Algebraically determine the domain and range of the function y=x/x2-16

AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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To find the arc length of the curve \(\displaystyle x=\frac{y^{4}}{4}+\frac{1}{8}y^{2}\) on the interval \(\displaystyle 2\leq y\leq 3\), we can use the arc length formula for a curve given by \(\displaystyle y=f(x)\):

\(\displaystyle L=\int _{a}^{b}\sqrt{1+\left( \frac{dy}{dx}\right)^{2}}\, dx,\)

where \(\displaystyle a\) and \(\displaystyle b\) are the corresponding x-values of the interval \(\displaystyle y=a\) and \(\displaystyle y=b\), and \(\displaystyle \frac{dy}{dx}\) is the derivative of \(\displaystyle y\) with respect to \(\displaystyle x\).

First, let's find the derivative of \(\displaystyle y\) with respect to \(\displaystyle x\):

\(\displaystyle \frac{dx}{dy}=\frac{d}{dy}\left( \frac{y^{4}}{4}+\frac{1}{8}y^{2}\right) =y^{3}+\frac{y}{4}\).

Now, we can calculate the arc length using the given interval \(\displaystyle 2\leq y\leq 3\):

\(\displaystyle L=\int _{2}^{3}\sqrt{1+\left( y^{3}+\frac{y}{4}\right)^{2}}\, dy.\)

This integral represents the arc length of the curve. Evaluating this integral will give us the desired result. However, this integral does not have a closed-form solution and must be numerically approximated using methods such as numerical integration or calculus software.

To calculate the expected value of the game, we need to consider the probability of winning and losing, as well as the corresponding payouts.

There are 52 cards in a standard deck, and we want to calculate the probability of not getting any Aces in a 5-card hand. The total number of possible 5-card hands is given by the combination formula:

C(52, 5) = 52! / (5! * (52 - 5)!) = 2,598,960.

Now let's calculate the number of hands without any Aces. There are 48 non-Ace cards in the deck, so we need to choose 5 cards from these 48:

C(48, 5) = 48! / (5! * (48 - 5)!) = 1,712,304.

The probability of not getting any Aces is the ratio of the number of hands without Aces to the total number of possible hands:

P(lose) = 1,712,304 / 2,598,960 = 0.6599.

The probability of winning is the complement of losing, so:

P(win) = 1 - P(lose) = 1 - 0.6599 = 0.3401.

Now, let's consider the payouts. If you win, you get $1, and if you lose, you lose $1. Therefore, the payout for winning is $1, and the payout for losing is -$1.

The expected value (EV) of the game is calculated as the sum of the products of the probabilities and payouts:

EV = P(win) * payout(win) + P(lose) * payout(lose)

= 0.3401 * 1 + 0.6599 * (-1)

= 0.3401 - 0.6599

= -0.3198.

Therefore, the expected value of the game is -$0.3198, indicating that on average, you can expect to lose approximately $0.32 per game.

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Answer:

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

Step-by-step explanation:

\((7x^2-2x+1)-(9x^2+2x-1)=\\(7x^2-9x^2)+(-2x-2x)+(1+1)=\\-2x^2-4x+2\)

Hope this helps!

Part A: Let "h" be the monkey's current height above the ground. After swinging up 10 ft, the monkey is at a height of (25 + 10) = 35 ft above the ground.

After jumping down 13 ft, the monkey is at a height of (35 - 13) = 22 ft above the ground. Therefore, the expression that represents how far off the ground the monkey is now is:

h = 22 ft.

Part B: The monkey is currently 22 ft off the ground.

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Let's assume that the monkey starts at a height of h = 25 ft above the ground.

After swinging up, the monkey will be at a height of h + 10 ft. After jumping down, the monkey will be at a height of (h + 10 ft) - 13 ft. Therefore, the expression for how far off the ground the monkey is now is:h - 3 ft

Part B:

Starting from a height of 25 ft, the monkey swings up 10 ft to reach a height of 35 ft.

Then, the monkey jumps down 13 ft from that height, which leaves it at a height of 35 - 13 = 22 ft above the ground.

Therefore, the monkey is currently 22 ft off the ground.

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The bar representing her 7-day vacation will have a class width of 16 - 22 and a height of 1.

The frequency distribution of a collection of data reveals how frequently each unique value appears.

The most typical graph for displaying frequency distributions is a histogram. Although it closely resembles a bar chart, there are significant variances.

In the given histogram class width(horizontal width)  represents the number of days and frequency(vertical height) represents the number of vacations taken.

Therefore, The 7-day vacation yet she took this summer will be represented by a bar having a class width 16 - 22 and a height of 1.

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The rate of each plane is,

First plane = 110 mph

Second plane = 15 mph

Let x = rate of the slower plane (First plane!)

x + 45 = rate of the faster plane (Second plane!)

The planes fly for 3 hours, where Distance = RT

Distance between the planes = SUM of the distances.

RT + RT= 795 miles

3x + 3(x + 45) = 795

3x + 3x + 135 = 795

6x + 135 = 795

6x = 795 - 135

6x = 660

x = 110 mph First plane

And, x + 45 = 110 + 45 = 15 mph Second plane.

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Integral value is finite since the given integral converges when the function is \(\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx\).

Given that,

Analyze the integral to see if it is convergent or divergent. convergent integrals should be evaluated.

\(\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx\)

We have to simplify the equation.

Finding the area of the curve's undersurface is the process of integration. To do this, draw as many little rectangles as necessary, then add up their areas.

We know that,

I= \(\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx\)

Let p = x²then xdx= dp/2

Then

I= \(\int\limits^\infty_\infty {3/2e^{-p} } \, dp\)

I= 3/2(\(e^{-p}\))infinity to minus infinity

I= 3/2 (\(e^{-x^{2} }\))infinity to minus infinity

I=0

Therefore, integral value is finite since the given integral converges when the function is \(\int\limits^\infty_\infty {3xe^{-x^{2} } } \, dx\).

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Answer:

x^6y^6

Step-by-step explanation:

Answer:

x^6 y^6

Step-by-step explanation:

The greatest length of the considered pendent is given by: Option A: 1.25 cm

Suppose the considered function is \(y = f(x)\)

Then, we will plot points as \((x,y) =(x,f (x))\) for all values of 'x' which are in domain of the function.

For this case, the given function's graph (the graph of \(y = \dfrac{x^2}{20}\) ) is shown below.

We're given that the largest dimension is of 10 units.

Let this be the line segment parallel to the x-axis, intersecting y-axis at \(y = y_0\)

Now, since the curve is symmetric over (as for x or -x, we get same y), so the line segment that is parallel to x axis also intersects the graph at symmetric places. Let those points be in front of \(x_0\) and \(-x_0\)

For those inputs, the output is \(y = y_0\),

Also, we have length of the line segment as of 10 units, this is the difference between those symmetric inputs.

Thus, we get two equations:

\(x_0 - (-x_0) = 10\)

\(f(x_0) = y_0 = \dfrac{x_0^2}{20}\)

From first one, we get:

\(x_0 = 10/2= 5\)

Thus, we get:

\(f(x_0) = y_0 = \dfrac{x_0^2}{20}\\\\f(5) = y_0=\dfrac{25}{20} = 1.25\)
Since the length of y_0 is the shortest distance from x-axis to that parallel line segment, this is the second dimension needed.

Thus, the greatest length of the considered pendent is given by: Option A: 1.25 cm

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Answer:

x=100

Step-by-step explanation:

50/x=10/20 and 10/50=20/x

50/x=10/20

Cross multiplication

50*20=x*10

1000=10x

x=1000/10

x=100

Check:

50/100=

Divide by 5

10/20

10/50=20/x

Cross multiplication

10*x=50*20

10x=1000

x=1000/10

x=100

They are the same because the fraction that has the unknown both have the same ratio

Answer:

The anser is d edge 2020 lol

Step-by-step explanation:

Answer:

B,D,E

Step-by-step explanation:

b-multiply by 2 for both

d- multiply by 7 for both

e-multiply by 11 for both

A hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. The statement that is true is, a hypothesis can be differentiated from a theory because it is a specific prediction arising from the theory. A hypothesis is a suggested explanation of a phenomenon or observed data that is testable.

Hypotheses are more detailed, and are written to explain precisely what you think is going to occur in your research and the reason for that prediction. A hypothesis will be rejected if it does not fit the data, whereas a theory will be modified to fit the data.

A hypothesis is more like a forecast, and a theory is more like a law that explains how certain events operate. Thus, we can conclude that a hypothesis is a specific prediction arising from the theory.

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Given statement solution is:- The function y = √(x + 3) - 2 with at least four integer points on the axes.

To plot points and graph the function y = √(x + 3) - 2, we can utilize technology tools such as graphing calculators or online graphing tools. I'll demonstrate how to use an online graphing tool called Desmos, which is user-friendly and widely accessible.

Please follow these steps to plot the points and graph the function:

Visit the Desmos website or use any other graphing tool of your choice.

Clear any existing equations or plots on the graph.

Enter the function y = sqrt(x + 3) - 2 into the equation field.

The graphing tool will automatically plot the function.

To plot integer points, simply choose four different integer values for x and calculate the corresponding y values.

Let's choose the following integer values for x: -3, -2, 0, and 2.

Calculate the corresponding y values:

For x = -3: y = sqrt(-3 + 3) - 2 = -2

For x = -2: y = sqrt(-2 + 3) - 2 = -1

For x = 0: y = sqrt(0 + 3) - 2 = 1

For x = 2: y = sqrt(2 + 3) - 2 = 0

Plot these points on the graph by clicking on the appropriate locations.

