If f(x) = x2-9/x+5, find f(0), f(-1), f(1/k)

Answer:

The last one

Step-by-step explanation:

First one is a parabola

Second one is an absolute value

Third one is a cubic

Fourth one is a linear

The given data does not belong to the function.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

A function is defined as a relation between a set of inputs having one output each.

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and codomain or range.

Since in the given data,

at the different values of y, the value of x is the same. that is the first violation of the rule of function.

Therefore, the given data does not belong to the function.

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Answer:

Step-by-step explanation:

Well when rotating 90° RSTU counterclockwise we get MNPQ.

When rotating 90° RSTU clockwise we get it the reflection across the y-axis.

Answer:

Step-by-step explanation:

[tex]I=Prt[/tex]  P=principal, r =interest rate, t=time

[tex]I=1,320[/tex] × [tex]\frac{3.2}{100}[/tex] × [tex]5[/tex]

 [tex]= 211.20[/tex]

He will earn $211.20 interest.

The graph of the two functions is different from each other.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function.

In the function as the value of the independent variable varies the value of the dependent variable also varies.

When we plot the graph of the function [tex]f(x) = \dfrac{x + 2 }{x^2-4}[/tex] and the function g(x) = |(x + 2 )} - 6.

Both graphs are different in nature and shape from each other. The graph of both functions is attached with the answer below.

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Check the picture below.

[tex](x+18)(18)=(24+16)(16)\implies 18x+324=640 \\\\\\ 18x=316\implies x=\cfrac{316}{18}\implies x=\cfrac{158}{9}\implies x=17\frac{5}{9}[/tex]

1.y=6  2. y=3  3. y=9/5   4.y=3/2  5. y=3   6. y= 3

The polynomial expressions when simplified are 2g² + 3g - 1, 24c⁵d - 8cd² + 12c³d³ + 4cd, (m² + 5m + 4) ÷ (m + 1) = m + 4.

Others are added below

Expression 1

The expression is given as

(14g³ + 21g² - 7g)/7g

Divide the numerator by the denominator

So, we have

2g² + 3g - 1

Expression 2

Here, we have

24c⁵d - 8cd² + 12c³d³ + 4cd

The expression is in its simplified state

Expression 3

Given that

(m² + 5m + 4) ÷ (m + 1)

By long division, we have

           m + 4

m + 1 | m² + 5m + 4

           m² + m

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

              4m + 4

              4m + 4

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

                0

This means that (m² + 5m + 4) ÷ (m + 1) = m + 4

Expression 4

Given that

(c² - 2c - 15)(c + 3)⁻¹

By long division, we have

           c - 5

c + 3 | c² - 2c - 15

          c² + 3c

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

              -5c - 15

              -5c - 15

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

                0

This means that (c² - 2c - 15)(c + 3)⁻¹ = c - 5

Expression 5

Here, we have

(2y² + 10y + 17) ÷ (y + 3)

By synthetic division, we have

-3 | 2  10  17

    |__-6_-12______

      2  4   5

This means that (2y² + 10y + 17) ÷ (y + 3) = 2y + 4 + 5/(y + 3)

Expression 6

Here, we have

(2p³ - p² - 10p + 8)(p - 2)⁻¹

By synthetic division, we have

2 | 2    -1   -10    8

    |___4__6__-8____

      2    3   -4     0

This means that (2p³ - p² - 10p + 8)(p - 2)⁻¹ = 2p² + 2p - 4

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The inverse function of the given is y^-1=x/2 -4.

The domain of the original function becomes the range of the inverse function, and the range of the given function becomes the domain of the inverse function. The inverse function is denoted by the notation f-1 in relation to the original function f. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function. Only when f is both a one-one and an onto function does it have an inverse, indicated by the symbol f-1. Keep in mind that f-1 is NOT f's inverse. The domain value of x is given by combining the function f and the reciprocal function f-1.

Here the given function is,

=> y = 2x+8

Now interchange x and y then

=> x=2y+8

Now simplify the expression with respect to y then,

=> x-8=2y

=> y =x/2 -4

=>y^-1=x/2 -4

Hence inverse function is, y^-1=x/2 -4

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Answer:

y = (3a + sqrt(11a^2 - 8b + 41)) / 2

y = (3a - sqrt(11a^2 - 8b + 41)) / 2

Step-by-step explanation:

To find the tangent lines that are perpendicular to the given line, we need to find the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal will be the slope of the tangent lines we are looking for.

The given line is 2x + y = 10, which can be rewritten as y = -2x + 10. Therefore, the slope of the given line is -2.

The center of the circle can be found by completing the square of the x and y terms. We have:

x^2 - 4x + y^2 = 1

(x - 2)^2 + y^2 = 5

Therefore, the center of the circle is (2,0), and the radius is sqrt(5).

