Find the surface area of the composite solid below. (2 ft, 2 ft, 2 ft, 3 ft)

The statement to prove is that PQ is the shortest segment from point P to plane M when PQ is perpendicular to plane M.

To prove that PQ is the shortest segment from point P to plane M, we can use the concept of perpendicularity. When PQ is perpendicular to plane M, it forms a right angle with the plane.

In Euclidean geometry, it is known that the shortest distance between a point and a plane is along the line perpendicular to the plane passing through the point.

Therefore, since PQ is perpendicular to plane M, it follows that PQ is the shortest segment from point P to plane M. This can be mathematically proven using the principles of geometry and the definition of perpendicularity.

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Answer:

358 and remainder of 3

Step-by-step explanation:

1. Divide it like any other problem

Hope this helps

The solution of the quadratic equation is x=5±√35 .

A quadratic equation is given by the equation which can be written in the form ax²+bx +c.

the given quadratic equation is :

x²-10x+25=35

Simplifying the equation we get:

or, x²-10x+25-35=0

or, x²-10x-10=0

Now we will solve the equation by completion squares method:

x²-10x-10=0

or, x²-2×x×5+5²-5²-10=0

or, (x-5)²=35

or, x-5=±√35

or, x= 5±√35

Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .

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If David, Malachy and Paul share some sweets in the ratio 4:3:3 then Paul get 7.2 number of sweets

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that David, Malachy and Paul share some sweets in the ratio 4:3:3

All three shared 24 sweets together.

Let x be the number of sweets

4x+3x+3x=24

Add the like terms

10x=24

Divide both sides by 10

x=2.4

Now paul has 3x sweets so 3×2.4=7.2

Hence, Paul get 7.2 number of sweets

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At the end of the fifth day, a bricklayer has laid 324 bricks on the job.

Multiplication is a mathematical arithmetic operation.

It is also a process of adding the same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given, a bricklayer lays 4 bricks on the first day on the job.

On each day thereafter, he lays three times the number of bricks he laid on the previous day.

And he continued his pattern.

Let x be the number of bricks he laid in the previous day.

Then according to the question,

The number of bricks in total is = 3x

For the second day, x =4

Number of the bricks he laid on the second day = 12

Now the x =12 for the third day.

Number of the bricks he laid on the third day = 36

Now x = 36 for the fourth day.

Number of the bricks he laid on the fourth day = 108

Now the x = 108 for the fifth day.

Number of the bricks he laid on the fifth day = 324

Therefore, 324 bricks he has laid at the end of the fifth day.

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Answer:

1.75n

Step-by-step explanation:

First we should just ignore the 'n' in '4n' for now.

So we have 7 and 4 left.

Now we would do 7/4=1.75

Now, we just add on the 'n' to 1.75 and we would get 1.75n

Hope this helps! :)

Answer:

(0,1/3)

Step-by-step explanation:

always remember, the y-intercept is when x=0 because its on the y-axis.

so, the y-intercept would always just be the constant :1/3.

Answer:

(0, 1/3)

y-int is 1/3

Step-by-step explanation:

Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

9514 1404 393

Answer:

  (x, y) = (3, 5)

Step-by-step explanation:

Equate the two expressions for y and solve for x.

  x +2 = 2x -1

  3 = x . . . . . . . . add 1-x

  y = 3 +2 = 5 . . . . using the first equation

The solution is (x, y) = (3, 5).

Answer:

hope this pic helps you

The value of x in the given equation is 2.To find the value of x in the equation 8^(1/6) × 2^x = 32^(1/2), we can simplify both sides of the equation step by step.

Starting with the left side of the equation:

8^(1/6) = (2^3)^(1/6) = 2^(3/6) = 2^(1/2) = √2

Now, we have the equation:

√2 × 2^x = 32^(1/2)

Simplifying the right side of the equation:

32^(1/2) = (2^5)^(1/2) = 2^(5/2) = √32

Substituting these values into the equation, we get:

√2 × 2^x = √32

To simplify further, we can rewrite the square root as an exponent:

2^(1/2) × 2^x = 2^(5/2)

Using the property of exponents that states a^(m+n) = a^m × a^n, we can combine the terms on the left side:

2^(1/2 + x) = 2^(5/2)

For the equation to hold true, the exponents on both sides must be equal:

1/2 + x = 5/2

Subtracting 1/2 from both sides, we have:

x = 5/2 - 1/2

x = 4/2

x = 2.

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Answer: Answer: A

Explanation:

Just plug in numbers since you know the unknown values,

x + r = 4 + 5

4 + 5 = 9

Step-by-step explanation:

Answer:

44 dollars

Step-by-step explanation:

Since we need to find the total sales, we do 152 * .29, but we are estimating, therefore, instead we can do 150 * .29, which is 43.5. Rounding up we get 44, thus 44 is our answer

Answer:

-102

Step-by-step explanation:

-38

-120

-158

+56

-102

119.07 feet fence would be required.