If you accidentally click on a point and want to delete it, simply click on the point again to remove it.

Make sure the graph displays the axes and all the plotted points.

By following these steps, you should be able to plot the points and graph the function y = √(x + 3) - 2 with at least four integer points on the axes.

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Answer:

279.987

this is da answer

Step-by-step explanation:

There are 280.035 lbs in 127 kilograms. The answer is obtained by applying the unit conversion.

What is unit conversion?

A unit conversion is used to express the same property in a different unit of measurement. For instance, you could use minutes instead of hours to represent time or feet instead of miles to indicate distance. It commonly occurs when measurements are provided in one system of units, such as feet, but are required in a different system, such as chains.

Now,

we have been given 127 kilograms which are to be converted into pounds and to be represented in lbs.

We know that 1 kilogram = 2.205 lbs (approx)

Therefore,

⇒127 kilograms = 127 * 2.205

⇒127 kilograms = 280.035 lbs

Hence,

          There are 280.035 lbs in 127 kilograms.

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Answer:

Rate positively and give brainlist

The sample space between A to C is A,B,C

The likelihood that a sample point will occur is quantified by its probability.

The likelihood of a sample point

According to tradition, statisticians have adopted the following guidelines.

Any sample point's probability can be between 0 and 1.

The probability of every sample point in a sample space added together is 1.

Let's say we run a straightforward statistical experiment. One coin is flipped. Heads or tails are the possible results of the coin flip. These results taken as a whole serve as our experiment's sample space. Each result stands in for a single sample point in the sample space. What is each sample point's probability?

Solution: the total of all sample points' probability

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The quadratic function with leading coefficient 1 and roots of 22 and p is: f(x) = x^2 - (p + 22)x + 22p

To write a quadratic function with leading coefficient 1 and roots of 22 and p, we can use the fact that the roots of a quadratic function in standard form (ax^2 + bx + c) can be found using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Given that the leading coefficient is 1, the quadratic function can be written as:

f(x) = (x - 22)(x - p)

Expanding this expression:

f(x) = x^2 - px - 22x + 22p

Rearranging the terms:

f(x) = x^2 - (p + 22)x + 22p

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Answer:

22

Step-by-step explanation:

we have the sequence

6 10 14 18

well we can see that from 6 to 10 we add 4

and from 10 to 14 we continue to add 4

and that pattern applies to the next

so we can conclude that to 18 we need to add 4 to get the next one

18 + 4 = 22

so the next number is 22

Permutation helps us to know the number of ways an object can be arranged in a particular manner. The correct option is D.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

The example which is an example of permutation is Selecting a first-, second-, and third-place winner at baking.

Hence, the correct option is D.

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Answer:

14

Hope this helps

Answer:

14

Step-by-step explanation:

2 x 7 = 7 + 7

7+7=14

Answer:

csc x = -5/4

Step-by-step explanation:

The official formula for sin is opposite/hypotenuse and csc is just sin flipped so...

The official formula for csc is hypotenuse/opposite.

sin x = -4/5  would be    csc x = -5/4

Answer:

Step-by-step explanation:

What number multiplied by itself is equal to the product of 6 and 150?

30

30 x 30 = 900

6 * 150 = 900

We are given the production function of the economy to be Y=F(K,L)=1.0K^3/2L^1/2. It is also given that people generally save 32.3% of their income and that 14.2% of the capital stock depreciates per year. And we are also given that the economy has 38 units of capital per worker.

The steady state value of output can be defined as the value of output when the capital stock, labor and production become constant. Therefore, Y/L = f(K/L)

= K^3/2 / L^1/2Y/L

= K^3/2 / (K/L)^1/2Y/L

= K^3/2 / (K/L)^1/2

= K^3/2 L^1/2 / K

= K^1/2 L^1/2where Y/L is output per worker. Therefore, we can substitute the values given to us and solve for Y/L.K/L = 38, S

= 0.323, and δ

= 0.142K/L

= S/δK/L

= 0.323/0.142K/L

= 2.28Therefore, K

= (2.28)LTherefore, the economy's steady-state value of output is 1.512. Hence, 1.512.

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Answer:

7

Step-by-step explanation:

derivate of 7x = 1(7)x⁰, or 7

derivate of 4 is 0

derivative of 7x + 4 = 7

Answer: B  x>0

Step-by-step explanation:

Answer:

x> 0

Step-by-step explanation:

There is an open circle at zero which means it does not include zero

The line goes to the right which means greater than

x> 0

Answer:

2/1 or 2

Step-by-step explanation:

so first, you have to count the rise/run. This line rises up 2 and runs to the right 1. To find out the rise/ run, find a place in the graphed line where it is on a plot point. For example: (40, 30). Then just see how much it rises and how much it runs.

Answer:

19) -2 and 7  20) -1, 1/4, 3/4, 2

Step-by-step explanation:

Use desmos graphing calculator for the sketch, and just copy the graph it give you.