Find the length of segment MN. Round to the nearest tenth.
Write your response in the answer box.
-N(-1, 2)
y
M(-4,-4)

Answer:

162 units³

Step-by-step explanation:

Original solid:

V = 6 units³

SA = 22 units²

Dilated solid:

V = ?

SA = 198 units²

The ratio of the areas is 198/22 = 9

The ratio of the area is the square of the scale factor.

The scale factor is:

scale factor = √9 = 3

The ratio of the volumes is the cube of the scale factor.

ratio of volumes = 3³ = 27

The dilated volume is:

6 × 27 = 162 units³

Answer: 162 units³

Answer:

y = 3/4x - 8/3

Step-by-step explanation:

y = 3/4x + b

1/3 = 3/4(4) + b

1/3 = 3 + b

-8/3 = b

Answer:

y=3/4x-8/3

Step-by-step explanation:

y-y1=m(x-x1)

y-1/3=3/4(x-4)

y-1/3=3/4x-12/4

y-1/3=3/4x-3

y=3/4x-3+1/3

y=3/4x-9/3+1/3

y=3/4x-8/3

Answer: x=-1

Step-by-step explanation:

3x+2(2x+8)=9

Answer:

3x+2y=9

3x+2(2x+8)=9

3x+4x+16=9

7x=-7

x=-1

y=2(-1)+8

y=-2+8

y=6

Step-by-step explanation:

An object moving horizontally will always have a negative acceleration ax if it is slowing down or decelerating.

An object moving horizontally will always have a negative acceleration ax if it is slowing down or decelerating. Acceleration is a measure of the change in velocity of an object and is typically defined as the second derivative of the position with respect to time.

If an object is slowing down or decelerating, its velocity will be decreasing, and its acceleration will be negative. This means that the direction of the acceleration will be opposite to the direction of motion, resulting in a negative value for ax. In physics, acceleration is a vector quantity, meaning it has both magnitude and direction.

If an object is moving horizontally and slowing down, the direction of the change in velocity will be perpendicular to the direction of motion, resulting in a negative acceleration ax.

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the domain of the graph is where on the x axis there is a graph.

here the domain, x, is less than or equal to 6, isnce it goes down on the negative side

the arrow means the line goes on forever, so

x<=6

(x is less than or equal to 6)

For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

As given in the question,

Height of the right circular cone = 2.5 units

And radius of right circular cone = 7.5 units

Let r be the radius of the cylinder and h be the height of the cylinder.

Volume of a cylinder 'V' = π r² h

Cylinder is inscribed in right circular cone

From origin edge cylinder is inscribed at x distance in right circular cone.

r = 7.5 - x

h = (2.5 /7.5) x

  = x/3

V  = π ( 7.5 - x )² ( x / 3)

⇒ V = π ( x² -15x + 56.25 ) (x/3)

⇒ V = (π /3)( x³ - 15x² + 56.25x)

For maximum volume ,

dV/dx = 0

dV/dx = (π/3)( 3x² -30x + 56.25)

(π/3) ≠ 0

⇒ 3x² -30x + 56.25 = 0

⇒ 3 ( x² -10x + 18.75) = 0

3 ≠ 0

⇒ x² -10x + 18.75 = 0

x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)

⇒ x = [ 10 ± √ 100 -75]/2

⇒ x=  ( 10 ± 5 ) / 2

⇒ x = 7.5 or 2.5

As r = 7.5 -x

Hence x ≠ 7.5

r = 7.5 -2.5

 = 5 units

h = x/3

  = 2.5/3

  = 0.8333 units

Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

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Answer:

Step-by-step explanation:

(h)

\(KE= \frac{1}{2}mv^{2} \\KE=\frac{mv^{2} }{2} \\2KE=mv^{2}\\2KEm=v^{2} \\v=\sqrt{2KEm}\)

(g)

\(s=\frac{(u+v)t}{2} \\2s=(u+v)t\\\frac{2s}{t}=u+v\\u= \frac{2s}{t}-v\)

(i)

