

7x3.14=21.98

The missing values of y are 19, 29, 34,  and 49.

The values of y missing in the table is determined by substituting the value of x into the given linear equation.

y = 4 + 5x

when x = 3, the value of y is calculated as;

y = 4 + 5 (3) = 19

when x = 5, the value of y is calculated as;

y = 4 + 5 (5) = 29

when x = 6, the value of y is calculated as;

y = 4 + 5 (6) = 34

when x = 9, the value of y is calculated as;

y = 4 + 5 (9) = 49

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Answer:

Step-by-step explanation:

To solve the problem, we start by labeling 1/3 of 3/8 like this:

N1/D1 of N2/D2

Then we use this fraction of a fraction formula to solve the problem:

(N1 x N2) / (D1 x D2)

When we enter 1/3 of 3/8 into the formula, we get:

(1 x 3) / (3 x 8) = 3/24

Therefore, the answer to 1/3 of 3/8 in its lowest form is:

1/3 of 3/8 = 1/8

Answer:

Use -3 as a factor 4 times to find the value of (-3)^4. The answer is 81

Step-by-step explanation:

To solve (−3)^4, use -3 as a factor four times. This can be done by multiplying -3 by itself four times: (-3)(-3)(-3)(-3) = 81. Alternatively, you can use the square root property to find the value of (−3)^4. The square root property states that if a number is multiplied by itself two times, then the square root of that number is equal to one of the numbers used in the multiplication. In this case, the square root of 81 is -3, which is equal to one of the numbers used in the multiplication. Therefore, (−3)^4 = 81.

The different scenarios given in the question are categorized as legitimate variables or not as given below.

What is a variable?

A variable is a symbol used to denote a mathematical object in mathematics. Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable. A variable is a letter that stands in for an unknown; it always represents a number but can take on several meanings when used in an expression.

a) Numer of states that have a female governor has only one value and it cannot be varied. So it is not a legitimate variable(N).

b) The percentage of state's residents over 65 years of age is a legitimate variable (L) because the number will vary for different states.

c) The highest speed limit in the state is a legitimate variable(L) as the limits are different for different states.

d) Whether or not the state's name consists of one word is a legitimate variable(L) as it varies for different states.

Therefore the different scenarios are categorized as legitimate variables or not.

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The value of side DE is 9 units

From the question, we have the following parameters that can be used in our computation:

ABC~ ADEF.

So, we have the following equoialent ratio

J : K = DE : L

Substitute the known values in the above equation, so, we have the following representation

3 : 4 = DE :12

Express as fraction

So, we have

DE/12 = 3/4

Make DE the subject

DE = 12 * 3/4

Evaluate the expression

DE = 9

Hence, the value is 9

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When going from home to school, Fernando travel 10 meters.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Fernando lives in a house that is 8 meters below sea level.

Fernando goes to school every day, which is 2 meters above sea level.

The total distance from home to school,

= 8 + 2

= 10 meters.

Therefore, the distance is 10 meters.

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1. line parallel to given line is:  y = 5/3 x + 2

2.  

parallel line becomes: y = 1/2x - 6

perpendicular line becomes: y = - 2x + 14

Slope intercept form is a method of formulating an equation for a line in the form y = mx + b in mathematics. The b stands in for the line's y-intercept, while the m denotes the line's slope. In order to identify a point on a line or to solve for y given an input of x, the slope intercept form is utilised. A straight line's slope and the location of its y-axis intersection are utilized to get the general equation of the line using the slope intercept equation. y = mx + b is the formula for the slope intercept.

1.

3y - 5x = 15

or, 3y = 5x + 15

or, y = 5/3 x + 5

This is slope intercept form of line.

Thus, slope (m) = 5/3

Parallel lines have same slope. Thus, all lines having slope m = 5/3 will be parallel to each other.

Thus, example of line parallel to given line is:  y = 5/3 x + 2

2.

for parallel line:

Given that,

y = 1/2x - 4

The slope intercept form of line is: y = mx + b

goes through the point (8, -2)

now comparing these two equations we get:

y = 1/2x + b

or, -2 = 1/2 (8) + b

or, b = - 6

thus, parallel line becomes: y = 1/2x - 6

for perpendicular line:

y = 1/2x - 4

as we know, m₁ = - 1/m₂

so, slope becomes: - 2

Thus, y = mx + b

after putting the point (8, -2) we get the value of b:

-2 = -2 (8) + b

or, b = 14

Thus, perpendicular line becomes: y = - 2x + 14

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As the ratio of the lengths of the altitudes in related triangles, the altitude PS is 15 in length and represents the scale factor from XPZ to TPR.

The ratio of just an object's main sample to that of its new, smaller representation is described as the exponent (bigger or smaller). For example, to make a rectangle with sides proportional 2 cm and 4 cm longer, scale each side by a specific integer, therefore in case 2. If the original and new dimensions are determined, it is possible to calculate the scaling factor. The following straightforward formula can be used to find a figure's scale factor: Scale factor is equal to the new shape's size divided by the previous structure's diameter. Think about two quantities that are the same except for their size.

given

Find the scaling factor going from XPZ to TPR first.

TR/XZ = (6 + 6)/(8 + 8) =12/16 =3/4

You can write the following percentage because the scale factor is equal to the ratio of the lengths of the altitudes in related triangles.

PS/PY =3/4

Write the ratio.

PS/20 =3/4

For PY, substitute 20.

PS = 15/ 20 times per side, then simplify.

As the ratio of the lengths of the altitudes in related triangles, the altitude PS is 15 in length and represents the scale factor from XPZ to TPR.

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