Now, we can find the equation of the tangent lines. Let (a,b) be the point where the tangent line intersects the circle. Since the tangent line is perpendicular to the given line, its slope is the negative reciprocal of -2, which is 1/2. Therefore, the equation of the tangent line passing through (a,b) is:

y - b = (1/2)(x - a)

To find the points of intersection of this line and the circle, we substitute y = -2x + 10 into the equation of the tangent line and solve for x:

(x - a)^2 + (-2x + 10 - b)^2 = 5

Expanding and simplifying this equation, we get:

5x^2 - 4ax + 4a^2 + 4bx - 40b + 84 = 0

This is a quadratic equation in x, so we can solve for x using the quadratic formula:

x = [4a ± sqrt(16a^2 - 4(5)(4a^2 + 4b - 84))] / 10

Simplifying this expression, we get:

x = [2a ± sqrt(11a^2 - 8b + 41)] / 5

Now we can substitute these values of x into the equation of the tangent line to find the corresponding values of y:

y = -2x + 10

y = -a + b + (1/2)(2a ± sqrt(11a^2 - 8b + 41))

This gives us two equations for the tangent lines passing through (a,b), one for each value of x. We can simplify these equations to get:

y = (3a ± sqrt(11a^2 - 8b + 41)) / 2

Therefore, the equations of the tangent lines that are perpendicular to the given line are:

y = (3a + sqrt(11a^2 - 8b + 41)) / 2

y = (3a - sqrt(11a^2 - 8b + 41)) / 2

where (a,b) is any point on the circle (x - 2)^2 + y^2 = 5.

Answer: Yes

Step-by-step explanation:

Well, since 6+2, 6+2+3 does equal 8 plus 3 because 6+2+3 is basically saying 8+3, but just broken up.

The box volume, entrance volume and building volume are 50x², y³ and 50x² - y³ respectively

An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.

a) The volume of the whole box is:

Volume = length * width * height = x * x * 50 = 50x²

b) The volume of the entrance is:

Volume = length * width * height = y * y * y = y³

c) Volume of building is:

Building volume = volume of the whole box - volume of the entrance

Building volume = 50x² - y³

The building volume is 50x² - y³

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The percentage of annual returns is 25.63% and total return is $5400.

A percentage is a way of expressing a portion or part of a whole as a fraction of 100. The word "percent" comes from the Latin per centum, which means "per hundred". Percentages are commonly used to represent rates of change, such as growth rates or inflation rates, and to express proportions, such as the percentage of people in a population who have a certain characteristic or the percentage of a product's ingredients that are natural.

To calculate a percentage, you can use the following formula:

percentage = (part / whole) x 100

Now,

To calculate the total return on your investment, we need to find the profit made over the 4-year period.

Total return = final value of investment - initial investment

Total return = $8400 - $3000 = $5400

To calculate the annual return, we can use the formula:

Annual return = ((1 + total return percentage)^(1/number of years)) - 1

We can find the total return percentage by dividing the total return by the initial investment and multiplying by 100:

Total return percentage = (total return / initial investment) x 100

Total return percentage = ($5400 / $3000) x 100 = 180%

Using the formula for annual return, we get:

Annual return = ((1 + 1.8)¹/⁴-¹

Annual return = 0.2563 or 25.63%

Therefore, your total return on the investment was $5400 and the annual return averaged 25.63% over the 4-year period.

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Answer:

Step-by-step explanation:

Blue shirts: [tex]\frac{1}{6}[/tex]×[tex]12=2[/tex]

White shirts: [tex]\frac{2}{3}[/tex]×[tex]12=8[/tex]

∴ there are 2 students(12-2-8=2) wearing a different shirt.

Answer

La respuesta es 264.00

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

In Mathematics, a set is a group of unique elements. Here, the set M consists of three-digit numbers where the first digit is greater than the second by 4, and the third digit is greater than the first by 2. Examples of such numbers could be 530, 641, 752, etc.

The subject of the question is Mathematics, more specifically, the definition and properties of a set. In Mathematics, a set is a collection of distinct elements. A three-digit number has three digits: the first, second and third digit. In this case we need numbers where the first digit is greater than the second by 4, and the third digit is greater than the first by 2.

For example, let's take 501. Here, 5 is the first digit, 0 is the second and 1 is the third. The first digit is greater than the second by 5, not 4, therefore 501 does not belong to the set. But if we consider 640, here 6 is the first digit, 4 is the second and 0 is the third. The first digit is greater than the second by 2 and the third digit is less than the first by 6. So 640 belongs to the set. Therefore, our set M can include numbers like 530, 641, 752, and so on.

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The value of b from the given hyperbolic equation is 10. Therefore, option A is the correct answer.

