find the general solution of the homogeneous differential equation (x^2-y^2)dx+(3xy)dy=0

The expression 1 over 2x + 6 in factored form is written as 1/2(x+3)

Algebraic expressions are described as mathematical operations that consist of variables, coefficients, terms, constants and factors.

They are also made up arithmetic operators, which includes;

From the information given, we have to determine the factored form of the expression;

1 over 2x + 6

This is represented as;

1/2x + 6

Let's factorize the denominator

1/2(x + 3)

Hence, the expression is 1/2(x+3)

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The time taken by cook to make one sandwich is equals to forty-five seconds.

let "x" be the time (in seconds) to make 1 sandwhich and " y " be the time (in seconds) to make 1 salad. Now, it takes 3 min 45 sec to make 3 sandwiches and 3 salads.

time in seconds , 3 min 45 sec = 225 sec

so, 3x + 3y = 225

=> x + y = 75 --(1)

Also, it takes 8 min 30 sec to make 6 sandwiches and 8 salads, i.e ,8min 30sec = 510 sec

so, 6x + 8y = 510

=> 3x + 4y = 255--(2)

We have a system of linear equations consists equation (1) and (2). We solve this system of equations by using Substitution,

Substitute the value of x = 75 - y in equation (2),

3x + 4y = 255

=> 3(75- y) + 4 y = 255

=> 225 - 3y + 4y = 255

=> y = 255 - 225 = 30

from equation (1) , x = 75 - 30 = 45.

So, it takes 45 seconds to make one sandwich and 30 seconds for one salad .

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Answer: {1024/3 r^3

Step-by-step explanation:

Similar Question

An expression for the electric field at points on the x-axis is [tex]$\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)$[/tex]

The electric field at a point P on the x-axis for which X is much larger than the distance between the charges​.

Let us consider two charge -q and +q separated by small distance 2d.

P is a point along the axial line of the dipole at a distance X from the midpoint O of the electric dipole.

The electric field at the point P due to +q placed at B

[tex]E_1=\frac{1}{4 \pi \epsilon_0} \frac{q}{(X-d)^2}[/tex]...(I)

The electric field at the point P due to -q placed at A

[tex]E_2=-\frac{1}{4 \pi \epsilon_0} \frac{-q}{(X+d)^2}[/tex]...(II)

We need to calculate the magnitude of resultant of electric field

Using formula of electric field

[tex]E=E_1+\left(-E_2\right)[/tex]

Put the value into the formula

[tex]& E=\frac{1}{4 \pi \epsilon_0} \frac{q}{(X-d)^2}-\frac{1}{4 \pi \epsilon_0} \frac{q}{(X+d)^2} \\[/tex]

[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{1}{(X-d)^2}-\frac{1}{(X+d)^2}\right) \\[/tex]

[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 X d}{\left(X^2-d^2\right)^2}\right)[/tex]

If the point P is far away from the charges, and X is much larger than the distance between the charges

The electric field will be

[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 X d}{X^4}\right) \\[/tex]

[tex]& E=\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)[/tex]

Hence, the electric field will be [tex]$\frac{q}{4 \pi \epsilon_0}\left(\frac{4 d}{X^3}\right)$[/tex]

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Derive an expression for the electric field at a point P on the x-axis for which X is much larger than the distance between the charges​.

The coefficient of y in the expression -2x² * y² * z is 0

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

An algebraic expression

The algebraic expression is given as

- 2x ^ 2 * y ^ 2 * z

Express the exponents as proper subscripts

So, we have the following representation

-2x² * y² * z

There is no term in the expression with the variable y

Instead, the term has a y² as its variable

This means that the coefficient of y is 0

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Answer:The answer is -18

Step-by-step explanation: Add -13+5 and you will get the correct answer.

Answer: 3 words

Step-by-step explanation:

what is 9 in a fraction

The distance between two points is D and E, E and F, C and D, A and B, B and C, when the points are arranged in increasing order.

Discover the distance formula, a Pythagorean theorem application, to determine the separation between two places. To get the separation between any two points, we can rewrite the Pythagorean theorem as [tex]d= \sqrt{x_{2} -x_{1} + y_{2} -y_{1} }[/tex]

In geometry, distances are always positive unless the points are exactly adjacent. The distance between A and B is equal to the distance between B and A. We consider two points A(a,b) and B to get the formula for the distance between two points in the plane (c,d).