\(s=ut+\frac{1}{2} at^{2} \\s-ut=\frac{at^{2} }{2} \\2s-2ut=at^{2} \\\sqrt{2s-2ut}=at\\a=\sqrt{2s-2ut}-t\)

(j)

\(\frac{pV}{T} =nR\\T=\frac{pV}{nR}\)

(k)

\(a^{2} -b^{2} +c^{2} \\a^{2} +c^{2} =b^{2} \\b=\sqrt{a^{2} +c^{2} }\)

(i)sinθ\(=\frac{a}{b}\)

       θ=\(\frac{a}{sin(b)}\)

Answer:

  2.76×10^-3 m/s²

Step-by-step explanation:

You want to know the acceleration of the moon toward the Earth, given its distance is 3.8×10^8 meters, Earth's mass is 5.98×10^24 kg, and the gravitational constant is 6.673×10^-11 N·m²/kg².

The acceleration of one body by another is ...

  a = GM/r²

where G is the gravitational constant, M is the body creating the gravitational field, and r is the distance between the masses.

  a = (6.673×10^-11)(5.98×10^24)/(3.8×10^8)² N/kg

  a = (6.673·5.98/3.8²)×10^(-11+24-16) m/s² ≈ 2.76×10^-3 m/s²

Answer:

D. 53

Step-by-step explanation:

To calculate total length, just add all those lengths:

5.5 + 6 + (6.5 x 3) + (7 x 2) + 8

5.5 + 6 + 19.5 + 14 + 8

11.5 + 19.5 + 14 + 8

31 + 14 + 8

45 + 8

53

These lines will be parallel to the initial line and will intersect the final velocity line at the corresponding values (122 for the lower estimate and 298 for the upper estimate)

To sketch the velocity against time, you can take the following steps:

First, calculate the acceleration using the given data by using the formula;

acceleration = (final velocity - initial velocity)/time

Where; Initial velocity is the velocity before applying the brakes

Final velocity is the velocity at which the car comes to stop

Time is the time it takes to stop the car (6 seconds in this case)

Now, calculate the lower and upper estimates using the formula;

Lower estimate = initial velocity + (acceleration x time)

Upper estimate = initial velocity + (2 x acceleration x time)

Sketch the graph using the following steps;

On the vertical axis, plot the velocity of the car

On the horizontal axis, plot the time

Start from the initial velocity and draw a straight line with the calculated acceleration until the end of the time (6 seconds)This straight line will give you the final velocity (0 in this case)

Now, draw two more lines, one with the lower estimate and the other with the upper estimate

Finally, label the axes and the lines with their corresponding values.'

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To show that the vector field F(x,y,z) = (8ycos(-6x), -6xsin(8y), 0) is not a gradient vector field, we compute its curl, which is given by ∇ × F = (_, _, _).

The curl of a vector field measures its rotational behavior. If the curl of a vector field is non-zero, it implies that the field is not conservative and cannot be expressed as the gradient of a scalar function.

Let's compute the curl of F(x,y,z):

∇ × F = (∂/∂x, ∂/∂y, ∂/∂z) × (8ycos(-6x), -6xsin(8y), 0)

Using the properties of the cross product, we can expand this as:

∇ × F = (∂/∂x, ∂/∂y, ∂/∂z) × (8ycos(-6x), -6xsin(8y), 0)

       = (∂(0)/∂y - ∂(-6xsin(8y))/∂z, ∂(8ycos(-6x))/∂z - ∂(0)/∂x, ∂(-6xsin(8y))/∂x - ∂(8ycos(-6x))/∂y)

       = (0 - 0, 0 - 0, -6sin(8y) - (-48ycos(-6x)))

Simplifying further:

∇ × F = (0, 0, -6sin(8y) + 48ycos(-6x))

Since the curl of F is non-zero, specifically in the z-component, it indicates that F is not a conservative field and cannot be expressed as the gradient of a scalar function. Therefore, F(x,y,z) = (8ycos(-6x), -6xsin(8y), 0) is not a gradient vector field.

