The circle has a diameter of 16 inches. What is the area of the circle?

Answer:

Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.

Step-by-step explanation:

We are asked to describe the transformation of function [tex]y=\frac{3}{4x-12}[/tex] as compared to the graph of [tex]y=\frac{1}{x}[/tex].

We can write our transformed function as:

[tex]y=\frac{3}{4(x-3)}[/tex]

[tex]y=\frac{3}{4}*\frac{1}{(x-3)}[/tex]

Now let us compare our transformed function with parent function.

Let us see rules of transformation.  

[tex]f(x-a)\rightarrow\text{Graph shifted to the right by a units}[/tex],

[tex]f(x+a)\rightarrow\text{Graph shifted to the left by a units}[/tex],

Scaling of a function: [tex]a*f(x)[/tex]

If a>1 , so function is stretched vertically.

If 0<a<1 , so function is compressed vertically.

As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.

As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.

Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.

Final answer:

The equation y=3/4x-12 represents a linear function with a straight line graph, while y=1/x depicts a rectangular hyperbola with a curved graph showcasing an inverse relationship. These graphs exhibit fundamentally different behaviors, one being constant and the other varying.

Explanation:

The student's question involves comparing the graph of y=3/4x-12 to the graph of y=1/x. The first equation, y=3/4x-12, describes a linear function with a slope of 3/4 and a y-intercept of -12. This means it is a straight line that increases as x increases, crossing the y-axis at (0, -12).

On the other hand, the graph of y=1/x is a rectangular hyperbola. This curve approaches the x-axis and y-axis but never touches them, known as asymptotes. The hyperbola is divided into two parts, one in the first quadrant where both x and y are positive, and another in the third quadrant where both x and y are negative. This graph does not resemble a straight line at any part.

Comparatively, the key difference lies in the nature of their graphs - one is a straight line and the other a curved hyperbola, showcasing completely different behaviors. The linear equation reflects constant change, whereas the hyperbola’s rate of change varies with x, indicating an inverse relationship.

Answer: We want to evaluate g(x) in x = n -5, where g(x) = (x^2-6)/2x

then, doing it step by step: [tex]g( n- 5)= \frac{(n-5)^{2} - 6 }{2*(n-5)}= \frac{(n^{2} - 2*5*n + 25) - 6 }{2n - 10} = \frac{n^{2} - 10n + 19 }{2n - 10}[/tex]

where i used that (a - b)^2 = a^2 -2ab + b^2

So the correct option is C.

The Mean of the combined class is 70.19.

Mean is the average of a set of two or more numbers. The arithmetic and geometric mean are the types of mean that can be calculated.

[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}[/tex]

Given

The test scores of a class of 34 students have a mean of 73.1 and

The test scores of another class of 26 students have a mean of 66.4.

To find

The mean of the combined group.

The sum of the total of the test score = Total number of students x Mean

Class 1 sum will be

The sum of the total test score = 34 x 73.1

The sum of the total test score = 2485.4

Class 2 sum will be

The sum of the total test score = 26 x 66.4

The sum of the total test score = 1726.4

Than Mean for the combine will be

[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}\\\\Mean = \dfrac{2485.4+1726.4}{34+26} \\\\Mean = \dfrac{4211.8}{60} \\\\Mean = 70.19[/tex]

Thus the Mean of the combined class is 70.19.

More about the Mean link is given below.

https://brainly.com/question/521501

Another way to write the given rule is (x, y) → (x – 3, y + 5).

Given that,

Based on the information, we can conclude that another way to write the given rule is (x, y) → (x – 3, y + 5).

Hence, the other options are incorrect.

Learn more: brainly.com/question/22264506

Answer:  The square of the orbital period, T, of a  planet is equal to the cube of the average distance, A, of the planet from the Sun.

Step-by-step explanation:

In mathematics, A number or variable 'a' to its second power is said to be square of 'a' i.e. [tex]\ a^2[/tex] is the square of a.

A number or variable 'b' to its third power is said to be cube of 'b' i.e. [tex]\ b^3[/tex] is the cube of b.

In the given equation: [tex]T^2 = A^3[/tex]

Here,  [tex]T^2 [/tex] is square of T.

And  [tex]A^3[/tex] is cube of A.

Therefore, The square of the orbital period, T, of a  planet is equal to the cube of the average distance, A, of the planet from the Sun.

