Function 1 is defined by the equation y =
; 3
- 2
- 1
Function 2 is defined by the following table.
0
3
7
11
-2
-8
-16
- 24
Which function has a more negative slope ?

the general solution of the given differential equation is:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

To find the general solution of the given differential equation:

(x^2 - 4) dy/dx + 4y = (x + 2)^2

We can rearrange the equation to isolate the derivative term:

dy/dx = [(x + 2)^2 - 4y] / (x^2 - 4)

First, let's simplify the numerator:

[(x + 2)^2 - 4y] = (x^2 + 4x + 4) - 4y

= x^2 + 4x + 4 - 4y

= x^2 + 4x - 4y + 4

Now, substitute this simplified expression back into the differential equation:

dy/dx = (x^2 + 4x - 4y + 4) / (x^2 - 4)

This is a first-order linear homogeneous differential equation. To solve it, we can use the integrating factor method.

First, let's write the equation in the standard form: dy/dx + P(x)y = Q(x)

dy/dx + (4x / (x^2 - 4))y = (x^2 + 4x + 4) / (x^2 - 4)

The integrating factor is given by the exponential of the integral of P(x):

μ(x) = exp ∫ (4x / (x^2 - 4)) dx

To find the integral, we can use substitution. Let u = x^2 - 4, then du = 2x dx:

μ(x) = exp ∫ (2x dx) / (x^2 - 4)

= exp ∫ (du / u)

= exp(ln|u|)

= |u|

Substituting back u = x^2 - 4:

μ(x) = |x^2 - 4|

Now, multiply the entire differential equation by the integrating factor:

|x^2 - 4| dy/dx + (4x / (x^2 - 4)) |x^2 - 4|y = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

The left side can be simplified using the product rule for differentiation:

d/dx [ |x^2 - 4|y ] = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

Now, integrate both sides with respect to x:

∫ d/dx [ |x^2 - 4|y ] dx = ∫ (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4) dx

Integrating the left side gives:

|x^2 - 4|y = ∫ (x^2 + 4x + 4) dx

= (1/3) x^3 + 2x^2 + 4x + C1

where C1 is the constant of integration.

Finally, divide both sides by |x^2 - 4| to solve for y:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

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Answer:

D. -60 + (-30) = -30

Step-by-step explanation:

Put the word problem into an equation: -60 + (-30) = -30

I hope this helped, please mark Brainliest, thank you so much!!

Answer:

5.989x10 with the power of 0

Step-by-step explanation:

Can I have crown?

Answer:

1,688 items

Step-by-step explanation:

So they had at total of 2,150 items at the start of the year. They had 400 sweatshirts, now they have 96(a decrease of 304), 650 T-shirts now they have 139(a decrease of 511), and 1100 notebooks to 227(a decrease of 873). They now have 462 items left. This means that they sold 1,688 items.

Hope this helps.

The series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other is a combination of translation and rotation that involves 150 degrees. A transformation refers to the process of changing an object's position, size, or shape.

Translation, reflection, rotation, dilation, and skew are the five basic transformation types that modify an object.In geometry, congruent shapes have the same shape and size. To superimpose one shape onto another means to make them coincide with each other.

The following series of transformations would show that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other: Step 1: Translation. Translate the parallelogram ABCD by 5 units to the right and 6 units down to obtain parallelogram A1B1C1D1.Step 2: Rotation. Rotate parallelogram A1B1C1D1 by 150 degrees counterclockwise around point A1 to obtain parallelogram A2B2C2D2.Step 3: Translation. Translate parallelogram A2B2C2D2 by 8 units to the right and 3 units up to obtain parallelogram A'B'C'D'.Thus, the series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other involves translation and rotation, with a rotation of 150 degrees.

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Answer:

x<8

Step-by-step explanation:

2x+5>3x-3

2x+8>3x

8>x

Answer:

n < 8

Step-by-step explanation:

Let n represent the unknown number.  Then:

2n + 5 > 3n - 3

Collecting like terms:

8 > n or n < 8

The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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If the individual switches to a hybrid car, they will save approximately 8,021.24 gallons of gas in a year for their commute.

To determine how much gas the individual will save if they switch to a hybrid vehicle, we need to calculate the total amount of gas consumed by both the current car and the hybrid car.