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The circle intersects the x-axis at x = -17 and x = 17 and y-axis at y = -17 and y = 17.

To determine where the circle intersects the x-axis and y-axis when the point (8,15) lies on a circle centered at (0,0), we can use the equation of a circle.

The equation of a circle with center (h, k) and radius r is given by:

\((x-h)^{2}\) + \((y-k)^{2}\) = \(r^{2}\)

In this case, the center of the circle is (0,0), so the equation becomes:

\(x^{2}\) + \(y^{2}\) = \(r^{2}\)

Substituting the point (8,15) into the equation, we have:

\(8^{2}\) + \(15^{2}\) =  \(r^{2}\)

64 + 225 =  \(r^{2}\)

289 =  \(r^{2}\)

Taking the square root of both sides, we find:

r = 17

Therefore, the equation of the circle is:

\(x^{2}\)  +  \(y^{2}\)  = \(17^{2}\)

Now, to determine where the circle intersects the x-axis, we set y = 0 in the equation:

\(x^{2}\)  + \(0^{2}\) = \(17^{2}\)

\(x^{2}\)  = 289

Taking the square root, we find:

x = ±17

So, the circle intersects the x-axis at x = -17 and x = 17.

To determine where the circle intersects the y-axis, we set x = 0 in the equation:

\(0^{2}\) +  \(y^{2}\)  = \(17^{2}\)

\(y^{2}\)  = 289

Taking the square root, we find:

y = ±17

Thus, the circle intersects the y-axis at y = -17 and y = 17.

By substituting the point (8,15) into the equation of the circle, we were able to determine its radius. Then, by setting y = 0 and x = 0 in the equation, we found the points where the circle intersects the x-axis and y-axis.

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Answer:

11.1%

Step-by-step explanation:

Looks like it's asking for 7 years.

Seeing the graph, we have 2 x's, indicating 2 students have been playing for 7 years.

Now that we got that information, let's first count all the X's. Total X's is 18, which indicates 18 students

So 2 out of 18 students have played for 7 years

2/18

A percentage is pretty much dividing a fraction, so let's divide 2 and 18

2 divided by 18 = 11

Meaning 11% have played for 7. Tenth place would be 11.1%

Answer:

Improper fraction: 39/34

Proper fraction: 1 5/34

Decimal: 1.147 (rounded to the nearest thousandths).

Step-by-step explanation:

Solve each expression given, if it has the same result, then the expressions is equivalent. Solve the given expression:

4 7/8 ÷ 4 1/4

First, change all fractions into improper fractions:

4 7/8 = (4 * 8)/8 + 7/8 = 32/8 + 7/8 = 39/8

4 1/4 = (4 * 4)/4  + 1/4 = 16/4 + 1/4 = 17/4

Next, find common denominators. Note that what you do to the denominator, you must do the numerator:

(17/4) * (2/2) = (34/8)

39/8 ÷ 17/4

Solve. First, change the division sign into multiplication, and then flip the second fraction:

39/8 ÷ 17/4 = 39/8 x 4/17

Multiply straight across:

39/8 x 4/17 = (39 x 4)/(8 x 17) = 156/136 = 39/34 (simplified), or 1 5/34.

~

The statement a base class cannot contain a pointer to one of its derived classes is false because a base class can indeed contain a pointer to one of its derived classes.

In object-oriented programming, a base class can have a pointer to one of its derived classes. This is known as upcasting or polymorphism. Upcasting allows for the flexibility of treating derived class objects as instances of the base class.

By using pointers, a base class can refer to derived class objects and access their member functions and variables. This enables the base class to work with different derived classes without needing to know their specific types.

Pointers to derived classes can be stored in base class member variables or passed as function parameters. This allows for dynamic binding and the ability to invoke overridden functions based on the actual derived class type at runtime.

This concept is fundamental to achieving polymorphism and code reusability in object-oriented programming languages like C++ and Java. It facilitates the implementation of inheritance hierarchies and the ability to work with objects of different derived classes through a common base class interface.