Answer: the first option, d.

Step-by-step explanation:

Let ΔABC be isosceles triangle with legs AB=BC=5 in. Draw an arbitrary point D on the base AC and spend two lines DE and DF such that DE || BC and DF || AB.

You get the parallelogram BFDE.

1. Consider ΔAED. This triangle is isosceles, because ∠ADE≅∠ACB as corresponding angles at parallel lines. The legs of this triangle are AE=ED.

2. Consider ΔDFC. This triangle is isosceles, because ∠FDC≅∠BAC as corresponding angles at parallel lines. The legs of this triangle are DF=FC.

3. Find the perimeter of parallelogram BFDE.

[tex]P_{BFDE}=BF+FD+ED+BE.[/tex]

Since AE=ED and DF=FC, you have that

[tex]P_{BFDE}=BF+FC+AE+BE=AB+BC=5+5=10\ in.[/tex]

Answer: 10 in.

The original loan amount for which the final amount payable is $130.50 over nine years at an interest rate of 10% was approximately $55.39.

To find out the original amount of the loan for which the final amount payable is $130.50 over nine years at an interest rate of 10%, we will use the formula for the present value of a loan.

The formula given is P = A / (1 + r/n)^nt, where P is the principal (initial loan amount), A is the final amount, r is the annual interest rate (expressed as a decimal), n is the number of times that interest is compounded per year, and t is the time the money is borrowed for in years.

As the question doesn't specify how many times the interest is compounded per year, we will assume it is compounded once a year (n=1).

We have:

Plugging these values into the formula:

P = $130.50 / (1 + 0.10/1)^(1*9)

P = $130.50 / (1 + 0.10)^9

P = $130.50 / (1.10)^9

P = $130.50 / 2.35794769

P = $55.39 approximately

Therefore, the original loan amount was approximately $55.39.

Step 1: Let us assign variable for the unknown that we need to find.

' x ' be the actual distance between Los Angeles and San Francisco

Step 2: Set up an equation based on the given statement "The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm."

[tex] \frac{distance \; in \; cm}{distance\; in\; miles}=\frac{1}{35}=\frac{10.8}{x} \\ \\ Cross \; Multiply\\ \\ 1 \cdot x = 35 \cdot 10.8\\ \\ x = 378 [/tex]

Conclusion:

The actual distance between Los Angeles and San Francisco is 378 miles.

Answer:

  x = 5 or x = -1

Step-by-step explanation:

x^2 – 4x = 5

Solve it by completing the square method

In completing the square method, we take the coefficient of x that is -4, divide it by 2 and then square it

-4/2 = -2  

square it (-2)^2 = 4

Now add 4 on both sides

x^2 – 4x +4 = 5+4

x^2 – 4x +4 = 9

Now factor the left hand side

(x-2)(x-2)=9

(x-2)^2 = 9

Take square root on both sides

x-2 = +-3

x-2 = 3 , so x= 5

x-2 = -3, so x= -1

The Geometric mean of the pair of number 6 and 10 is [tex]7.74[/tex]

The geometric mean of two number m and n is given as,

                       [tex]G.M=\sqrt{m*n}[/tex]

Geometric mean of the pair of number 6 and 10 is,

                    [tex]G.M=\sqrt{6*10} =\sqrt{60} \\\\G.M=7.74[/tex]

Learn more about the Geometric mean here:

https://brainly.com/question/47038

As per linear equation, in 2010 the expected firearm death U.S. had is 3270.

A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.

Australia’s population was 22.3 million people in 2010.

Australia had 236 firearm deaths in 2010.

Therefore, portion of Australian population had firearm deaths is

[tex]= \frac{236}{22.3(10)^{6} } \\= 0.000011[/tex]

The U.S. population was 309 million in 2010.

Therefore, the expected firearm deaths in U.S. in 2010 was

[tex]= (309) (10^{6}) (0.000011)\\= 3270.13\\= 3270[/tex]

Learn more about linear equation here: https://brainly.com/question/5280825

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We need to group the like terms and combine like terms to get the simplified equation.

[tex] 4x+x-3-9+4x=6\\ \\ Step \; 1: \; Group \; like\; terms\\ \\ 4x+x+4x-3-9=6\\ \\ Step \; 2: \; Combine \; like\; terms\\ \\ 9x-12=6 [/tex]

Conclusion:

Option C is the right answer !!