Simplify (4r - s) - (r + 2s) + (3r - s)
A.) 6r - 3s
B.) 8r
C.) 3r - 2s
D.) 6r - 4s

Answer:

Step-by-step explanation:

D.The sign of h must be negative and the signal of k must be positive *it’s for sure the answer.

Answer:

D.The sign of h must be negative and the signal of k must be positive EDGE 2021

\((-1,\infty)\cap (-2,2) ---- > (-1,2)\)

Generally, the equation for the function is mathematically given as

f(x) = -5x + 11 + 10

Therefore

When x >= -1, the function decreases because f(x) = -5(x+1)+10.

This means that the function is dropping throughout this range\((-1,\infty).\)

b)

A look at the graph reveals a decreasing trend in the function over the timeframe (-2,2).

In conclusion, The number line will represent

Using the point where the intervals with decreasing functions overlap

\((-1,\infty)\cap (-2,2) ---- > (-1,2)\)

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Answer:

see photos

Step-by-step explanation:

Plato/Edmentum

The equation obtained for Kim will be t = x/2

Equation obtained for Jake will be t = (x - 6)/1.5

As for the problem, Kim and Jake are competing in the big race. And the values of their speed are given below.

Kim moves at a 2-meter-per-second running pace.

Jake moves at a 1.5 meter per second running pace (3 meters per 2 seconds)

Jake gets 6 meters ahead of Kim.

To get equations for the same case to both persons we should get it as,

Let x be the complete race distance and t be either Kim's or Jake's total race time.

Time = Speed/Distance

Kim's time equation is t = x/ 2.

The time equation that Jake uses is t = (x - 6)/1.5.

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A rhombus. Since a rhombus is a parallelogram, its diagonals bisect each other. Its diagonals are also perpendicular.

a) Critical numbers: π/6, 5π/6. Increasing: (0, π/6), (5π/6, 2). Decreasing: (π/6, 5π/6).  b) Local Maxima: x = 0. Local Minima: x = π/6 + √3.
c) Absolute Maxima: None. Absolute Minima: x = π/6 + √3.

a) To find the critical numbers of f(x), we need to find the values of x where f'(x) = 0 or f'(x) is undefined.

Taking the derivative of f(x), we have f'(x) = 1 - 2sin(x).

Setting f'(x) = 0, we get 1 - 2sin(x) = 0. Solving for x, we find sin(x) = 1/2. The solutions in the interval [0, 2π] are x = π/6 and x = 5π/6.

Analyzing the sign of f'(x), we can use the intervals between these critical numbers and the endpoints of the interval [0, 2] to determine where f is increasing or decreasing.

Sign analysis of f'(x) (number line):
Intervals where f is increasing: (0, π/6) and (5π/6, 2)
Intervals where f is decreasing: (π/6, 5π/6)

b) To find the points where f has local extrema on [0, 2], we need to examine the critical numbers and endpoints of the interval.

Since we only have two critical numbers, we can evaluate f(x) at these points and the endpoints.

f(0) = 0 + 2cos(0) = 2 (local maximum)
f(π/6) = π/6 + 2cos(π/6) = π/6 + √3 (local minimum)
f(2) = 2 + 2cos(2) (no local extremum)

c) To find the absolute maximum and minimum values of f(x) on the interval (0, 2], we need to examine the critical numbers, endpoints, and any potential maximum or minimum values within the interval.

Since the interval is open on the left side, we don't have an endpoint to consider. We already found the critical number at x = π/6, so we evaluate f(x) at this point.

f(π/6) = π/6 + 2cos(π/6) = π/6 + √3 (absolute minimum)

Since there is no endpoint on the right side, there is no absolute maximum value for f(x) on the interval (0, 2].

Therefore:
a) Critical numbers of f in [0, 2]: π/6 and 5π/6
Intervals where f is increasing: (0, π/6) and (5π/6, 2)
Intervals where f is decreasing: (π/6, 5π/6)

b) Local Maxima (Points): x = 0
Local Minima (Points): x = π/6 + √3

c) Absolute Maxima (Points): None
Absolute Minima (Points): x = π/6 + √3

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Answer: 3.175%

Step-by-step explanation:

(63/100)(2/1)

Cross multiply = 200

Then divide 200÷63= 3.175

Answer:

39.69%

Step-by-step explanation:

\(\frac{63}{100}\) * \(\frac{63}{100}\) = .3969

The largest 6-digit number having different digits is 987,654.

In symbols, this number can be written as 987,654 or

9 × 10⁵ + 8 × 10⁴ + 7 × 10³ + 6 × 10² + 5 × 10¹ + 4 × 10⁰.

In words, this number is nine hundred eighty-seven thousand six hundred fifty-four.

To find the largest 6-digit number with different digits, we start by determining the largest possible digit for each position. Since we want different digits, we use the largest digit available for each position, starting from left to right.

