Select all of the transformations that have occurred to the graph below as
compared to the parent function, f (x) = log x.

Using the equation, the center is (-2,5) and the radius is 12 units.

Use the formula (x-a) ² + (y-b) ² = r² to determine a circle's equation when you are aware of its radius and center.

Here, stands for the circle's center, and is its radius. This equation is essentially a variant way of writing the general equation for a circle.

The given question is:

(x - 2) ² + (y + 5) ² = 144.

Now this can be written as:

(x - 2) ² + (y + 5) ² = 12²

The circle of center (x₁, y₁) and radius r is written as:

(x - x₁) ² + (y - y₁) ² = r²

Hence, the center is (-2,5) and the radius is 12 units.

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The slope intercept form of the equation is y = [tex]\frac{1}{2}x+2[/tex].

What is slope intercept form of the equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here the given line coordinates are [tex](x_1,y_1) = (2,3)[/tex] and [tex](x_2,y_2)=(-4,0)[/tex].

Now using slope formula , slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> m = [tex]\frac{0-3}{-4-2}=\frac{-3}{-6}=\frac{1}{2}[/tex]

Now using equation formula then [tex]y-y_1=m(x-x_1)[/tex]

=> y-3= [tex]\frac{1}{2}[/tex] (x - 2)

=> 2y-6 = x-2

=> 2y = x-2+6

=> 2y = x+4

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

Hence the slope intercept form of the equation is y = [tex]\frac{1}{2}x+2[/tex].

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The complete table of trigonometric functions:

Row 1: θ = π / 3, sin θ = √3 / 2, cos θ = 1 / 2, tan θ = √3

Row 2: θ = 5π / 4, sin θ = - √2 / 2, cos θ = - √2 / 2, tan θ = - 1

Row 3: θ = 7π / 6, sin θ = - 1 / 2, cos θ = √3 / 2, tan θ = - √3 / 3

In this problem we must complete a table with three angles, measured in radians, and three kinds of trigonometric functions (two fundamental function and a derivate function). The procedure to complete the table is shown below:

Now we proceed to complete the table of trigonometric functions:

θ = π / 3, sin θ = √3 / 2, cos θ = 1 / 2, tan θ = √3

θ = 5π / 4, sin θ = - √2 / 2, cos θ = - √2 / 2, tan θ = - 1

θ = 7π / 6, sin θ = - 1 / 2, cos θ = √3 / 2, tan θ = - √3 / 3

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The author develops the connection between Mourne Textiles and the history and culture of Ireland by mentioning that local Irish weavers taught Gerd Hay-Edie how to weave and make the designs. Additionally, the author highlights the significance of the landscape and natural resources in Northern Ireland to the design and production of the textiles.

Hence, the correct answer is option B.

In the article, the author describes how Gerd Hay-Edie learned traditional weaving techniques from local weavers in Northern Ireland, and how she incorporated these techniques into her designs. The author also emphasizes the importance of the Mourne Mountains and the surrounding natural resources in shaping the textiles produced by the company.

Furthermore, the author highlights how the designs and techniques used by Mourne Textiles are rooted in Irish tradition and history. Through these details and examples, the author establishes a strong connection between Mourne Textiles and the history and culture of Ireland.

Hence, the correct answer is option B.

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--The question is incomplete, answering to the question below

"How does the author develop the connection between Mourne Textiles and the history and culture of Ireland?

A. by explaining major historical events in Ireland and how Gerd Hay-Edie took part in them

B. by mentioning that local Irish weavers taught Gerd Hay-Edie how to weave and make the designs

C. by describing Gerd Hay-Edie’s career and how events in Ireland impacted the company

D. by comparing the Norwegian fjords to the Irish landscape and Gerd Hay-Edie’s fashion sense to the typical Irish style" --

The baseball game lasted 2 hours and 10 minutes.

To calculate how long the baseball game lasted, we must begin by taking the start time of 7:05. We can convert this time to a numerical value by adding 7 hours and 5 minutes, which equals 705 minutes. Next, we must do the same with the end time of 9:15. Adding 9 hours and 15 minutes gives us a total of 915 minutes. Subtracting the start time from the end time gives us a difference of 210 minutes. Finally, we must convert the minutes back to hours and minutes, which gives us 2 hours and 10 minutes. Therefore, the baseball game lasted 2 hours and 10 minutes.

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Answer:

look in explanation

Step-by-step explanation:

In this equation, y can only be equal to 5 if x is labeled as 3.

Why? Because when you input the numbers into the equation, y=5 and x=3 then it will make sense.  5=3+2  If you put y as any other number the equation will not be true.

Answer:

18.5

Step-by-step explanation:

25-6.5=18.5

x=18.5

Answer:

6 hours - 5 = 2, so 15 = 6 , as its constant

The two random variables from this list that are continuous are: a) The average temperature in NYC during May. b) The compensation of a Top 500 CEO.

A continuous random variable is a variable whose values are any member of an uncountable set or any uncountable combination of such members. A continuous random variable has an infinite number of possible values, which are represented by an interval (a,b), where a and b can be any value on the real number line. A continuous random variable cannot take on individual values because there are an infinite number of values between any two points.For example, temperature, length, and weight are examples of continuous random variables.

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Answer:

The image of triangle ABC after the translation 5 units to the right and 5 units down is A'B'C' with vertices at (3, -1), (-2, -6), and (2, -8).

Step-by-step explanation:

To prove that triangle ABC is isosceles, we need to show that at least two of its sides have the same length. We can use the distance formula to calculate the length of each side:

AB = sqrt[(−7−(−2))^2 + (−1−4)^2] = sqrt[25 + 25] = 5sqrt(2)

AC = sqrt[(−3−(−2))^2 + (−3−4)^2] = sqrt[1 + 49] = sqrt(50)

BC = sqrt[(−7−(−3))^2 + (−1−(−3))^2] = sqrt[16 + 4] = 2sqrt(10)

Since AB and AC have different lengths, triangle ABC cannot be equilateral. However, if we compare AB and BC, we see that they have the same length, 5sqrt(2). Therefore, triangle ABC is isosceles.

To find the coordinates of A'B'C' after the translation 5 units to the right and 5 units down, we simply add 5 to the x-coordinates and subtract 5 from the y-coordinates of each vertex. Thus:

A' = (-2+5, 4-5) = (3, -1)

B' = (-7+5, -1-5) = (-2, -6)

C' = (-3+5, -3-5) = (2, -8)

Therefore, the image of triangle ABC after the translation 5 units to the right and 5 units down is A'B'C' with vertices at (3, -1), (-2, -6), and (2, -8).

Check the picture below.

Using the standard normal distribution table, we can find that the probability of a student typing more than 50 words per minute is 0.2033 or 20.33%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

It seems like you have given me information about the distribution of typing speed for Mes Fuller's 120 keyboarding students. The distribution is normally distributed with a mean (μ) of 45 words per minute and a standard deviation (σ) of 6 words per minute.

A normal distribution is a continuous probability distribution that is symmetric around the mean value. The mean value is the center of the distribution, and the standard deviation measures the amount of variability or spread of the data.

With this information, we can calculate probabilities for different values of typing speed using the standard normal distribution table or a statistical software program.

For example, if we want to know the probability of a student typing more than 50 words per minute, we can calculate the z-score as follows:

z = (x - μ) / σ = (50 - 45) / 6 = 0.83

therefore, the standard normal distribution table, we can find that the probability of a student typing more than 50 words per minute is 0.2033 or 20.33%.

Similarly, we can calculate probabilities for other values of typing speed using the same method.

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Answer:

Question #3 *I need help*

Step-by-step explanation:

Students need to be in the top 2% in order to be eligible for the national typing competition, if Carla can type 56 wpm, is she eligible?

Answer:

1.11111111

Step-by-step explanation:

Answer: 1/0.9

Step-by-step explanation:

Simply put 1 as the numerator of the given number to get the reciprocal.