[tex]d= \sqrt{x_{2} -x_{1} + y_{2} -y_{1} }[/tex]

The distance is provided in the following equation as

A and B are [tex]\sqrt{39}[/tex] miles apart.

B and C are [tex]\sqrt{41}[/tex] miles apart.

C and D are five miles apart.

D and E are four miles apart.

E and F are [tex]\sqrt{17}[/tex] miles apart.

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Answer:

Step-by-step explanation:

you have to count the distance between each point then list them from smallest to greatest. The other answers on here made it more convoluted than necessary.

Answer:

6

Step-by-step explanation:

There is a 0.5 probability that the first toss and the last toss yield different outputs.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The sample space for a coin tossed three times is:

P = {HHH, HTH, HHT, HTT, TTT, THH, THT, TTH}

Now, out of this, we have to find the probability that the first and last toss are different results, i.e., if first toss is heads then last toss should be tails, and vice-versa.

The sample space for this is:

P = {HHT, HTT, THH, TTH}

The probability is:

[tex]P = \frac{4}{8} = \frac{1}{2}[/tex]

Therefore, there is a 0.5 probability that the first toss and the last toss yield different outputs.

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There is a 0.5 probability that the first toss and the last toss yield different outputs.

Now, According to the question:

Let's know:

What is probability and example?

It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.

The sample space for a coin tossed three times is:

P = {HHH, HTH, HHT, HTT, TTT, THH, THT, TTH}

Now, out of this, we have to find the probability that the first and last toss are different results, i.e., if first toss is heads then last toss should be tails, and vice-versa.

The sample space for this is:

P = {HHT, HTT, THH, TTH}

Probability = Number of Favorable Outcomes / Total Number of Outcomes.

P = 4/8 = 1/2
Therefore, there is a 0.5 probability that the first toss and the last toss yield different outputs.

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The total amount the homeowner would pay for the damages would be $5,150.

In this situation, the homeowner would pay $5,000 for the deductible, plus the premium of $150. The remaining amount of $165,000 would be covered by the policy up to the limit of $300,000. Therefore, the total amount the homeowner would pay for the damages would be $5,150.

To calculate this, we can use the following formula:

Total Cost = Deductible + Premium + (Damages - Limit)

Total Cost =[tex]$5,000 + $150 + ($170,000 - $300,000)[/tex]

Total Cost =[tex]$5,000 + $150 + (-$130,000)[/tex]

Total Cost = [tex]$5,150[/tex]

The total amount the homeowner would pay for the damages would be 5,150.

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The loan amount that Ahmad needs to relay will be RM 901600

From the information, Ahmad obtained a car loan of RM 700000 from a bank with an interest rate of 3.2% per annum for 9 years.

The interest based on the information will be:

= Principal × Rate × Time

= 700000 × 3.2% × 9

= $201600

The loan amount that Ahmad needs to relay will be:

= 700000 + 201600

= 901600

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The equation of this parabola in vertex form is y = ( -1/2) x² - 0.5

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We are given that Focus (0,-1), Directrix is the line y=0

so, we have a vertical parabola open downward

Remember that the distance from the vertex to the directrix must be the same that the distance from the vertex to the focus

This means that the vertex is the point (0,-0.5)

The midpoint between the focus and the directrix

Find out the value of p (focal distance)

p=0.5

The equation of the parabola is given by

y =( -1/2) x² - 0.5

The vertex is (0,-0.5)

The value of p=0.5

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The line of best fit for the data that is present is Line C. Option C

We have to note that the graph is one of the means by which we can be able to present information. We know that the information that we present in the graph model would have to axes. It would have the x axis and it would have the y axis.

Now, we know that the plot of the graph is going to result in data points on the graph and the data points on the graph are the points that we can be able to use determine which of the lines would be the line of best fit of the data that we have.

Looking up the models that we have we can see that the best line would have a line that fit into most of the points that occur in the graph and would be the best regression line.

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The System of Linear Equations with at least one solution is called as Consistent .

Consider the two linear equations , [tex]a_{1}x +b_{1}y =c_{1}[/tex] and [tex]a_{2}x +b_{2}y =c_{2}[/tex] ;

Case(i) If the ratio is [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex] ,

then we say that the system of linear equations has a unique solution and the solutions are called as consistent .