The largest digit for the hundreds of thousands place is 9, followed by 8 for the ten thousands place, 7 for the thousands place, 6 for the hundreds place, 5 for the tens place, and 4 for the ones place.

By arranging these digits in descending order, we get the largest 6-digit number with different digits: 987,654.

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Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.

A rigid transformation, also called isometry,  is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:

1. Reflection

→  is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.  

The figure is reflected across \(x-\) or \(y-\) axis, and then change \(x-\) or \(y-\) coordinate.

2. Rotation

→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.

The figure is rotated by a degree (ex: 90°), and then change \(x-\) or \(y-\) coordinate. Meanwhile, a point's center rotation stays at the same.

3. Translation

→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right),  or vertical reflections (make a figure up or down).

Vertical translation is shifting the graph along  \(y-\) axis

Horizontal translation is shifting the graph along  \(x-\) axis.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The surface area of this triangular prism is 258 square units

Given parameter is

The triangular prism

The surface area of triangular prism is calculated as

Surface area = Perimeter * Length + 2 * Base area

Using the given dimensions, we have

Surface area = (5 + 6.5 + 6.5) * 11 + 2 * 5 * 6

Evaluate

Surface area = 258

Hence, the surface area is 258 square units

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Answer:

12.4

Step-by-step explanation:

Answer:

Parenthesis

(18)

Explanation:

3 · [9 - (4+2) ÷ 2]

= (3)(9 + −3)

= (3)(9) + (3)(−3)

= 27 − 9

= 18

It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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Given 2nd order Initial-Value ODE as, y" + 3y' – 4y + 12e-2x = 0Convert the 2nd order ODE into a system of 1st order ODE equations as follows:Let y'=zdy/dx = dz/dxSo, y" = d²y/dx² = d/dx(dz/dx) = dz²/dx².

Again, the equation becomes, dz²/dx² + 3z – 4y + 12e^(-2x) = 0The given Initial values for the problem is:y(0) = 2y'(0) = -4Therefore, using Euler's Method, over the interval from x = 0 to x = 0.4 and using 2 integration steps,We can say that the h = 0.2 (since we are taking 2 integration steps and the interval is from 0 to 0.4, which gives 0.4/2 = 0.2)So, the Main answer is:

Given y" + 3y' – 4y + 12e-2x = 0 Initial values:y(0) = 2, y'(0) = -4We know that, y'=zdy/dx = dz/dxSo, y" = d²y/dx² = d/dx(dz/dx) = dz²/dx²Now, dz²/dx² + 3z – 4y + 12e^(-2x) = 0.

We need to solve this system of first-order differential equations by applying Euler's method to find out the value of y at x=0.2 and x=0.4.

Substituting h = 0.2 in the above equations and using Euler's Method, we getThe first step is: x = 0, y = 2, z = -4 Therefore, z1 = z0 + h (-4).

Substituting the values we get, z1 = -4 – (0.2) (3) ( -4) – (0.2) (4) ( 2 + 12 e^(-2(0)) ) = -2.12So, the value of z at x=0.2 is -2.12. Similarly, we can get the value of y at x=0.2 using Euler's method.The second step is: x = 0.2, y = 1.56, z = -2.12Therefore, z2 = z1 + h ( -2.12 ).

Substituting the values we get,z2 = -2.12 - (0.2) (3) ( -2.12) - (0.2) (4) ( 1.56 + 12 e^(-2(0.2)) ) = -1.3148So, the value of z at x=0.4 is -1.3148.Similarly, we can get the value of y at x=0.4 using Euler's method.

Hence, the required answer is, y (0.4) = 0.2281

Solve the given initial value problem using Euler's method over the interval from x = 0 to x = 0.4 using 2 integration steps.

The given initial conditions for this problem is y(0) = 2, and y'(0) = -4. The 2nd order ODE is given as y" + 3y' – 4y + 12e-2x = 0.

We need to convert this 2nd order ODE into a system of 1st order ODE equations. Let y' = z. Therefore, dy/dx = dz/dx. So, y" = d²y/dx² = d/dx(dz/dx) = dz²/dx². Substituting these values in the given equation, we get dz²/dx² + 3z – 4y + 12e^(-2x) = 0.

To solve this system of first-order differential equations, we will apply Euler's method to find out the value of y at x=0.2 and x=0.4. Substituting h = 0.2 in the above equations and using Euler's Method, we get the values of y and z at x=0.2 and x=0.4.

Therefore, the required answer is y (0.4) = 0.2281. Hence, the solution to the given problem using Euler's method is y (0.4) = 0.2281.

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x=-10, 2

you would have to factor it.

refer to picture

Answer:

4,6

Step-by-step explanation:

because the distance 3 so the distance from r to s has to be the same pretty sure

There are several reasons why so many Superfund sites are located in cities. First, cities are often centers of industrial and commercial activity, and historically, many of these industries did not prioritize environmental safety.