In mathematics, a hyperbola is an important conic section formed by the intersection of the double cone by a plane surface, but not necessarily at the center. A hyperbola is symmetric along the conjugate axis, and shares many similarities with the ellipse. Concepts like foci, directrix, latus rectum, eccentricity, apply to a hyperbola.

Given that, the equation x²/24² -y²/b² =1 represents a hyperbola centered at the origin with a directrix of x=576/26.

Here, a=24

Then c²=a²+b²

c²= 24²+b²

c=√(576+b²)

We know that, directrix = x =± a²/c

Now, 576/26 = 576/√(576+b²)

√(576+b²)=26

576+b²=26²

576+b²=676

b²=100

b=10

Therefore, option A is the correct answer.

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Answer:

in photo I provided :)

Step-by-step explanation:

hope this helps <3

Answer:

∠x and ∠y are congruent or equal

Step-by-step explanation:

∠x and ∠y are congruent or equal because their vertical angles are alternate interior angles.

OR vertical angle of ∠x is congruent with ∠y because they are both corresponding angles

OR vertical angle of ∠y is congruent with ∠x because they are both corresponding angles

Answer:

x=2

Step-by-step explanation:

Answer: 2 over 3

Step-by-step explanation: The GCF of 90 and 135 is 45. So,

divide 90 by 45 = 2

divide 135 by 45 = 3

Answer: 2/3

-2x - 4 is not greater than 14

Step-by-step explanation:

I don't understand the question but I hope this helps

(-2 × X) + (-2 × 2)

Answer:

Moving the decimal 3 places to the left.

Step-by-step explanation:

Take the number 3000 and divide it by 1000 in your calculator.  You will get the answer 3.  Although we do not write it, the decimal in the number 3000 is at the end of the number (after the last zero).  When we divide by 1000, we move the decimal 3 places to the let.  The decimal in the number 3 is at the end or to the right of the 3, we just do not write the decimal.

Helping in the name of Jesus.

From the equation x²+ (y-5)² = 64, the coordinates of the center of the circle are (0, 5), and the radius of the circle is 8 units.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation of the circle is in the standard form -

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Comparing this standard form with the given equation, we get -

(x - 0)² + (y - 5)² = 8²

So the center of the circle is (0, 5) and the radius is 8.

Therefore, the center of the circle is (0, 5), and the radius is 8 units.

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Answer:

5175 7 ehsjdjdrusjskskekrirr

Answer:

5%

Step-by-step explanation:

So how I figured this out was I subtracted 570 and 541.50 to find how much of a difference there was. I got 28.50 so now I know thats how much the sale took off. I'm sure there was a better way of figuring out this next part but this is how I did it, I took 570 and multiplied it by 0.10 to see what that would be. It ended up being 57 and thats not 28.50 so I multiplied 570 by 0.05 and ended up with 28.50. You coulda also divided the 57 by two to figure out is 0.05 which equals 5%.

The total price of the 50-inch Panasonic Plasma TV is $687.44.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Given that, 50-65 inch TV's $150 rebate and delivery charge is $35.

50 inch Panasonic Plasma TV costs $734.95

Rebate is $150

So, cost of TV is 734.95-150

= 584.95

Cost of TV including delivery charge

= 584.95-35

= 549.95

Here, tax is 25%

So, cost of TV including tax

= 549.95+25% of 549.95

= 549.95+25/100 ×549.95

= 549.95+0.25×549.95

= 687.4375

Therefore, the total price of the 50-inch Panasonic Plasma TV is $687.44.

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In linear equation, Tammy will have made a profit of $103,768.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Let x be the number of years after Tammy purchased her home.

We have been given that Tammy’s home cost her $184,000. She lives in an area with a lively real estate market, and her home increases in value by 3.5% every year.

We can see that value of house will increase exponentially as the value of increases 3.5% per year.

Since an exponential function is in form

           y = a * bˣ

a = Initial value,

b = For growth b is in form (1+r) where r represents growth rate in decimal form.

Let us convert our given growth rate in decimal form.

   3.5% = 0.035

Upon substituting our values in exponential form of function we will get the value (y) of Tammy's home after x years as

  y = 184000(1 + 0.035)ˣ

 y =  184000(1.035)ˣ

  Therefore, the function   y =  184000(1.035)ˣ represents value of Tammy's home after x years of purchase.

Let us find the value of home after 13 years by substituting x=13 in our function.

     y =  184000(1.035)¹³

     y =  184000 * 1.56395606

  y = 287767.915

  Let us subtract cost of the home from the value of home after 13 years to find the amount of profit.

   The amount of profit, if tammy sells her home after 13 years = 287767.915  - 184000  

 The amount of profit, if tammy sells her home after 13 years = 103767.915 - 103,768

Therefore, Tammy will have made a profit of $103,768.

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Answer:

Step-by-step explanation:

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Answer:x=7,1

Step-by-step explanation: