Which of these triangle pairs can be mapped to each other using both a translation and a rotation about C?

Triangles X Y C and A B C are shown. Both triangles are congruent and share common point C. Triangle A B C is slightly lower than triangle X Y C.
Triangles X Y Z and A B C are shown. Both triangles are congruent. Triangle X Y Z is identical to triangle A B C but is slightly higher.
Triangles X Y Z and A B C are shown. Both triangles are congruent. Triangle X Y Z is reflected across a line to form triangle A B C.
Triangles X Y Z and A B C are shown. Both triangles are congruent. Triangle X Y Z is rotated down and to the left to form triangle A B C. It is also slightly higher than triangle A B C.

The rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

We know that,

The Base is growing at the rate of 1 cm per sec.

Height is growing at the rate of 2 cm per sec.

Area of triangle: 1/2 × b × h

The rate of change will be:

1/2 × b × h

1/2 × 4/1 × 7/2

28/4

7 cm per sec

Therefore, the rate of change of the area of the triangle is 7cm/sec when the base is 4cm and height is 7cm.

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When data are transformed to ranks and the Pearson correlation is performed, the Spearman correlation is what is obtained as a correlation.

Therefore, the correct answer is A)the Spearman correlation

The complete question is:

What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks?

a) the Spearman correlation

b) the point-biserial correlation

c) the phi coefficient

d) it is still called a Pearson correlation

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Benjamin Franklin was an American whose official education stopped in 1716 when he was 10 years old, whilst the others went to college.

Franklin's official education was shortened due to financial restrictions, despite the fact that he was a well-known polymath and one of the Founding Fathers of the United States. He dropped out of school when he was 10 and started working for his father's candle manufacturing company. Franklin, however, became a self-taught person who deeply studied a variety of disciplines and made great contributions to science, literature, and politics as a result of his intellectual curiosity and quest for information. Franklin's accomplishments are proof of the effectiveness of lifelong learning and self-education.

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Answer:

3 pieces

Step-by-step explanation:

Given: Figure

To find: Number of 8.5 in. ×  11 in. pieces used to cover the floors  of a room and a hallway in  her dollhouse

Solution:

In the given figure, AC = 22 in.

AB + BC = 22 in.

AB + EF = 22 (As BC = EF being opposite sides of rectangle)

AB + 10 = 22

AB = 22 - 10 = 12 in.

Area of rectangle ABGH = AB × AH = 12 × 5 = 60 square inches

(area of rectangle = length × breadth )

CE = CD + DE = AH + GF (As CD = AH and DE = GF)

CE = 5 + 15 = 20 inches

Area of rectangle BCEF = BC × CE = 10 × 20 = 200 square inches

(BC = EF = 10 in.)

Total area of the figure = Area of rectangle ABGH + Area of rectangle BCEF = 60 + 200 = 260 square inches

Area of pieces of felt = 8.5 × 11

So,

Number of pieces required = Total area of the figure / Area of pieces of felt  =   3 pieces

Answer:

Look at the image given below :)

Step-by-step explanation:

In order to figure out the missing values inside the box, we have to use the values given to us and work backwards.

First, we have to figure out what value multiplied by 1 would equal 1. This can also be written as:

1 * x = 1

Let's solve for 1:  

Divide both sides by 1 to isolate x:  x = 1

1 multiplied by 1 equals 1. Now we know the value on the left side of the bottom left box.

To find the value on the bottom side of the bottom left box, we have to figure out what value multiplied by 8x equals 16x^2. This can be written as:

8x * y = 16x^2

Divide both sides by 8x: y = 2x

8x multiplied by 2x equals 16x^2.

Now that we know all of the outside values, we can find the missing values on the inside of the boxes.

First, let's multiply the bottom left 1 by the bottom 2x to find the value inside the bottom left box.

2x * 1 = 2x

The value inside the bottom left box is 2x.

To find the value inside the top right box, multiply the bottom right 1 by the top left 8x: 8x * 1 = 8x

The value inside the top right box is 8x.

In the end, your box should end up looking like this:

Answer:

It is 2 miles per hour

Step-by-step explanation:

Because you divided 6 and 3

Answer:

The secant function is undefined for angles where the cosine function equals zero, because dividing by zero is undefined. Therefore, we need to find the values of Θ where cos Θ = 0.

The cosine function equals zero at 90° and 270° (or π/2 and 3π/2 in radians), so we have:

cos 90° = 0, cos 270° = 0

Therefore, the angles that satisfy sec Θ = undefined are:

Θ = 90° + 360°k, Θ = 270° + 360°k

where k is an integer (positive, negative, or zero) that allows us to generate all possible angles in the range 0° ≤ Θ ≤ 360°.

So, the solutions for Θ are:

Θ = 90° + 360°k, Θ = 270° + 360°k

where k is an integer.

Step-by-step explanation:

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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A poster of area 11760 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. The dimensions that maximize the printed area are 500 cm x 23.52 cm.

The problem can be solved using the following concept:

Suppose we have a function f(x), then at the maximum/minimum point, it holds:

          f '(x) = 0

In the given problem, let:

q = length of the poster

p = width of the poster

Then,

p x q = 11760

or q = 11760/p

Let f(p,q) be the function of printed area, then:

f(p,q) = (p - 20)(q - 12)

f(p) = (p - 20) (11760/p - 12)

f(p) = -p² + 1000p - 980 x 20

At the maximum point:

f '(p) = 0

-2p + 1000 = 0

p = 500

Substitute p = 500 to get q:

q = 11760/p = 11760/500 = 23.52

Hence, the maximum printed area obtained if the dimensions are 500 cm x 23.52 cm

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In permutation, ³¹C₅  are there to select 5 scoops of ice cream to put into a bowl .

What are some examples of permutation?

Total ice cream flavor n = 31 flavor

selection of (r) = 5 scoop

total number of ways to select 5 scoops of ice cream from 31 flovers

                                                   = ³¹C₅

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Answer:

32

Step-by-step explanation:

0+0+32

Answer:

The answer is 32

The rotation matrices must have their signs switched from positive to negative in order to retain the same definition of a positive rotation in a left-handed system.

In a left-handed system, the rotation matrices must be changed to their negative counterparts in order to retain the same definition of a positive rotation. This means that the matrices must have their signs switched from positive to negative. For example, in the 3D rotation matrix, the elements of the matrix must be changed from (1, 0, 0; 0, cosθ, -sinθ; 0, sinθ, cosθ) to (1, 0, 0; 0, -cosθ, sinθ; 0, -sinθ, -cosθ). This is done to ensure that the rotations in the left-handed system are in the opposite direction than the rotations in the right-handed system. This change will retain the same definition of a positive rotation, but the direction of the rotation will be inverted.

The rotation matrices must have their signs switched from positive to negative in order to retain the same definition of a positive rotation in a left-handed system.

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Answer:

Nwm miałem to dawno powodzenia

If the condition km - (2mb)^2 < 0 holds for the cushioned harmonic oscillator, the time scale of the damping is relatively short, indicating rapid dissipation of energy and a quick approach to the rest state.

The time scale of damping in the cushioned harmonic oscillator can be determined by examining the damping factor, which is represented by the term km - (2mb)^2. If this damping factor is less than zero (km - (2mb)^2 < 0), it indicates that the movement is not oscillatory but purely cushioned.

In the context of the harmonic oscillator, damping refers to the process by which the system loses energy over time and eventually comes to rest. The damping factor is a crucial parameter that determines the behavior of the system. When the damping factor is negative, it implies that the system experiences overdamping, where the energy is dissipated quickly without oscillation.

The time scale of the damping can be thought of as the time it takes for the system to lose a significant amount of energy and approach a rest state. Since the damping factor is negative in this scenario, the time scale of the damping would be relatively short, indicating rapid dissipation of energy and a quick approach to the rest state. The exact value of the time scale would depend on the specific parameters of the system, such as the mass (m), spring constant (k), and damping coefficient (b).

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The exponential model for the given data set is \(y(x) = 70 + (110)e^{-0.135x}\).

Given that cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F and the table shows temperature readings for the cake and the room temperature is 70°F.