Case(ii) If the ratio is [tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]  ,

then we say that the system of linear equations has infinitely many solution and the solutions are called as consistent .

Case(iii) If the ratio is [tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]  ,

then we say that the system of linear equations has No Solution and the solutions are called as inconsistent .

So , if the system has at least one solution , then the solutions are consistent .

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Answer: D. y = 1/2x + 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 1/2

y-intercept: (0,3)

x|y

0|3

2|4

Hope this helps :D

Graph of a sine function ,The sinusoidal graph, often known as the sine graph, is an up-down graph that repeats every 360 degrees, or at 2[tex]\pi[/tex]. Amplitude is 7

Graph of a sine function ,The sinusoidal graph, often known as the sine graph, is an up-down graph that repeats every 360 degrees, or at 2[tex]\pi[/tex].

Trigonometric functions include sine functions. Keep in mind the intercepts, maximum points, and minimum points throughout one period if you wish to sketch the graph of the fundamental sine function. As a result, the graph is  h(x) = 7 sin x depicted in the image below.

h(x) = 7 sin x

Those intercepts are

(0 0) , ([tex]\pi[/tex] ,0) ,  and (2[tex]\pi[/tex], 0)

A maximum of:

([tex]\pi[/tex]/2 , 7)

Minimum score:

(3[tex]\pi[/tex]/2 , -7)

Period:

2[tex]\pi[/tex]

Amplitude = 7

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4,067.2

Step-by-step explanation:

—4067.23

You rounded to the nearest tenths place. The 2 in the tenths place rounds down to 2, or stays the same, because the digit to the right in the hundredths place is 3.

4,067.2

When the digit to the right is less than 5 we round toward 0.

4067.23 was rounded down toward zero to 4,067.2

Answer:

72 m

93 m

Step-by-step explanation:

1)  A = length x width

6264 m² = (87 m)w

w = 6264 m²/87 m = 72 m

2)  P = 2l + 2w

342 m = 2l + 2(78 m)

342 m - 156 m = 186 m = 2l

l = 186 m/2 = 93 m

Answer:

1/2

Step-by-step explanation:

The slope of a line is defined as the change in y-value divided by the change in x-value between two points on the line. To find the slope of the line joining (1, 4) and (-3, 2), we can use the formula:

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

Plugging in the coordinates of the two points, we get:

slope = (2 - 4) / (-3 - 1)

slope = -2 / -4

slope = 1/2

So the slope of the line joining (1, 4) and (-3, 2) is 1/2.

Answer:

1/2

Step-by-step explanation:

Answer:

To find the area of a triangle, you use the following formula:
[tex]\frac{1}{2}[/tex] x base x height

= [tex]\frac{1}{2}[/tex] x 13 x 4

= 6.5 x 4

= 26

If the Wardrobe consists of 2 shirts , 3 pair of pants and 16 bow ties , then the number of different outfits that can be made are 96 outfits .

The number of shirts in the Wardrobe is = 2  shirts ,

The number of pairs of pants in the wardrobe is = 3 pairs of pants ,

the number of bow ties in the wardrobe is = 16 bow ties ,

The number of different outfits that can be made from the wardrobe  can be calculated by the Multiplication Principle ;

That means , the number of different outfits made is = (number of shirts) × (number of pair of pants ) × (number of bow ties )

substituting the values ,

we get ,

= 2 × 3 × 16 ,

= 6 × 16 ,

= 96 .

Therefore , 96 different outfits can be made from the Wardrobe .

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By using probability You can mix and match the two shirts, three pairs of pants, and sixteen bow ties to create 48 different outfits.

To calculate the number of possible outfits, you would first multiply the number of shirts (2) and pants (3) to get 6. Then, you would multiply 6 and the number of bow ties (16) to get 96. Finally, you would divide 96 by the number of shirts (2) to get 48

2 x 3 = 6

6 x 16 = 96

96 / 2 = 48

You can create different outfits by mixing and matching the items in your wardrobe. To calculate the number of possible outfits, you would first multiply the number of shirts (2) and pants (3) to get 6. Then, you would multiply 6 and the number of bow ties (16) to get 96. Finally, you would divide 96 by the number of shirts (2) so that each shirt is accounted for only once, resulting in 48 different outfits.