As a result, hazardous waste and other contaminants were often disposed of improperly, leading to the contamination of nearby soil and water sources.

Second, cities also tend to have higher population densities, which means that there are more people who may be exposed to environmental hazards. This can be particularly concerning for vulnerable populations such as low-income communities or communities of color who may be more likely to live near contaminated sites.

When it comes to testing environmental issues near cities, there are several factors that need to be taken into consideration. For example, cities may have more complex environmental systems due to the presence of a variety of different land uses (e.g. residential, commercial, industrial). Additionally, urban areas may have higher levels of air pollution due to factors such as traffic congestion and industrial emissions.

As a result, testing environmental issues near cities may require more comprehensive sampling and analysis techniques in order to fully understand the extent of the problem. Additionally, there may need to be more involvement from local community groups and stakeholders in order to ensure that the testing and cleanup process is transparent and responsive to the concerns of affected communities.

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Answer: 3(2x+4), 6(x+2), and 2(3x+6)

Step-by-step explanation: tell me if you dont understand :)

The values of the inverse functions are f-¹ (3) = -1 and f-¹ (8) = 7

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

x   f(x)

-1   3

1     6

2    5

3    7

7   8

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

f-¹ (x) means that we calculate the value of x from the table when y = x in the function notation

So, we have

f-¹ (3) = -1 and f-¹ (8) = 7

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The value of the double integral  ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is  11.77

In this question we need to calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1

i.e., to find ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1]

First we integrate the function (8x)/(1 + xy)  as a function of y, treating the variable x as a constant.

G(x) = ∫_[0, 8] ((8x)/(1 + xy) ) dy

G(x) = 8 ln(8x + 1)

Now we calculate the integral of the previous result as a function of x.

i.e., ∫_[0, 1] G(x) dx

= ∫_[0, 1] [8 ln(8x + 1)] dx

= 9 ln(9) - 8

= 11.77

Therefore, the solution to the double integral (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is 11.77

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Answer:

c: y=(x-1)(x-3)

Step-by-step explanation:

The length of the long and short side of Brian's fence in backyard in Detroit is 47 and 25 respectively.

Total length = length of two long sides + length of short side

Let the length of short side be x. So, length of long side = 2x - 3

Keep the values in formula

x + 2 (2x - 3) = 119

Performing multiplication on Left Hand Side

x + 4x - 6 = 119

Rewriting the equation

x + 4x = 119 + 6

Performing addition on both sides of equation

5x = 125

x = 125/5

Performing division on Right Hand Side

x = 25

Length of short side = 25

Length of long side = 2×25 - 3

Length of long side = 50 - 3

Length of long side = 47

Hence, the lengths are 25 and 47.

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Answer:

I believe 1 foot away

Step-by-step explanation:

because if you take 1 away from 12 you get 11 and that is how tall the shelf is.

How much a statistic varies from one sample to another is known as the sampling variability of a statistic.

Testing variability arises due to the reality that exceptional samples of the same size can produce special values of a statistic, although the samples are described from the same populace. the quantum of slice variability depends on the scale of the sample, the variety of the populace, and the unique statistic being calculated.

The end of statistical conclusion is to apply the data attained from a sample to make consequences about the population, while counting for the slice variability of the statistic. ways similar as thesis checking out and tone belief intervals do not forget the sampling variability of a statistic to make redundant accurate consequences about the populace.

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The equation that best represents the relationship between age and the amount of weight lost in this group of women is "Weight loss 19.75 - 0.94 Age."The correct answer is option B.

Based on the given scenario, the goal is to investigate the relationship between age and the amount of weight lost in a group of 45 women participating in a 12-week diet program.

To determine the correct linear regression equation, we need to analyze the data provided.

Since we don't have access to the actual data, we can't directly verify the correct equation. However, we can make an educated guess based on the options provided.

The correct linear regression equation would be the one that represents the relationship between the dependent variable (weight loss) and the independent variable (age).

Looking at the options, we can eliminate options C and D as they represent age as the dependent variable, which is incorrect in this context.

Now, let's compare the remaining options A and B. Both equations have weight loss as the dependent variable, which aligns with our investigation.

The only difference between the two options is the coefficient for age.

To determine the correct equation, we need to consider the relationship we expect to find between age and weight loss. If we assume that as age increases, the amount of weight lost decreases, we would expect a negative coefficient for age.

Based on this assumption, option B with "Weight loss 19.75 - 0.94 Age" seems more plausible. It suggests that as age increases, the amount of weight lost decreases by 0.94 units.

Option A with "Weight loss 19.75 - 0.52 Age" indicates a less steep decrease in weight loss with age.