Answer:

Step-by-step explanation:

(a)   [tex]5\frac{1}{8} =\frac{41}{8}[/tex]

      So we get

          [tex]5\frac{1}{8}\% =\frac{41}{8}\div100[/tex]

                   [tex]= \frac{41}{8} \times \frac{1}{100}[/tex]

                   [tex]=\frac{41}{800}[/tex]  

(b)    [tex]91.4=91\frac{4}{10} =91\frac{2}{5} =\frac{457}{5}[/tex]  

       So we get

               [tex]91.4\%=\frac{457}{5} \div100[/tex]

                          [tex]=\frac{457}{5} \times \frac{1}{100}[/tex]

                          [tex]=\frac{457}{500}[/tex]                

Answer:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

I think they are all correct except for the last one

I think the last one should be b

Answer:

Step-by-step explanation:

function

slope

x value

y value

Therefore , the solution of the given problem of triangle comes out to be  Cosine B = 9/41 is the solution (b).

A polygon is a hexagon if it has a minimum of one extra segment. It has a simple rectangular shape. Only the edges A and B can differentiate something like this from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a part of the cube. Three edges and three angles make up a triangle.

Here,

Using the cosine definition:

=> adjacent/hypotenuse = cos(B)

We are aware that AB is the hypotenuse, with a length of 41, and that the neighboring side, BC, has a length of 9. Therefore:

=> cos(B) = 9/41

=> Cosine B = 9/41 is the solution (b).

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The ordered pair that describes the location of V" is (5, -2).

In mathematics, reflection is a transformation in which a geometric figure is mirrored or flipped over a line, plane or point. It is a type of transformation that changes the position of an object without changing its shape or size. Reflection can occur in any number of dimensions, including two-dimensional space (plane), three-dimensional space (solid objects), or even higher dimensions.

The reflection of point V over the x-axis will change the sign of the y-coordinate, so point V' will be located at (-5, -2).

The reflection of point V' over the y-axis will change the sign of the x-coordinate, so point V" will be located at (5, -2).

Therefore, the ordered pair that describes the location of V" is (5, -2).

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The complete question is:

Point V is located at (-5,2) on the coordinate plane. Point V is reflected

over the x-axis to create point V'. Point V' is then reflected over the y-axis

to create point V". What ordered pair describes the location of V"?*

The functions from the graph are x = -10, y = x + 5 and y = x² + 6x + 10, while the identities are listed below

Constant function

This is a function that does not change its value irrespective of the input and/or the output

From the graph, we have the vertical line

x = -10

This is a constant function with the following identities

Domain: x = -10

Range: 0 ≤ y ≤ 12.25

Linear function

This is a function that changes constantly with x and y

From the graph, we have the points

(-4, 1) and (-2, 3)

The equation is calculated as

y = mx + c

So, we have

-4m + c = 1

-2m + c = 3

This gives

2m = 2

m = 1

So, we have

-2(1) + c = 3

-2 + c = 3

c = 5

This means that the function is y = x + 5 with the following identities

Domain: -4 ≤ x ≤ -2

Range: 1 ≤ y ≤ 3

Quadratic function

This function is represented as

y = a(x - h)² + k

Where

Vertex = (h, k)

From the graph, we have

(h, k) = (-3, 1) and (x, y) = (-2, 2)

So, we have

y = a(x + 3)² + 1

Also, we have

2 = a(-2 + 3)² + 1

a + 1 = 2

a = 1

So, we have

y = (x + 3)² + 1

y = x² + 6x + 10

This means that the function is y = x² + 6x + 10 with the following identities

Domain: -4 ≤ x ≤ -2

Range: 1 ≤ y ≤ 2

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Therefore, the probability that the student plays neither tennis nor netball is 1/5 = 0.2 or 20%.

There are 40 students in a class. 19 students play tennis, 20 students play netball, and 8 students play neither of these sports.

