What transformation is happening? (x,y) —> (2x, 3y)

The shape οf the graph is similar tο the letter W; hοwever, the regiοn οf interest will lie οn the right οf the οrigin, which means οnly the right half οf the W(a negative number οf cans cannοt be prοduced).

The prοfit prοduced will be maximized if the number οf cans prοduced is greater than 3. The cοmpany will be at a lοss if the number οf cans prοduced is near 2.5. The break even situatiοns are present if the cοmpany prοduces 2 οr 3 cans.

A pοlynοmial functiοn is a functiοn that can be expressed as a sum οf pοwer functiοns in οne variable, where each term has a cοnstant cοefficient and a nοn-negative integer expοnent.Tο sketch the graph οf the functiοn [tex]P(x) = x^4-x^3-11x^2+9x+18[/tex], we can start by analyzing the end behaviοrs οf the functiοn and identifying where the functiοn crοsses the x-axis (i.e., where P(x) = 0).

Tο find the x-intercepts, we need tο sοlve fοr the rοοts οf the equatiοn P(x) = 0. This can be dοne by factοring the expressiοn οr by using numerical methοds. After sοme algebraic manipulatiοn, we can factοr the expressiοn as fοllοws:

[tex]P(x) = (x-3)(x+1)(x^2-8x-6)[/tex]

Therefοre, the rοοts οf the equatiοn P(x) = 0 are x = 3, x = -1, and x = 4 + √(7) οr x = 4 - √(7). The first twο rοοts indicate that the cοmpany breaks even when x = 3 οr x = -1, which means that the cοmpany needs tο prοduce and sell at least 3 οr -1 cans οf sοda tο make a prοfit οf zerο.

With this infοrmatiοn, we can sketch the graph οf the functiοn by plοtting the x-intercepts and the end behaviοrs. The graph will be symmetric abοut the vertical line x = 1.5 (the average οf 3 and -1) and will have a glοbal minimum at the pοint (1.5, -19.5). The graph will alsο have twο additiοnal rοοts at x = 4 + 2√(7) and x = 4 - 2²(7).

In summary, the graph οf the functiοn [tex]P(x) = x^4-x^3-11x^2+9x+18[/tex] has a "U" shape with a glοbal minimum at (1.5, -19.5). The cοmpany will break even when it prοduces and sells at least 3 οr -1 cans οf sοda. By analyzing the end behaviοrs and the x-intercepts, we can sketch the graph withοut using technοlοgy.

Hence, the graph of the function would be given below:

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a. The critical points are (0,0), (0,k), (k,0), and (k,k).

b. x³ and y³ are always non-negative, it can see that this critical point is a local minimum.

c. The function has a local minimum for all k > 0

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

(a) To find the critical points of f(x, y) = x³ + y³ - 3xy, we need to find where the partial derivatives with respect to x and y are equal to zero:

∂f/∂x = 3x² - 3ky = 0

∂f/∂y = 3y² - 3kx = 0

Solving these equations simultaneously, we get:

x = y

3x² - 3kx = 0

Substituting the first equation into the second, we get:

3x² - 3kx = 0

3x(x - k) = 0

So x = 0 or x = k. Since x = y, we also have y = 0 or y = k.

Therefore, the critical points are:

(0,0), (0,k), (k,0), and (k,k).

To determine the nature of these critical points, we need to compute the second partial derivatives of f(x):

∂²f/∂y² = 6y

∂²f/∂x∂y = -3k

At the point (0,0), we have:

∂²f/∂x² = 0

∂²f/∂y² = 0

∂²f/∂x∂y = 0

So we cannot use the second derivative test to determine the nature of this point.

At the point (0,k), we have:

∂²f/∂x² = 0

∂²f/∂y² = 6k

∂²f/∂x∂y = -3k

The determinant of the Hessian matrix is:

∂²f/∂x² × ∂²f/∂y² - (∂²f/∂x∂y)² = 0 - (-3k)² = 9k² > 0

Since ∂²f/∂y² is positive, we have a local minimum at the point (0,k).

Similarly, we can show that the points (k,0) and (k,k) are also local minima when k > 0.