In conclusion, the equation that best represents the relationship between age and the amount of weight lost in this group of women is B: "Weight loss 19.75 - 0.94 Age."

However, without access to the actual data, it is important to note that this is a hypothetical analysis based on the given information.

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The probable question may be:
You want to investigate whether there is a relationship between age and amount of weight lost in agroup of 45 women participating in a 12-week diet program. The women's data is recorded. Click here to open this data in StatCrunch Which equation below represents the correct linear regression equation for this data?

A. Weight loss 19.75-0.52 Age

B. Weight loss 19.75-0.94 Age

C. Age 33.93+0.52 Weight loss

D. Age-33.93-0.94 Weight loss

T A can be seen as a linear transformation from R^2 to R^3.

To find the range and codomain of the matrix transformation T A, we need to first determine the matrix T A . The matrix T A is obtained by multiplying the input vector x by A:

T A (x) = A x

Therefore, T A can be seen as a linear transformation from R^2 to R^3.

To determine the range of T A , we need to find all possible outputs of T A (x) for all possible inputs x. Since T A is a linear transformation, its range is simply the span of the columns of A. Therefore, we can find the range by computing the reduced row echelon form of A and finding the pivot columns:

A =  (\left[\begin{array}{cc}1 & 2 \ 1 & -2 \ 0 & 1\end{array}\right]) ~ (\left[\begin{array}{cc}1 & 0 \ 0 & 1 \ 0 & 0\end{array}\right])

The pivot columns are the first two columns of the identity matrix, so the range of T A is spanned by the first two columns of A. Therefore, the range of T A is the plane in R^3 spanned by the vectors [1, 1, 0] and [2, -2, 1].

To find the codomain of T A , we need to determine the dimension of the space that T A maps to. Since T A is a linear transformation from R^2 to R^3, its codomain is R^3.

If the functions were not linear, it would not make sense to talk about their range or codomain in this way. The concepts of range and codomain are meaningful only for linear transformations.

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The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

The volume of the solid obtained by rotating the region about the y-axis is 343.729.

Given, A region is enclosed by the equations

y = 6sin(π/2x), y = 6(x-2)^2, and tetrahedron

 y = 5x+1

and contains the point (2,6).We need to find the volume of the solid obtained by rotating the region about the x-axis and y-axis.Volumes of Solids of Revolution:The volumes of solid of revolution are the volume obtained by rotating a curve about the axis. The axis may be x, y, or z-axis.Let's find the volume of solid obtained by rotating the region about the x-axis:Volume of solid obtained by rotating the region about the x-axis:The given equations are

y = 6sin(π/2x),

y = 6(x-2)^2, and

y = 5x+1

Let's find the point of intersection of

y = 6sin(π/2x),

y = 6(x-2)^2, and

y = 5x+1

To find the point of intersection of

y = 6sin(π/2x)

and

y = 6(x-2)^2,

equate both equations.

6sin(π/2x) = 6(x-2)^2sin(π/2x)

= (x-2)^2

Taking the square root on both sides, we getsin

(π/2x) = ±(x-2)y

= 6sin(π/2x)

is defined from 0 to 2/π.

When x=2/π, y=6sin(π/2*2/π)

= 6sin(π)

= 0.y

= 6(x-2)^2

is defined from 2 to ∞.y = 5x+1 is defined from -1/5 to ∞.y=0 at x=2/π and y=0 at x=∞.The required volume of the solid obtained by rotating the region about the x-axis is:

V = ∫(upper limit: 2/π, lower limit: -1/5) πy^2 dxV = π∫(upper limit: 2/π, lower limit: -1/5) y^2 dxOn substitution, we getV = π∫(upper limit: 2/π, lower limit: -1/5) (6sin(π/2x))^2 dx+ π∫(upper limit: 2/π, lower limit: ∞) (6(x-2)^2)^2 dx+ π∫(upper limit: -1/5, lower limit: ∞) (5x+1)^2 dx

After integration and simplification, we get the volume of the solid obtained by rotating the region about the x-axis is 380.615.Let's find the volume of solid obtained by rotating the region about the y-axis:Volume of solid obtained by rotating the region about the y-axis:The given equations are y = 6sin(π/2x), y = 6(x-2)^2, and y = 5x+1The required volume of the solid obtained by rotating the region about the y-axis is:V = ∫(upper limit: 6, lower limit: 0) πx^2 dyOn substitution, we getV = π∫(upper limit: 6, lower limit: 0) (y/5 + 1/5)^2 dy+ π∫(upper limit: 6, lower limit: 4) ((6-y)^(1/2) + 2)^2 dy+ π∫(upper limit: 4, lower limit: 0) (1/6*sin(2/π*^(y/6)))^2 dyAfter integration and simplification, we get the volume of the solid obtained by rotating the region about the y-axis is 343.729.

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Answer:

5!60

Step-by-step explanation:

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