Temperature at time = 0 min, y₀= 180° F

Ambient (room) tempertaure = y₁ = 70° F

Using Newton's cooling method,

y(x) = y₁ + (y₀ - y₁)e⁻ⁿˣ

y(x) = 70 + (180-70)e⁻ⁿˣ

y(x) = 70 + (110)e⁻ⁿˣ

Given, at x=5 min, y(5) = 126,

y(5) = 70 + (110)e⁻⁵ⁿ  = 126

Solving,  e⁻⁵ⁿ  = (126-70)/110 = 0.5091

Taking and log and solving for n,

- 5n = log(0.5091)

-5n= -0.67511

n = 0.135

Thus, the exponential model is \(y(x)=70+(110)e^{-0.135x}\)

Hence, an exponential model for given data set when a room temperature  of 70°F is \(y(x)=70+(110)^{-0.135x}\).

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The number of salads were ordered with Italian dressing is 26.

Given that, the Soto Salad restaurant served \(6\frac{1}{2}\) cups of Italian salad dressing.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

If the restaurant serves 1/4 cup of dressing with each salad

Then, the number of salads were ordered with Italian dressing

= \(6\frac{1}{2}\div\frac{1}{4}\)

= 13/2 ÷ 1/4

= 13/2 × 4/1

= 13 × 2

= 26

Therefore, the number of salads were ordered with Italian dressing is 26.

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The probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer is 5/45, or approximately 0.11.

To calculate the probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer, we need to consider the number of possible combinations of socks that result in a match and divide that by the total number of possible combinations of two socks.

The man has a total of 5 pairs of socks, or 10 socks, so there are 10 choose 2, or 45, possible combinations of two socks. Out of these, 5 of them result in a match, because there are 5 pairs of matching socks in the drawer.

Therefore, the probability of getting a matched pair of socks is 5/45, or approximately 0.11. This means that there is an 11% chance that the man will select a matched pair of socks if he randomly selects two socks from the drawer.

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The equation of the circle shown on the graph with center point at \(\((2, 4)\)\) and radius \(\(4\) is \((x-2)^2 + (y-4)^2 = 16\)\).

The equation of a circle with center point \(\((h, k)\)\) and radius \(\(r\)\) can be represented as \(\((x-h)^2 + (y-k)^2 = r^2\)\).

In this case, the center point is given as \(\((2, 4)\)\) and the radius is \(\(4\)\). Plugging in these values into the equation, we get:

\(\((x-2)^2 + (y-4)^2 = 4^2\)\)

Expanding and simplifying:

\(\((x-2)^2 + (y-4)^2 = 16\)\)

The concept of the equation of a circle involves representing the relationship between the coordinates of points on a circle and its center point and radius. By using the equation \(\((x-h)^2 + (y-k)^2 = r^2\)\), where \(\((h, k)\)\) represents the center point and \(\(r\)\) represents the radius, we can determine the equation of a circle on a graph.

This equation allows us to describe the geometric properties of the circle and identify the points that lie on its circumference.

Thus, the equation of the circle shown on the graph with center point at \(\((2, 4)\)\) and radius \(\(4\) is \((x-2)^2 + (y-4)^2 = 16\)\).

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You have the following expression:

In order to express the previous number as an expression with the imaginary unit, you consider the following:

where the square root of -1 is the imaginary unit i by definition. Thus, by replacing you obtain:

Hence, the given expression in terms of the imaginary unit is :

Answer:

x=66

hope this helped :)

Answer:

The third one

Step-by-step explanation:

\(\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=158055.04\\ h=78 \end{cases}\implies 158055.04=\cfrac{\pi r^2(78)}{3} \\\\\\ (3)158055.04=78\pi r^2\implies \cfrac{(3)158055.04}{78\pi }=r^2 \\\\\\ \sqrt{\cfrac{(3)158055.04}{78\pi }}=r\implies \sqrt{\cfrac{(3)158055.04}{78(3.14) }}=r\implies 44=r\)

Answer:

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Initial height is the y-intercept of the line.

Yearly growth rate is the slope.

So we have:

The equation of the line with these constants is:

Answertank cu

Step-by-step explanation:

Answer:

Answer:

i really need the points sorry