Perimeter is a measure of the distance around the boundary of a two-dimensional shape. It is the total length of all the sides or edges of a shape. For example, if you have a rectangle with a length of 5 units and a width of 3 units, the perimeter would be:

2(5 + 3) = 2(8) = 16 units

In this case, we added up the lengths of all four sides of the rectangle to get the perimeter.

Perimeter is typically measured in units of length, such as meters, feet, or centimeters, depending on the context of the problem. It is an important concept in geometry and is used to calculate the amount of material needed for things like fencing or paving.

Now to find the total length of the fence required, we need to find the perimeter of the garden. We can break the garden into two parts: the rectangle and the semicircle.

The rectangle has a length of 30 feet and a width of 23 feet, so its perimeter is:

2(30) + 23 = 83 feet

The semicircle has a diameter equal to the width of the rectangle (23 feet), so its radius is half of the diameter, or:

r = 23/2 = 11.5 feet

The circumference of the semicircle is half of the circumference of a full circle with the same radius, so it is:

(1/2) * 2 * 3.14 * 11.5 = 36.07 feet (rounded to two decimal places)

To find the total perimeter, we add the perimeter of the rectangle and the circumference of the semicircle:

83 + 36.07 = 119.07 feet

Therefore, the gardener needs 119.07 feet of fence to surround the rose garden.

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The distance around the track along its outer edge is  238 + 100 x π metres and the area of the track is  1250 x π  + 2380 square metres.

The racetrack is divided by two parallel sections and two semi-circular endpoints. The two parallel segments are 119 metres long, and the track is 10 metres wide. The inner length of the two parallel sections is 70 metres.

To calculate the distance around the track's outer edge, multiply the lengths of the two parallel segments by the diameter of the two semi-circular ends. C = 2 x π x r, where r is the radius of the semi-circle, may be used to compute the circumference of each semi-circular end.

The radius of each semi-circle is calculated by subtracting the track width (10 metres) from half the inner distance between the two parallel sections (70 metres / 2 = 35 metres). So, the radius of each semi-circle is 35 metres - 10 metres = 25 metres.

As a result, the circumference of each semi-circle is 2 x π x 25 = 50 x π  metres. As a result, the circumference of the track along its outside border is 119 metres + 119 metres + 50 x π  metres + 50 x π  metres = 238 + 100 x π metres.

To calculate the area of the track, first calculate the areas of the two semi-circular ends and the two parallel segments, then add them. A = π\(r^{2}\), where r is the radius of the semi-circle, may be used to compute the area of each semi-circular end.

Each semi-circle has an area of π x \(25^2\) = 625 x π  square metres. The size of the two parallel lengths is 1190 square metres (119 metres x 10 metres). The track's total area(A) = 625 x π  + 625 x π  + 1190 + 1190

A= 1250 x π  + 2380 square metres.

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Solving for y in the equation -8x + y = 9 gives y = 9 + 8x

From the question, we have the following parameters that can be used in our computation:

-8x + y = 9

To solve for y, we make it the subject of the formula

In this case, we simply add 8x to both sides of the equation

Using the above as a guide, we have the following:

8x -8x + y = 9 + 8x

Evaluate the like terms

y = 9 + 8x

Hence, teh solution is y = 9 + 8x

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(a) The predictor variable is Fall in feet and the response variable is Duration in seconds.

(b) The slope is in seconds per foot.

(c) The slope may be negative, as greater drop heights generally result in longer travel times.

(a) The predictor variable in this regression is Drop, which represents the drop height of the roller coaster, in feet, in feet. The response variable is Duration, which represents the duration of the trip, in seconds, in seconds.

(b) The units of slope in this regression are seconds per foot. This means that for each unit of increase in descent height in feet, the travel time will increase or decrease the value of the slope, measured in seconds per foot.

(c) The slope can be negative, as greater drop heights generally result in longer ride times, and the Tower of Terror roller coaster, which was exceptionally short despite its large drop height, has were removed from the analysis.

Therefore, the remaining 90 roller coasters in the dataset likely exhibit a negative relationship between drop height and time, meaning that as drop height increases, ride time decreases .

The Low R-value squared 29.4% means that the relationship between roller coaster drop and ride time in the data set is highly variable, but the negative slope indicates a general downward trend.

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The time-series model that assumes that demand in the next period will be equal to the most recent period's demand is A) Naive approach.

This model is based on the simplest assumption of all, that the next period's demand will be equal to the current period's demand. It is called the naive approach because it assumes no underlying pattern in the data and provides a baseline prediction. The formula for the naive approach is as follows:

y(t) = y(t-1) where y(t) represents the demand in period t and y(t-1) represents the demand in the previous period.