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Answer:

=  2617.9938779915 meters3

Step-by-step explanation:

Base Radius (r): 10m

Height (h): 25m

Volume =  

1  πr2h

3

=  

1 ×π×102×25

3

=  2617.9938779915 meters

Hope this helps.

The rate of constant for the above-given first-order reaction is b.) 8.77 × 10–3 h–1.

The half-life of a first-order reaction can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.

In this case, we know that the reaction goes to half completion in 79 hours. Therefore, the half-life is also 79 hours.

Plugging this into the equation, we get:

79 = ln(2)/k

Solving for k, we get:

k = ln(2)/79

Using a calculator, we can evaluate this expression to get:

k = 8.77 × 10–3 h–1

Therefore, the correct answer is b) 8.77 × 10–3 h–1.

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a. Here's how you can represent the given equation in the Direct-Form 2:
y(n) = x(n) + a1 * y(n-1) + a2 * y(n-2)

b. you need to substitute this input signal into the difference equation and solve for y(n).

c. To find the total solution, you need to sum the zero-state solution and the zero-input solution.

a) To implement the system defined by the given difference equation using the Direct-Form 2, you can break down the equation into a set of smaller equations.

The Direct-Form 2 implementation involves using two delay elements (z^(-1)) and one gain (a). Here's how you can represent the given equation in the Direct-Form 2:

y(n) = x(n) + a1 * y(n-1) + a2 * y(n-2)

Where a1 and a2 are the coefficients of the y(n-1) and y(n-2) terms respectively. In this case, a1 = -1 and a2 = -2.

b) The particular solution of the equation refers to the solution that satisfies the given input signal. In this case, the input signal x(n) is given as (-1)^n * u(n). To find the particular solution, you need to substitute this input signal into the difference equation and solve for y(n).

c) To find the zero-state solution, you need to assume that there are no initial conditions (y(-1) and y(-2) are both zero). You can substitute the given input signal x(n) and solve the difference equation to find the zero-state solution.

To find the zero-input solution, you need to assume that the input signal is zero (x(n) = 0). You can then solve the difference equation with the given initial conditions to find the zero-input solution.

To find the total solution, you need to sum the zero-state solution and the zero-input solution.

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A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.


A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.

Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.

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a) F = (9/5)*C + 32

b)

c) The graph can be seen below, it is a linear function.

We have the formula:

C = (5/9)*(F - 32)

To solve it for F, we need to isolate the F in the formula:

F = (9/5)*C + 32

b) Now we want to convert some temperatures.

If C = 0° celcius, then:

F =  (9/5)*0 + 32 = 32

This means that: 0°C = 32°F

if C = 20° Celcius, then:

F =  (9/5)*20 + 32 = 68

then 20°C = 68°F

if C = 32°C then:

F = (9/5)*32 + 32 = 89.6°

So 32°C = 89.6°F

Finally, if C = 41°C then:

F = (9/5)*41 + 32 = 105.8

Then 41°C = 105.8°F

c)  Here the function is:

F = (9/5)*C + 32

This clearly is a linear function, and the graph can be seen in the image below.

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The limit of the sequence (1) {2}, (2) {(-1)^n}, and (3) {n sin(n)}, converges to DNE (does not exist) or the sequence diverges. The limit of the sequence (4) {sin(nπ)} is undefined, as it oscillates between -1 and 1.

In the case of sequence (1) {2}, the limit is a constant value, and the sequence converges to that value. However, in the case of sequence (2) {(-1)^n}, the sequence oscillates between -1 and 1, and there is no single value that it approaches as n tends to infinity. Therefore, the limit does not exist, and the sequence diverges.

Sequence (3) {n sin(n)} also does not have a limit as n tends to infinity. The term n sin(n) oscillates between positive and negative values without approaching a specific value. Hence, the limit of this sequence is DNE, and it diverges.

In the case of sequence (4) {sin(nπ)}, the term sin(nπ) oscillates between -1 and 1 as n varies. Since there is no convergence to a specific value, the limit of this sequence is undefined.

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1,156,530 members were in attendance in 2016. You can round it to $1,160,000.