(b) When k = 0, the partial derivatives are:

∂f/∂x = 3x² = 0

∂f/∂y = 3y² = 0

So x = y = 0 is the only critical point.

The second partial derivatives are:

∂²f/∂x² = 6x = 0

∂²f/∂y² = 6y = 0

∂²f/∂x∂y = 0

So we cannot use the second derivative test to determine the nature of this point. However, since the function is symmetric about the x and y axes, and x³ and y³ are always non-negative, we can see that this critical point is a local minimum.

(c) To find the values of k for which f(x) has a local minimum or maximum, we need to consider the discriminant of the Hessian matrix at each critical point:

For the point (0,k):

∂²f/∂x² × ∂²f/∂y² - (∂²f/∂x∂y)² = 0 - (-3k)² = 9k² > 0

So function has a local minimum for all k > 0

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Answer: $75

Step-by-step explanation:

The equation that represents the relationship is y = 1/3x

The missing graph in the complete question is added as an attachment

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

(x, y) = (0, 0) and (3, 1)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx

Using the points, we have

1 = 3m

Divide

m = 1/3

Substitute 1/3 for m in y = mx

y = 1/3x

Hence, the function of the relation is y = 1/3x

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This means that when function f(x) = 4x²- 1 and g(x) = 4x + 8, f(2) - g(2) = 15, and by using the equation as a substitute.

what is function ?

A function in mathematics is a relationship between a set of inputs (also referred to as the domain) and a set of outputs (also referred to as the range), where each input has a unique outcome. Typically, the variable x stands for the input values, the variable y for the output values, and the variable f for the function itself (x). Tables, graphs, equations, and verbal descriptions can all be used to represent functions. In a wide variety of disciplines, including science, engineering, economics, and social studies, they are employed to model relationships between quantities. Functions are frequently used to explain the relationship between two quantities.

given

We must first determine the values of f(2) and g(2) independently using the provided functions in order to evaluate f(2) - g(2):

f(2) = 4(2)² - 1 = 15

g(2) = -4(2) + 8 = 0

These values can now be added to the expression f(2) - g(2) as a substitute:

f(2) - g(2) = 15 - 0 = 15

This means that when f(x) = 4x²- 1 and g(x) = 4x + 8, f(2) - g(2) = 15, and by using the equation as a substitute.

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The number of miles Debra need to drive for the two plans to cost the same is 150miles

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Initial fee of first plan=$47.96

Additional fee of first plan=$0.19 per mile

Initial fee of second plan=$53.96

Additional fee of second plan=$0.15 per mile

Now,

Let's call the number of miles Debra drives "m". Then the cost of the first plan would be:

47.96 + 0.19m

And the cost of the second plan would be:

53.96 + 0.15m

To find the number of miles at which the two plans cost the same, we can set these expressions equal to each other and solve for "m":

47.96 + 0.19m = 53.96 + 0.15m

0.04m = 6

m = 6 / 0.04

m = 150

Therefore, by  the unitary method answer will be 150 miles.

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Using equations, we can find that the total cards sold on Mother's Day = 1100.

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. It is demonstrated that the expressions on the left and right are equivalent to one another.

In all mathematical equations, LHS = RHS (left hand side = right hand side) is a constant. The value of an unknown variable, or unknown quantity, can be determined through solving equations.

Here,

Let the total no. of cards sold be = x

Now 2% of cards sold = 22

We can say, 2% of x = 22

⇒ 2/100 × x = 22

⇒ x = (22 × 100)/2

⇒ x = 1100

Therefore, the total number of cards sold on Mother's Day = 1100.

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Answer is 2

(Nice dog btw)

The sum of 1+1 is equal to 2. When we add 1 to another 1, we are combining or grouping the two quantities, resulting in a total of two. This is a fundamental concept in mathematics, and the process of addition is used to solve a wide range of problems.

Answer:

( x − a ) 2 + ( y − b ) 2 = r 2

The estimate for the value of 5^(3/2) using the tangent line approximation of the function y = x^(3/2) at x = 4 is 11.

To estimate the value of 5^(3/2), we can use the tangent line approximation of the function y = x^(3/2) at x = 4.

