Which two transformations can be used to
obtain the graph of y = 3(x - 5)2 from the
graph of y = x2?
F. A vertical compression and a translation
5 units left.
G. A vertical stretch and a translation
5 units left.
H. A vertical compression and a translation
5 units right.
J. A vertical stretch and a translation
5 units right.

The tennis player hits the ball with an initial speed of 58 feet per second at an angle of 19°, from a height of 1.9 feet. The ball lands at a distance of 65.369 feet from the initial point.

We need to determine how far away the ball land in feet. The horizontal and vertical motions of the ball are independent of each other. The horizontal motion is unaffected by the vertical motion of the ball. It means the ball will move with a constant horizontal velocity of Vx = Vo × cos θ

Where

Vx is the horizontal velocity

Vo is the initial velocity

θ is the angle of the velocity vector with respect to the horizontal axis

Thus, the horizontal component of the initial velocity is given by:

Vx= 58 ft/s cos (19°)

Vx = 55.4 ft/s

Similarly, the vertical component of the initial velocity is given by:

Vy = Vo × sin θ

Vy = 58 ft/s sin (19°)

Vy = 18.8 ft/s

The time of flight (t) can be found using the vertical motion of the ball. Using vertical motion, the distance traveled in the horizontal direction can be found using

d = Vx × t.

The time of flight can be calculated as

t = 2Vy / g

where g is the acceleration due to gravity,g = 32.2 ft/s

2t = 2(18.8) / 32.2

t = 1.16 s

Therefore, the distance traveled in the horizontal direction can be calculated as:

d = Vx × td

  = 55.4 × 1.16d

  = 64.1 feet

The ball lands at a distance of 64.1 feet from the initial point. Hence, the correct option is 65.369 feet (rounded off to three decimal places).

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The question asks about the range of a tennis ball hit under specific conditions. Using the formula for the range of a projectile, and the given values for speed, angle, and gravity, it is found that the tennis ball will land approximately 63.495 feet away.

The subject of the question is Physics, specifically kinematics, and the motion of projectiles. This is a problem of projectile motion. We will determine where the tennis ball lands in terms of horizontal distance also known as range.

To calculate the range, we use the formula: Range = (v² sin (2θ)) / g, where v is the initial velocity of the ball, θ is the angle at which it's thrown, and g is the acceleration due to gravity. Here, v= 58 feet per second, θ= 19°, and g= 32.2 feet/second² respectively.

Through calculations, we will find that the tennis ball lands approximately 63.495 feet away from the starting point.

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Answer:

$7

Step-by-step explanation:

Since 100/20 = 5, 20% is 1/5, so 20% of 35 is 35/5, or 7

Answer:

If someone leave a 20% tip and the meal is 35$how much was the tip :

$35.00 ÷ 20% = $7.00

The answer is C: \(h = \frac{2A}{b}\)

Starting with the given formula for the area, A = 1/2hb, the first step is to isolate h by using the multiplicative inverse of b, which is \(\frac{1}{b}\) on both sides of the equation:

\(A(\frac{1}{b}) = \frac{1}{2}hb* (\frac{1}{b})\)

The result will be:

\(\frac{A}{b} = \frac{1}{2}h\)

The last step is to use the multiplicative inverse of \(\frac{1}{2}\), which is 2 or \(\frac{2}{1}\) to further isolate the variable h :

\(\frac{A}{b} (\frac{2}{1}) = (\frac{2}{1}) \frac{1}{2} h\)

The formula for h will be:

\(h = \frac{2A}{b}\)  which is the option C in your question.

the value of the given integral ∬ D \((x^2 + y^2)^{(3/2)}\) dxdy, where D is the disk \(x^2 + y^2\) ≤ 25, is 20000π.

To evaluate the given integral ∬ D \((x^2 + y^2)^{(3/2)}\) dxdy, where D is the disk \(x^2 + y^2\) ≤ 25, we can switch to polar coordinates.

In polar coordinates, the conversion from Cartesian coordinates (x, y) to polar coordinates (r, θ) is given by:

x = r cos(θ)

y = r sin(θ)

The Jacobian determinant of the transformation is r, which means that dxdy in Cartesian coordinates becomes r dr dθ in polar coordinates.

Now let's express the disk D in terms of polar coordinates. The disk D can be described by the inequality:

\(x^2 + y^2\)≤ 25

Substituting the expressions for x and y in terms of r and θ:

(r cos(θ\())^2\) + (r sin(θ\())^2\) ≤ 25

\(r^2 cos^2\)(θ) +\(r^2 sin^2\)(θ) ≤ 25

\(r^2 (cos^2\)(θ) + \(sin^2\)(θ)) ≤ 25

\(r^2\)≤ 25

Taking the square root of both sides:

|r| ≤ 5

Since r represents the distance from the origin, we can limit r to the interval [0, 5].