Although this model is simple, it is often used as a benchmark for comparison with more complex models and can provide reasonable results for stable demand patterns.

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Answer:

x = 12

Step-by-step explanation:

For the middle size triangle

short leg = x

long leg = (25 - 9) = 16

ratio = x/16

For the small triangle

short leg = 9

long leg = x

ratio = 9/x

Similar triangles are proportional so

Set the ratios equal

x/16 = 9/x

Cross multiply

x² = 144

Take the square root of both sides

x = 12

Answer:

D is the right answer

Step-by-step explanation:

Answer:

\(\sqrt{41}\)

Step-by-step explanation:

Hello!

In order to answer this question, we need to use the distance formula.

\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The order of these points can be chosen in any way, but they need to be done in the same pair (just like when you find the slope).

For this problem, let's let the J pair be the \(x_2, y_2\) pair and the K pair be the \(x_1,y_1\) pair.

\(x_2\) = -3

\(x_1\) = 2

\(y_2\) = 2

\(y_1\) = -2

Now, let's plug these points in.

\(\sqrt{(-3-2)^2+(2-(-2))^2}\)

\(\sqrt{(-3-2)^2+(2+2)^2}\)

\(\sqrt{(-5)^2+(4)^2}\)

\(\sqrt{25+16}\)

\(\sqrt{41}\)

Thus, the distance between points (-3,2) and (2,-2) is \(\sqrt{41}\).  

Answer:

D, y = 200x

Step-by-step explanation:

hope this helps! :D

have a miraculous day, and brainliest is immensely appreciated!! <3

Answer: D

Step-by-step explanation: this one models that y = 200 L times the number of minutes, which is correct

Answer: 23x3y

step 1 ((2 • (x2)) • (y3)) • 22xy(-2)

step 2 (2x2 • y3) • 22xy(-2)

step 3 3.1 x2 multiplied by x1 = x(2 + 1) = x3

3.2 y3 multiplied by y(-2) = y(3 + (-2)) = y1 = y

Multiplying exponents:

3.3 21 multiplied by 22 = 2(1 + 2) = 23

Answer:f

Step-by-step explanation:

its not that hard

The function is concave up for  x < 1 and concave down for x > 1 because the second derivative is positive for x < 1 and negative for x > 1. As a result, the critical point at x  < 1 is a relative maximum.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is common to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The derivative of the function f(x) can be found by taking the derivative of the expression e^(-x) (x^2 + 2x) using the product rule:

f'(x) = -e^(-x) (x^2 + 2x) + e^(-x) (2x + 2) = 2e^(-x) - 2xe^(-x) (x + 1)

Setting f'(x) equal to zero and solving for x gives us the critical points:

0 = 2e^(-x) - 2xe^(-x).(x + 1)

2xe^(-x).(x + 1) = 2e^(-x)

x(x + 1) = e^x

x^2 + x - e^x = 0

Next, we determine the concavity of the function at the critical points by analyzing the second derivative of the function:

f''(x) = 2e^(-x) + 2xe^(-x) + 2xe^(-x).(x + 1) - 2e^(-x).(x + 1)

= 2e^(-x).(1 - x)

Since the second derivative is positive for x < 1 and negative for x > 1, the function is concave up for x < 1 and concave down for x > 1. Thus, the critical point at x < 1 corresponds to a relative maximum.

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Answer:

x = 122°

Step-by-step explanation:

There is remote angle( non- adjecent angle) and their sum equal to the exterior angle .

Exterior angle is an angle formed from one side of the polygone and the extended side so

<A and <B are remot angle and <BCD is exterior angle .

And we write the equetion as

<A + <B = <BCD

58° + 64° = x°

122° = X°

so the exterior angle ( x ) measures 122° .

The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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The mathematical procedure for decomposing a complex waveform into simpler waveforms is known as Fourier analysis. It allows for the identification of the individual frequency components that contribute to the overall pattern.

Fourier analysis, named after the French mathematician Jean-Baptiste Joseph Fourier, is a fundamental technique used in many fields, including signal processing, physics, and engineering. It is based on the concept that any complex waveform can be represented as a combination of simpler sinusoidal waveforms. These simpler waveforms are characterized by their frequency, amplitude, and phase.

The procedure involves decomposing a complex waveform into its constituent frequencies by applying the Fourier transform. The Fourier transform converts the waveform from the time domain to the frequency domain, revealing the underlying frequency components. By analyzing the resulting spectrum, which shows the amplitude and phase of each frequency component, one can determine the simpler waveforms that make up the original complex pattern.

Fourier analysis has numerous applications, such as analyzing sound waves, image processing, and data compression. It enables us to better understand and manipulate complex signals by breaking them down into their fundamental building blocks.

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Answer:20ps

Step-by-step explanation:

Answer:

16+x=18

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