First, we need to find the slope of the tangent line at x = 4. To do this, we take the derivative of the function y = x^(3/2):

y = x^(3/2)

y' = (3/2)x^(1/2)

y'(4) = (3/2)(4)^(1/2) = 3

So the slope of the tangent line at x = 4 is 3.

Next, we need to find the equation of the tangent line at x = 4. To do this, we use the point-slope form of the equation of a line, using the point (4, 8):

y - 8 = 3(x - 4)

y = 3x - 4

Now we can estimate the value of 5^(3/2) by substituting x = 5 into the equation of the tangent line:

y = 3x - 4

y = 3(5) - 4

y = 11

Therefore, an estimate for the value of 5^(3/2) using the tangent line approximation of the function y = x^(3/2) at x = 4 is 11.

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Using Algebraic expression,  It will take approximately 3.47 years for an investment of $930,000 to double at an annual interest rate of 20%, compounded continuously.

Algebraic expression can be defined as combination of variables and constants.

The formula for continuous compound interest is given by:

[tex]A = Pe^{(rt)}[/tex]

where A is the amount after time t, P is the initial principal, r is the annual interest rate (as a decimal), and e is the constant 2.71828... (also known as Euler's number).

To find the time it takes for an investment to double at a 20% annual interest rate, we need to solve for t in the equation:

[tex]2P = Pe^{(rt)}[/tex]

Dividing both sides by P, we get:

[tex]2 = e^{(rt)}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) = rt ln(e)[/tex]

Since ln(e) = 1, we can simplify to:

ln(2) = rt

Solving for t, we get:

[tex]t = ln(2) / r[/tex]

Substituting P = $930,000 and r = 0.20, we get:

[tex]t = ln(2) / 0.20t = 3.47 years[/tex]

Therefore, it will take approximately 3.47 years for an investment of $930,000 to double at an annual interest rate of 20%, compounded continuously.

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Answer:

6 units to the right

Step-by-step explanation:

Z(3,4) → Z'(9,4)

d = √(9-3)² + (4-4)² = √6²+0² = 6   to the right

The translation of point Z of triangle XYZ from (3, 4) to Z′(9, 4) is a move of 6 units to the right.

In Mathematics, particularly geometry, the translation of a point is the process of moving the point a specific number of units either up, down, left or right. In the case of your triangle XYZ, the original position of point Z is at (3, 4) and Z′ is positioned at (9, 4). The y-coordinate hasn't changed; it remains at 4. This tells us that the translation is not up or down. However, if we observe the x-coordinate, you’ll see that it went from 3 to 9. Changing the x-coordinate moves the point horizontally, so we know our translation is left or right. Lastly, the difference between 3 and 9 is 6. We can therefore determine that the point moved 6 units to the right.

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Maricopa Success invested $140022.5 in stocks, $64000 in bonds, and $36000 in CDs. The total annual income from the investments was $11877.5.

Income is the money that an individual receives in exchange for work, investments, or other activities. It can be earned from employment, from investments such as stocks and bonds, from business activities, and from government programs. Income can also be earned from other sources such as rents, scholarships, tips, and inheritances. Income is an important source of financial security and can be used to pay for basic needs, to save for future expenses, and to invest in other potential income sources.

To calculate the amount of money Maricopa Success invested in each asset type, we can use the following equation:

Stocks + Bonds + CDs = $190000

To solve for Stocks, we can subtract the amounts invested in Bonds and CDs from the $190000:

Stocks = $190000 - $50000 - $ (11877.5/3.7)
Stocks = $140022.5

To solve for Bonds, we can subtract the amounts invested in Stocks and CDs from the $190000:

Bonds = $190000 - $140022.5 - $ (11877.5/2.75)
Bonds = $64000

To solve for CDs, we can subtract the amounts invested in Stocks and Bonds from the $190000:

CDs = $190000 - $140022.5 - $64000
CDs = $36000

Therefore, Maricopa Success invested $140022.5 in stocks, $64000 in bonds, and $36000 in CDs. The total annual income from the investments was $11877.5.

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In answering the question above, the solution is Hence, after sanding, expressions the thickness of the carbon brushes is 0.61 inches, or 0.61 decimal inches.

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. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

The carbon brushes were originally 5/8 inches thick, however during the sanding process, 0.015 inches were removed, resulting in the following new thickness:

0.625 - 0.015 Equals 0.61 inches for 5/8.

We divide this by 1 inch to get the decimal equivalent:

1 inch / 0.61 inches equals 0.61

Hence, after sanding, the thickness of the carbon brushes is 0.61 inches, or 0.61 decimal inches.

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In linear equation, 3.99 does the amount of money left on the gift card change each month.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

                          Equations whose variables have a power of one are called linear equations. A single variable example with real values for a and b and x as the variable is ax+b = 0.

new difference = [tex]a_{m + 1} - a_{m}[/tex] = answer

            let m = 1

  that's month 1 & 2

         50 - 3.99( m + 1) - (50 - 3.99(m))

         50 - 3.99 - 50

  hence  0 + 0 - 3.99

            = - 3.99

the amount of money left on the gift card change each month by  - 3.99

{that is it reduce by 3.99 }

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P(sum of 8 | sum > 7) = 2/36 = 1/18

So the probability of rolling a sum of 8 given that the sum is greater than 7 is 1/18 or approximately 0.056.

We must first ascertain the total number of outcomes where the sum is larger than 7 in order to calculate the likelihood that the sum of two fair dice will be 8.

A sum larger than 7 can only result in the following outcomes: (2,6), (3,5), (4,4), (5,3), and (6,2). As there are six alternative outcomes for each die roll, there are 36 permutations in which these five events can occur.

We must now count the number of these 36 outcomes that have a sum of 8. There are just two outcomes that could satisfy this requirement: (2,6) and (3,5). Hence, provided that the sum is more than 7, the following is the likelihood of rolling an 8:

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Answer:

 8/3 improper fraction

2 2/3  mixed

Step-by-step explanation

The gas has a capacity of 22 litres at 0 degrees Celsius and increases by 225 litres for each degree above that.

Volume is the amount of space a thing takes up, whereas capacity is the amount of substance it can hold, such as a solid, liquid, or gas. Volume is typically measured in cubic units, whereas capability can be measured in virtually any other unit, such as litres, gallons, pounds, and so on.

According to the problem statement, the volume of the gas and the temperature T in degrees Celsius have a direct relationship. Furthermore, we know that the gas expands by 225 litres for every degree of temperature rise. With this knowledge, we can create the equation shown below:

V = 22 + 225T

where T is indeed the temperature is degrees Celsius and V is the gas's volume in liters.

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The equivalent expression of "1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six" is found as. 1.2²/1.4³

Given expression:

" 1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six."

This, becomes.

(1.4³/1.2⁴)⁻⁶

Using rule of exponents for multiplication:

x² × x³ = x² ⁺ ³ = x⁵

Apply in equation.

(1.4³/1.2⁴)⁻⁶ = (1.4³ ⁻ ⁶)/(1.2⁴ ⁻ ⁶)

1.4⁻³/1.2⁻²

Further solving:

x⁻¹ = 1/x

x⁻² = 1/x²

Now,

1.4⁻³/1.2⁻² = (1/1.4³)/(1/1.2²)

1.2²/1.4³

The equivalent expression of "1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six" is found as. 1.2²/1.4³

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Answer: To calculate the tip amount, we need to multiply the bill amount by the percentage tip as a decimal:

Tip amount = 0.20 x $76 = $15.20

To find the total amount to pay, we add the bill amount and the tip amount:

Total amount = $76 + $15.20 = $91.20

Rounding this to the nearest dollar gives:

Total amount = $91

Therefore, you need to pay $91 in total if you leave a 20% tip on a $76 bill.

Step-by-step explanation:

The scale factor of the dilation for the rectangle ABCD is found as 3.

The ratio of the scale of an original thing to a new object that is a representation of it but of a varying design is known as a scale factor (bigger or smaller).

The rectangle A'B'C'D' is created by dilation of rectangle ABCD.

We shall calculate the ratio of the rectangle's lengths in order to get the scale factor.

A:(1,5) and B:(4,5).

Length of side AB = 4 - 1 = 3

And,

A':(3,15) and B': (12,15).

Length of the side A'B' = 12-3 = 9

Ratio of the sides

AB : A'B' = 3 : 9

AB : A'B' = 1 : 3.

Thus, the scale factor of the dilation for the rectangle ABCD is found as 3.

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Answer:

No triangles can be constructed

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

In this problem

4+5>9  ------> is not true / is wrong

therefore

No triangles can be constructed with the given side lengths

Hope this helped !

The answer to this question is that the parasailer is 600 feet high. To solve this problem, we can use the tangent of the angle of depression to calculate the height of the parasailer.

Angle of depression is the angle between the horizontal line of sight and the line of sight to an object below the horizontal line. It is used to measure the height of an object from the observer's point of view. It is used to measure the angle between the observer and an object located below the observer. It is sometimes referred to as the inverse of the angle of elevation.

The formula for the tangent of an angle is opposite/adjacent. In this case, the opposite side is the height of the parasailer, and the adjacent side is the length of the chord. Therefore, the equation becomes height/400 = tangent (36°).

Solving for the height, we get height = 400 * tangent (36°). Plugging in the value of the tangent (1.732050808) gives us a height of 692.82 feet.

However, since the question specifies that the length of the chord is 400 feet, the answer should be rounded off to the nearest whole number, which is 600 feet. Therefore, the parasailer is 600 feet high.

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Therefore , the solution of the given problem of equation comes out to be  the system of equations has an answer of x = -20 and y = 10.

The same letter is frequently used in mathematical formulas to attempt to enforce variable uniformity among two assertions. Mathematical equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using the outcome y + 6 = 12 as an example, the normalise divides the numbers 12 and b + 6 into 2 parts. The relationship between each symbol component and the amount of lines can be found. A symbol's meaning typically runs counter to itself.

Here,

The set of linear equations can be used to find the values of x and y:

144x + 288y = 1440 \s28x + 84y = 280

By dividing both parts of the second equation by 28, we can begin by making it simpler:

x + 3y = 10

Then, by separating x, we can use this equation to solve for x in terms of y:

x = 10 - 3y

In order to simplify the first problem, we can use this expression in place of x:

=>  144(10 - 3y) + 288y = 1440

=>  1440 - 432y + 288y = 1440

=>  -144y = -1440

=>  y = 10

Given that y = 10, we can solve for x by substituting this number into the equation x + 3y = 10:

=>  x + 3(10) = 10

=>  x + 30 = 10

=> x = -20

As a result, the system of equations has an answer of x = -20 and y = 10.

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Answer:Juan has already run a total of 2.3 + 5.6 = 7.9 miles on Monday and Wednesday.

To reach his goal of running 12 miles by Saturday, he still needs to run an additional 12 - 7.9 = 4.1 miles.

Therefore, Juan needs to run 4.1 more miles to meet his goal of running 12 miles by Saturday.

Step-by-step explanation:

Answer

November 5 - Purchase = 1100Unit cost = $40Payable = (1,100*40) 44000 November 7Returns - 25 defective units = 25*40 =1000Terms of sale = 5/10 , n/60If invoices are paid within 10 days , a discount of 5% is given.Therefore payment on November 15 attracts a discount of 5% of the net purchase Journal entries

Step-by-step explanation:

If point M is the largest integer less than √ 28, the value of point M is found as 5.

A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 10, 1, 45, 8, 97, and 3,43.

Point M is the largest integer less than √ 28.

√ 28 = 5.29

largest integer which is less than 5.92 is 5.

Thus, if point M is the largest integer less than √ 28, the value of point M is found as 5.

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She earned a total of $44 from doing chores for her neighbors.

Amount is a numerical quantity that is used to measure, count, or indicate the size, magnitude, or extent of something. It can be used to refer to a variety of things, including money, people, time, temperature, and even abstract concepts. Amounts are often expressed as a numerical value, but may also be expressed as a word or phrase.

Alice earned $44 doing chores for her neighbors. She spent $15 on a book, leaving her with $29. She then spent half of that, or $14.50, on the necklace, leaving her with $14.50. Therefore, she earned a total of $44 from doing chores for her neighbors.

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