Now, let's express the integral in polar coordinates:

∬ D (\(x^2 + y^2)^{(3/2)}\) dxdy = ∫[0 to 2π] ∫[0 to 5] \((r^2)^{(3/2)}\) r dr dθ

Simplifying:

∫[0 to 2π] ∫[0 to 5] \(r^3\) r dr dθ

= ∫[0 to 2π] ∫[0 to 5] \(r^4\) dr dθ

Integrating with respect to r:

∫[0 to 2π] [\(r^5/5\)] ∣ [0 to 5] dθ

= ∫[0 to 2π] (5^5/5 - 0) dθ

= ∫[0 to 2π] (\(5^5/5\)) dθ

= (\(5^5/5\)) ∫[0 to 2π] dθ

= (\(5^5/5\)) (θ ∣ [0 to 2π])

= \((5^5/5\)) (2π - 0)

= \((5^5/5\)) (2π)

= \(2^5 (5^4)\) π

= 32 * 625 * π

= 20000π

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Answer: 3 sqrt(21)

Step-by-step explanation:

wow this problem is gross!
making the triangle,

you need to use the law of cosines! searching "law of cosines" online should help a lot!

c^2 = a^2 + b^2 − 2ab cos(C)

you know C = 60 degrees (from 12 pm to 2pm!)

a = 12 cm and b = 15 cm

plug it into the equation and you get

c = 3 * sqrt(21) = 13.748

Answer: √70

Step-by-step explanation:

15^2=12^2 + x^2

225= 155 + x^2

X= √70

Answer:

Step-by-step explanation:

b) The value of 12⁰ will be?

→ 12⁰ = ?

→ 12⁰ = 1

Hence, the solution is 1.

c) The value of (3)^(-2) will be?

→ (3)^(-2) = ?

→ (3)^(-2) = 0.1

Hence, the solution is 0.1.

Answer: B) 38

Step-by-step explanation:

1) \(x+(x+6)+(3x-16)=180\) (sum of angles in triangle)

2) \(5x-10=180\) (Algebra)

3) \(5x=190\)

4) x= 38 degrees

Answer: x = 38

Step-by-step explanation:

1) Add 3x - 16 and x + 6 and x together. You get 5x - 10.

2) All sides of a triangle equals 180 degrees, so that means 5x - 10 = 180.

3) Add 10 to both sides, 5x = 190.

4) 190/5 = 38

5) 38 is your answer.

Answer:

The coordinates of the vertices of the original triangle are (-4, 2), (2, 4), and

(-2, -2).

To obtain the new triangle, subtract 2 from each x-coordinate, and subtract 4 from each y-coordinate. So the coordinates of the vertices of the new triangle are (-6, -2), (0, 0) and (-4, -6). Draw the new triangle.

Answer:

g=-1

Step-by-step explanation:

3(g+4)=9

Divide both sides by 3.

g+4=  9/3

Divide 9 by 3 to get 3.

g+4=3

Subtract 4 from both sides.

g=3−4

Subtract 4 from 3 to get −1.

g=−1

Answer:

3(g+4)=9

or, 3(g+4)/3=9/3 [Dividing both sides by 3.]

or, g+4=3

or, g+4-4=3-4 [Subtracting 4 from both sides.]

So, g=-1

Answer:

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

Given system:

Plot each line and find the intersection, this is the solution.

The solution is (-4, - 4) as per attached graph.

Answer:

B

Step-by-step explanation:

Use a calculator and do it step by step.

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Answer:

I Think earthier b, or C

Step-by-step explanation:

The equation for function g is given by using translational ideas:

g(x) = 7x/3 + 1.

According to operations like multiplication or sum/subtraction either in its definition or in its domain, a translation is represented by a change in the function graph. Examples include shifting to the left or right or up or down, compressing or stretching vertically or horizontally, and reflecting over the x- or y-axis.

Given that f(x) exists, obtaining f is equal to compressing horizontally by a factor of a. (ax).

The function in this issue is as follows:

f(x) = 7x + 1.

We have the following for a horizontal compression of 1/3:

g(x) = f(1/3x) = 7x/3 + 1.

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The effective mass on the opposite end of the lever is 4 kg and distance is given, which is incorrect as option D is 25 kg otherwise all option is correct .

In the given scenario, a 2 kg mass is placed at the end of a lever, which is 20 cm from the pivoting point. If the mass is transferred to the other side of the lever, which is 10 cm from the pivot,

Let's find out.The effective mass on the opposite end of the lever can be found using the following formula:

= Mass × distance of its center of gravity from the pivot

Let M be the effective mass that we have to find. Then, we have:

2 kg × 20 cm

= M × 10 cm40 cm

= 10 M4

= MM

= 4

Therefore, the effective mass is 4 kg. Hence, option D. 25 kg is incorrect as the effective mass is 4 kg.