First, let's calculate the total number of miles driven by the individual in a year:

Total number of miles driven = 6060 miles/week x 52 weeks = 315,120 miles

Next, let's calculate the total amount of gas consumed by the current car in a year:

Gas consumption of current car = Total number of miles driven / Miles per gallon of current car

= 315,120 miles / 22 miles per gallon

= 14,323.64 gallons

Now, let's calculate the total amount of gas that will be consumed by the hybrid car in a year:

Gas consumption of hybrid car = Total number of miles driven / Miles per gallon of hybrid car

= 315,120 miles / 50 miles per gallon

= 6,302.4 gallons

Therefore, the individual will save:

Gas saved = Gas consumption of current car - Gas consumption of hybrid car

= 14,323.64 gallons - 6,302.4 gallons

= 8,021.24 gallons

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Answer:

Itt takes Kelly 50 minutes to type 6 pages.

Step-by-step explanation:

First, find out how mant words per minute:  

210/5 = 42

This means 42 words are typed per minute.

Second, see how long it takes to type one page:

350/42 = 8 1/3

Last, multiply that by 6:

8 1/3*6 = 50

Final answer: it takes 50 minutes to type 6 pages.

Answer:

what is A and B

Step-by-step explanation:

I need more info pls

Answer:

B is correct.

Step-by-step explanation:

On number line and sequencing also, -3 is less than -2.

Answer:

b is correct -2 is less than-3

The correct statements about similarity of triangles are A, B, and C.

Similar triangles are triangles that have the same shape, but their sizes may vary. This type of triangles are said to have congruent angles and corresponding sides.

From the given figure,

Thus, the correct statements about similarity of triangles are A, B, and C.

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Answer:

  A, B, C

Step-by-step explanation:

In this figure, all of the right triangles are similar, easily shown using the AA similarity postulate. The idea here is to correctly identify the names of the similar triangles. We can do that by naming the triangles this way:

  shortest side - right angle vertex - longest side

__

Starting with the largest triangle, and working toward the smallest, we can identify the similar triangles as ...

  ΔABC ~ ΔBDC ~ ΔADB

From this statement, we can readily match choices A and B.

__

If we reorder the last two vertices in each similarity statement above, we get ...

  ΔACB ~ ΔBCD ~ ΔABD

We can match the last part of this similarity statement to choice C.

__

We note that points A, D, C are collinear, so do not form a triangle. This eliminates choice D.

  Similarity statements A, B, and C are true.

The type of transformation that preserves the symmetry is Vertical translation.

For instance, a parabola is still symmetric about the y-axis if you move it up. It loses its symmetry if you move it to the left or right. Reflection keeps both even and odd functions symmetrical.

The symmetry of a function is described using the terms even and odd. On a graph, an even function is symmetric about the y-axis. An odd function has symmetric behavior around a graph's origin \((0, 0)\). This means that if you rotate an odd function 180 degrees around the origin, the function you started with will still exist.

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Answer:

2  3/5 * 1  5/3

Step-by-step explanation:

Answer:

1\(\frac{5}{8}\)

Step-by-step explanation:

When working with mixed numbers, the first thing you would want to do is make them into improper fractions so that they are easier to work with.

2\(\frac{3}{5}\) ÷ 1\(\frac{3}{5}\) = \(\frac{13}{5}\) ÷ \(\frac{8}{5}\)

To change the ÷ sign to a × sign, swap the denominators and the numerators of the second fraction.

\(\frac{13}{5}\) ÷ \(\frac{8}{5}\) = = \(\frac{13}{5}\) × \(\frac{5}{8}\)

Directly multiply. (Numerators with numerators and denominators with denominators)

\(\frac{13}{5}\) × \(\frac{5}{8}\) = \(\frac{65}{40}\)

Simplify to mixed numbers.

\(\frac{65}{40}\) = 1\(\frac{25}{40}\)

1\(\frac{25}{40}\) = 1\(\frac{5}{8}\)

So, there are 3 more "parts" of students than of adults (5 - 2), right?

Those 3 parts are made up of 12 people.

12/3 = 4 people per part

2(4) = 8 adults

5(4) = 20 students

Answer:

2/5=8

Step-by-step explanation:

Answer:

x=-9

Step-by-step explanation:

M(slope)=y2-y1/x2-x1

m=-5-5/-9+9

m= -10/0

This means the slope is undefined. Whenever the slope is undefined, the line is vertical and is passing through the x-axis and parallel to the y-axis. Take the given coordinate (-9,5) and all you do is put x= -9. That's the equation of the line.

Answer:

==================================

Work Shown:

L = 5 = length

W = 2 = width

H = 1.7 = height

V = volume

V = L*W*H

V = 5*2*1.7

V = 17 cubic units

The only critical point of the function f is  (-0.216, -0.308).

To find the critical point(s) of the function f, we need to solve the system of equations ∇f(x,y) = 0:

∂f/∂x = xlny + 2 = 0

∂f/∂y = 6x + y + 2 = 0

From the second equation, we can solve for y in terms of x:

y = -6x - 2

Substituting this into the first equation, we get:

xln(-6x - 2) + 2 = 0

To find critical points we use numerical methods to find an approximate solution.

x = -0.216

Substituting this value of x back into the equation y = -6x - 2, we get:

y = -0.308

Hence, the only critical point of the function f is  (-0.216, -0.308).

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20 students are selected at random from each grade level, of random sampling within each stratum.

A random sample from each grade level, the survey plan ensures that each grade level is represented in the sample, and that the sample is likely to be representative of the entire school population.

The survey plan described in the question is a combination of two different sampling techniques:

stratified sampling and random sampling.

Stratified sampling involves dividing the population into subgroups, or strata, based on certain characteristics that are relevant to the research question.

The population is divided by grade level, which is likely to be a relevant factor when it comes to determining student support for the student-council president.

The purpose of stratified sampling is to ensure that each subgroup is represented in the sample in proportion to its size in the population.

This helps to minimize sampling bias and increase the precision of the estimates obtained from the sample.

Once the population is divided into subgroups, random sampling is used to select a sample from each stratum.

Random sampling involves selecting individuals from the population in such a way that each individual has an equal chance of being selected.

This helps to ensure that the sample is representative of the population and that any estimates obtained from the sample are unbiased.

In this survey plan, 20 students are selected at random from each grade level, which is an example of random sampling within each stratum.

By selecting a random sample from each grade level, the survey plan ensures that each grade level is represented in the sample, and that the sample is likely to be representative of the entire school population.

Overall, the survey plan described in the question is a good example of how different sampling techniques can be combined to obtain a representative sample of a population.

By using stratified sampling to divide the population into subgroups and random sampling to select individuals from each subgroup, the survey plan helps to minimize sampling bias and increase the precision of the estimates obtained from the sample.

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Answer:

  see attached for a graph

Step-by-step explanation:

It looks like you want to plot a graph of the function. For a piecewise function like this one, the effort is divided into pieces. The "or equal to" part of the comparison symbol tells you the end value is included in that interval.

__

For the piece between x=-8 and x=-6, you can find the y-values by evaluating the function for those x-values.

For x = -8: y = -1/2(-8) = 4.

For x = -6: y = -1/2(-6) = 3.

So, the left piece can be plotted by drawing a line segment between points (-8, 4) and (-6, 3).

__

For the piece between x=-6 and x=1, you can do the same thing:

For x=-6: y = -(-6) -3) = 6-3 = 3

For x=1: y = -(1) -3 = -4

So, the right piece can be plotted by drawing a line segment between points (-6, 3) and (1, -4). We notice that (-6, 3) is already the end point of the first piece, so the function is continuous at x=-6. (Sometimes there is a discontinuity between pieces. Not here.)

You can also plot the right piece by recognizing it is a line with a y-intercept of -3 and a slope of -1. That is, point (0, -3) will be on that line, and it will have a "rise" of -1 for each "run" of 1 (to the right).

__

A graph is shown. We have made the pieces different colors, so you can see what they are. And we have plotted a filled dot at (-6, 3) to indicate that point is part of the function definition. (The dot is unnecessary.)

The scale factor used in the dilation is 3

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

Image = 9

Pre-image = 3

The scale factor is calculated as

Scale factor  = Image/Pre-Image

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = 9/3

Evaluate

Scale factor  = 3

Hence, the scale factor is 3

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Answer:

The area of the space that will be covered bricks is 4/15 ft^2

Step-by-step explanation:

Here, we are interested in calculating the area of the space that will be covered by bricks.

This can be obtained directly by finding the area of the rectangular shape;

Mathematically;

area of a rectangle = L * B

Since we have both measurements already;

Then the area of the space will be 3/5 * 4/9 = 12/45 = 4/15 ft^2

Given that we have to find the probability of each of the following when we roll a pair of fair dice:

Probability of getting a sum of 1 = 0

Probability of getting a sum of 5= {4}/{36}=0.1111

Probability of getting a sum of 12= {1}/{36}= 0.0278

Explanation: When we roll a pair of dice, there are 36 possible outcomes or events. When we roll the dice, the number on the dice will be an integer from 1 to 6.

The following table represents the possible outcome when we roll a pair of dice.

There is only one way to obtain the sum of 1, i.e., when both dice show 1. As there is only one way, the probability is 0.

There are 4 possible ways to obtain the sum of 5. They are (1,4),(2,3),(3,2),(4,1). The probability is 4/36.

There is only one way to obtain the sum of 12, i.e., when both dice show 6. As there is only one way, the probability is 1/36.

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To find a vector normal to the sphere at the point P(4), we need to compute the partial derivatives of the parametric equation and evaluate them at the given point.

The parametric equation of the sphere is given by: x(u, v) = cos(u) cos(v); y(u, v) = sin(u) cos(v); z(u, v) = sin(v). Taking the partial derivatives with respect to u and v, we have: ∂x/∂u = -sin(u) cos(v); ∂x/∂v = -cos(u) sin(v); ∂y/∂u = cos(u) cos(v);∂y/∂v = -sin(u) sin(v); ∂z/∂u = 0; ∂z/∂v = cos(v). Now, we can evaluate these derivatives at the point P(4):  u = 4; v = √2. ∂x/∂u = -sin(4) cos(√2); ∂x/∂v = -cos(4) sin(√2); ∂y/∂u = cos(4) cos(√2); ∂y/∂v = -sin(4) sin(√2); ∂z/∂u = 0;∂z/∂v = cos(√2). So, the vector normal to the sphere at the point P(4) is given by: N = (∂x/∂u, ∂y/∂u, ∂z/∂u) = (-sin(4) cos(√2), cos(4) cos(√2), 0).

Therefore, the vector normal to the sphere at the point P(4) is (-sin(4) cos(√2), cos(4) cos(√2), 0).

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Taking a difference, we can see that the trip to city C is 482.6 mi longer.

Here we know that the distance from city a to city b is 256.8 miles, and the distance from city a to city c is 739.4 miles

To find how much farther is the trip to city c than the trip to city b, we just need to take the difference between the two distances above.

That means that we need to take the distance to city c and subtract the distance to city b.

We will get:

739.4 mi -  256.8 mi = 482.6 mi

The trip to city C is 482.6 mi more than the trip to city B.

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The choice that best represents David monthly interest rate is 0.625%. The correct option is C.

From the information, David opens a savings account with a 7.5% annual interest rate.

It should be noted that there are 12 months in a year.

Therefore, the monthly interest rate will be:

= Annual interest rate / Number if months in a year

= 7.5% / 12

= 0.625%

The interest is 0.625%.

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Complete question

David opens a savings account with a 7.5% annual interest rate. Which choice best represents his monthly interest rate?

A. 7.5%

B. 12%

C. 0.625%

D. 5%

Answer:

Step-by-step explanation:

Complement angle is the sum of two angles forming a right angle.

Follow the given steps to find the angle:

< a + 65° = 90°

< a = 90 - 66

< a = 25°

Sample mean of 2.4% or higher is somewhat unlikely to occur by chance alone, and may indicate that the true mean childhood asthma prevalence in the sampled cities is higher than the Population mean of 2.16%.

We can use the Central Limit Theorem (CLT), which states that the sample mean of a sufficiently large sample size from a population with any distribution will be approximately normally distributed. The mean of the sampling distribution of the sample mean will be the same as the population mean, and the standard deviation of the sampling distribution of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

In this problem, we are given that the population standard deviation sigma is 1.27%, the population mean mu is 2.16%, and the sample size n is 34. Therefore, the standard error of the sample mean is:

standard error = sigma / sqrt(n) = 1.27% / sqrt(34) = 0.218%

The probability that the sample mean is greater than 2.4%, we need to standardize the sample mean using the formula:

z = (x - mu) / standard error

where x is the sample mean. Substituting the given values, we get:

z = (2.4% - 2.16%) / 0.218% = 1.10

Using a standard normal table or calculator, we find that the probability of a standard normal random variable being greater than 1.10 is approximately 0.1379. Therefore, the probability that the sample mean is greater than 2.4% is 0.1379, or about 13.79%.

Interpreting this probability, we can say that if we take many random samples of size 34 from the population of 43 cities and compute the sample mean for each sample, about 13.79% of these sample means will be greater than 2.4%. This suggests that a sample mean of 2.4% or higher is somewhat unlikely to occur by chance alone, and may indicate that the true mean childhood asthma prevalence in the sampled cities is higher than the population mean of 2.16%.

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