Functions that take the form f(x) = axe are referred to as exponential functions. where an is a constant and x is a variable.

500,000 people are registered members of the website as of 2010.

Y members grew by 15% annually.

Members and year have an exponential relationship that is

y = 500,000(1.15)^t

Then in 2016 the number of members present are given by,

y = 500,000(1.15)^6 = 1,156,530.

Hence, 1,156,530 members present in 2016. It can rounded to 1,160,000.

The complete question is:

A website 500,000 members in 2010. The number y of members increases by 15% each year. Write an exponential growth function that represents the website membership t years after 2010. How many members will there be in 2016? Round your answer to the nearest ten thousands

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Find the amount of the increase and divide that by the original amount:

7.70 - 7.00 = 0.70 increase

0.70 / 7.00 = 0.1

Multiply by 100 to get the percentage:

0.1 x 100 = 10 %

The increase was 10 %

Answer: The dress was $66

Step-by-step explanation:

55(120) divided by 100 and you'll get the price of the dress :)

Answer:

x=416

Step-by-step explanation:

just did it its super fast problem to solve.

Step-by-step explanation:

Cross multiply

15x = 1560 x 4

15x = 6240

Divide both sides by 15

Therefore x = 416

The measure of the altitude NE in the triangle CNE for the given similarity  is equal to 4 units.

Here In the attached figure,

B is the unknown vertex where ray AM and DE intersects.

In the triangles,

Triangle ABE ~ Triangle CDE

⇒measure of ∠A = measure of ∠C  __(1)

AE = 15

CE = 5

ME = 12

Let 'x' be the measure of altitude NE.

In ΔAME and ΔCNE,

Measure of ∠A = Measure of ∠C  (from 1)

Measure of ∠AME = Measure of ∠CNE  ( each 90° )

Measure of ∠AEM = Measure of ∠CEN ( vertically opposite angles)

By AAA corollary we have,

ΔAME ~ ΔCNE

In similar triangles corresponding sides are in proportion .

AE / CE = ME / NE

Substitute the values we have,

⇒ 15 /5 = 12/ x

⇒x =12/3

⇒x = 4

⇒NE = 4 units.

Therefore , the length of the altitude NE is equal to 4 units.

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The above question is incomplete, the complete question is:

Use similar triangles to find the length of the altitude.

Triangle ABE ~ Triangle CDE. Find the length of altitude for NE.

Attached figure.

Answer:

0= 30

Step-by-step explanation:

-7(3x+5) +20=5)3-5x)+4x

-21x-35+20=5)3-5x)+4x

Add the numbers

-21x-35+20=5)3-5x)+4x

-21x-15=5)3-5x)+4x

Rearrange terms

-21x-15=5)3-5x)+4x

-21x-15=5(-5x+3)+4x

Distribute

-21x-15=-25x+15+4x

Combine like terms

-21x-15=-21x+15

Add 15 to both sides of the equation

-21x-15+15=-21x+15+15

Simplify

Add the numbers

-21x=-21x+30

add 21 to both sides of the equation

-21x+21x= 21x+30+21x

Simplify

combine like terms

0=30

Answer:

(9, -5)

Step-by-step explanation:

To find the vertex of the function h(x), we need to apply the given transformation to the vertex of the original function f(x).

The function h(x) = f(x - 3) - 4 represents a horizontal shift of 3 units to the right and a vertical shift of 4 units downward from the original function f(x).

Given that the vertex of f(x) is (6, -1), we can apply the horizontal shift of 3 units to the right by adding 3 to the x-coordinate of the vertex, resulting in (6 + 3, -1) = (9, -1).

Next, we apply the vertical shift of 4 units downward by subtracting 4 from the y-coordinate of the vertex, giving us (9, -1 - 4) = (9, -5).

Therefore, the vertex of the function h(x) is (9, -5).

Answer:

=> Equilateral Triangle

Step-by-step explanation:

Equilateral Triangle is having 2-d shape with all equal sides and the sum of angles of any triangle is 180° .