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Answer:

4b=x3(76)+10

Step-by-step explanation:

Step-by-step explanation:

Easy steps!

step 1

Find out the area of the complete quadrant of the circle (1/4 of the complete circle)

where

r=2 units

substitute

step 2

Find out the area of the semicircle removed

where the radius of the semicircle removed is half of the radius of the circle

so

r=2/2=1 unit

therefore

to find out the area of the falcata, subtract the area of the removed semicircle from the area of the quadrant of the circle

The area of the falcata is

A=pi-pi/2=pi/2 unit2

False. If X₁, X₂, ..., Xn are independent and identically distributed (i.i.d.) random variables

a) False. If X₁, X₂, ..., Xn are independent and identically distributed (i.i.d.) random variables following a uniform distribution U[a, b], the sample mean (Ẋn) is not normally distributed. The sample mean of a uniform distribution follows a triangular distribution, not a normal distribution. As the sample size increases, the distribution of the sample mean approaches a normal distribution due to the Central Limit Theorem. However, for finite sample sizes, the distribution of the sample mean from a uniform distribution is not normal.

(b) False. If X₁, X₂, ..., Xn are independent and identically distributed (i.i.d.) random variables following an exponential distribution with parameter λ, the sample mean (Ẋn) is not normally distributed. The exponential distribution is a positively skewed distribution with a heavy tail, and the sample mean from an exponential distribution does not follow a normal distribution.

Similar to the previous statement, as the sample size increases, the distribution of the sample mean approaches a normal distribution due to the Central Limit Theorem. However, for finite sample sizes, the distribution of the sample mean from an exponential distribution is not normal.

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Total 20 number cases should the manager order each month to server an average of 240 vashes of flowers.

Manager of a flower shop determines that an average of 240 vases of flowers is sold each month.

3 cases contain 36 vases.

so 1 case will contain 36/3 vases.

1 case will contain  = 12 vases.

How many cases of vases should the manager order each month.

Given is that 240 vashes of flowers each month is sold.

according to 12 vashes per case we need 20  cases to cover 240 vashes of flowers each month.

12* 20  = 240.

We need 20 cases here.

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Histogram is a visual representation of data distribution and a stem and leaf plot provide individual values in a set.

Pros of a histogram:

Cons of a histogram:

Pros of a stem-and-leaf plot:

Cons of a stem-and-leaf plot:

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Answer:

15 represents where Jerry is after the elevation dropped 25 meters and then rose 40 meters.

Step-by-step explanation:

It's given that Jerry hiked downhill to a valley where the elevation dropped 25 meters below his starting position. Then, he hiked up to a hill that was 40 meters higher than the valley

Hiked downhill = 25 meters

Hiked up = 40 meters

The given equation is

Here, hiked downhill represented by negative sign and hiked up resents by positive sign.

So, 15 represents that Jerry hiked up 15 meters from his starting position.

(2, the hill was 15 meters higher than the elevation of his starting point)

Answer:

2.

Step-by-step explanation:

The hill was -25 + 40 = 15 meters highe than starting point.

Answer:

B

Step-by-step explanation:

each time the step changes, the amount of vertices(points) increases by 1. the last number of points was 4, so if you increase 4 by 1 you will get 5. figure B has 5 points!

Answer:

Option B

Step-by-step explanation:

With the circle series, there is a figure with an increasing number of points that are on the circle.

Circle one has two dots, circle two has three dots, circle three has four dots, etc.

It would make the most sense if the circle in the next series have five dots.

Option B should be the correct answer.  

Answer:

You change the sign.

Step-by-step explanation:

Whenever you multiply or divide a negative number on each side of the inequality, you must flip the sign around.

Answer:

1,024

Step-by-step explanation:

In this number sequence or pattern we can see that the numbers are being multiplied by themselves. In this example 2 multiplied by itself is 4 and 4 multiplied by itself is 16 and so on. Hope this helps, have a great day!

Step-by-step explanation:

IF  x-4   is a factor, then putting in x = + 4    will make the polynomial = 0

5 ( 4^3) - 20 (4^2) - 5(4)  + 20   =   0    Yes...it is a factor

\(x - 4 = 0 \\ x = 4 \\ \)

substitute value of x in the function to see if it equals to zero , if not it won't be a factor of the function

\(5 {x}^{3} - 20 {x}^{2} - 5x + 20 = 0 \\ 5(4) ^{3} - 20( {4})^{2} - 5(4) + 20 = 0 \\ 5(64) - 20(16) - 20 + 20 = 0 \\ 320 - 320 - 20 + 20 = 0 \\ 0 = 0\)

so (x-4) is a factor for the function

2 + 7 = 9

6 + 4 = 10

2 + - 7 = -5

- 2 + 7 = 5

- 2 + - 7 = -9

6 + - 4 = 2

- 6 + 4 = - 2

- 6 + - 4 = -10

Answer:

Increasing

Domain: [-5, ∞)

Domain: x≥-5

Range: [-0.5,∞)

Range: y≥-0.5

The annually premium for health insurance will be $2,451.12.

Option A is true.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The health insurance premium is $102.13 each check.

And, We get paid semi-monthly.

Hence, Monthly premium = 2 x $102.13

                                        = $204.26

Since, 1 year = 12 months

Thus, The annually premium = 12 x $204.26

                                            = $2,451.12

So, The annually premium for health insurance will be $2,451.12.

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