A student is chosen randomly from the class, and we need to determine the probability that the student: Plays tennis If a student is randomly chosen from the class, the probability that the student plays tennis is: Probability of playing tennis= (Number of students playing tennis) /

(Total number of students in the class) Probability of playing tennis= 19 / 40Plays netball if  a student is randomly chosen from the class, the probability that the student plays netball is: Probability of playing netball= (Number of students playing netball) / (Total number of students in the class)Probability of playing netball= 20 / 40 = 1/2Plays neither of these sports a student is randomly chosen from the class, the probability that the student plays neither tennis nor netball is

:Probability of playing neither tennis nor netball= (Number of students who do not play either of the two sports) / (Total number of students in the class)Probability of playing neither tennis nor netball= 8 / 40Probability that the student plays tennis and netball

Probability of playing tennis and netball = (Number of students playing both tennis and netball) / (Total number of students in the class)We are given that none of the students play both tennis and netball, so the probability of playing both tennis and netball is 0.

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The probability that the jury makes the correct decision that the defendant is guilty is 0.7063.

In order to resolve this issue, we must determine the likelihood that the jury would find the defendant guilty. Let's divide the issue into more manageable components.

We are aware that there is a 0.80 chance that a single juror would choose correctly. If the defendant is found guilty, there is still an 80 percent chance that the jury will reach the right verdict. Consequently, if the defendant is found guilty, there is an 80 percent chance that one jury will reach the right verdict.

The likelihood that at least 10 out of 12 jurors will choose the right course of action may be calculated using the binomial distribution formula. The equation is:

[tex]P(X \geq k) = 1 - \sum (i=0, k-1) [\frac{i!}{(i!(n-i)!)} ]p^i*(1-p)^(^n^-^i^)[/tex]

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Using a calculator or software, we can calculate this to be approximately 0.7063.

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Answer:

Step-by-step explanation:

t=0

If you replace t with zero -9=-9(0+1)

0+1=1 and -9(1)=-9

so t=0

Answer:

180°

Step-by-step explanation:

Given the quadratic equation the condition that must apply to the constants a and c is c < 9a.

A quadratic equation is a second-degree polynomial equation in one variable, where the highest power of the variable is two.

1) Remember, a quadratic function can have either a maximum or minimum value and that the value of the function at the vertex (i.e., the maximum or minimum point) is given by [tex]-b/2a[/tex].

In this case, the coefficient of x is 6, so the x-coordinate of the vertex is [tex]-6/2a = -3/a[/tex].

Since the function is always negative, the vertex must be a maximum, and the value of the function at the vertex must be negative.

Therefore, this gives us:

[tex]ax^2 + 6x + c < 0[/tex] for all x

The x-coordinate of the vertex is[tex]-3/a[/tex], so the value of the function at the vertex is:

[tex]a(-3/a)^2 + 6(-3/a) + c = 9a/a - 18/a + c = c - 9a/a[/tex]

Since the value of the function at the vertex must be negative, we thus have:

[tex]c - 9a/a < 0[/tex]

Simplifying further, we get:

[tex]c < 9a[/tex]

Therefore, we can conclude that the condition for the constants a and c to satisfy the given inequality is [tex]c < 9a.[/tex]

ii) We can choose [tex]a = 1[/tex] and [tex]c = -8[/tex].

Then, the function [tex]ax^2 + 6x + c = x^2 + 6x - 8[/tex] has a maximum value at [tex]x = -3[/tex],

Therefore, this example shows that [tex]a = 1[/tex] and [tex]c = -8[/tex]  satisfies the conditions found in part (i).

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The length L of the curve is approximately 185.35 units.

To find the length of the curve, we first need to find the derivative of the given function:

f'(y) = 1 - (25/32) y^(-2/3)

Next, we need to find the integrand by squaring the derivative and adding 1:

g(y) = √(1 + [1 - (25/32) y^(-2/3)]^2)

Then, we can use this integrand to set up the integral:

L = ∫[0,243] g(y) dy

L= 185.35 units

Using a calculator or software, we can evaluate this integral to find the length L of the curve, which is approximately 185.35 units. Hence the length of curve is  185.35 units

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Answer:

Step-by-step explanation:

1