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The probability that Larry wins the game is [tex]$\tfrac{1}{2}$[/tex].

The probability that Larry knocks the bottle off the ledge on his first throw is

[tex]$\tfrac{1}{2}$.[/tex]

The probability that Larry knocks the bottle off the ledge on his second throw, given that he did not knock it off on his first throw, is

[tex]$\tfrac{1}{2}$[/tex]

Therefore, the probability that Larry wins the game is

[tex]$\tfrac{1}{2} \times \tfrac{1}{2} = \tfrac{1}{2}$.[/tex]

By the law of total probability, we have:

[tex]$P(W) = P(W|F)P(F) + P(W|F^c)P(F^c)$[/tex]

[tex]$P(W) = 1 \times \tfrac{1}{2} + \tfrac{1}{2} \times \tfrac{1}{2}$[/tex]

[tex]$P(W) = \tfrac{1}{2}$[/tex]

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Answer:  33.3% , 6.25%, 12.5%, 83.3%

Step-by-step explanation:

What percent of the pies are apples?

Number of apples = 80

Total pies = 240

Percentage of apple pies = 80/240 x 100% = 33.3% (3sf)

What percent of the pies are key lime?

Number of keylime = 15

Total pies = 240

Percentage of keylime pies = 15/240 x 100% = 6.25%

What percent of the pies are blueberry?

Number of blueberry = 30

Total pies = 240

Percentage of blueberry pies = 30/240 x 100% = 12.5%

What percent of the pies are NOT peach?

Number of peach = 40

Total pies = 240

Percentage of peach pies = 40/240 x 100% = 16.667%

Hence, percentage NOT peach pies = 100% - 16.667%

                                                             = 83.3% (3sf)

Answer:

5) 33%

6) 12.5%

7) 6.25%

8) 83%

Step-by-step explanation:

Not sure if this is a troll but I'll explain it to the best of my understanding:

5) Apple: 80/240 = 1/3 or 33%

You divide the # of apple pies by the # of total pies

6) Blueberry: 30/240 = 0.125 or 12.5%

You divide the # of blueberry pies by the # of total pies

7) Key Lime: 15/240 = 6.25%

8) There's 40 peach pies so you subtract 40 from 240. That leaves you with 200. So you do 200/240 and you get about 83%

The expansion of the trinomial 10x² - 61 x + 72 is (2x - 9) (5x - 8).

An algebraic expression known as a trinomial has three non-zero terms and more than one variable. An example of a trinomial is a polynomial having three terms. An algebraic expression with one or more terms is called a polynomial.

Given:

10x² - 61 x + 72

Calculate the roots of the trinomial as shown below,

10x² - 16 x - 45 x + 72

2x  (5x - 8) - 9(5x - 8)

(2x - 9) (5x - 8)

Thus, the expansion of the trinomial is (2x - 9) (5x - 8).

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The Riemann sum formula to find RN is RN = (5/n) × Σ(i=1 to n) [f(x_i) × (5/n)], and the area under the graph as a limit is 400.

The function f(x) = (5x)² is a polynomial function, and we can use the formula for the nth Riemann sum to find RN. The formula for the nth Riemann sum is:

RN = (5/n) × Σ(i=1 to n) [f(x_i) × (5/n)]

where x_i = -1 + (i-1)(5/n) and f(x_i) = (5x_i)²

Substituting these values into the formula, we get:

RN = (5/n) × Σ(i=1 to n) [(5x_i)² × (5/n)]

RN = (5/n) × Σ(i=1 to n) [(25x_i²) × (1/n)]

Therefore the formula for RN is (5/n) × Σ(i=1 to n) [(25x_i²) × (1/n)]

To find the area under the graph as a limit, we take the limit as n approaches infinity:

limN→[infinity] RN = limN→infinity × Σ(i=1 to n) [(25x_i²) × (1/n)]

The function is defined on the closed interval [-1,5], so the definite integral is the definite integral from -1 to 5 of (25x²) dx

limN→[infinity] RN = (25/3) × 5³ - (25/3) × (-1)³

limN→[infinity] RN = (25/3)×(125 -1)

limN→[infinity] RN = 400

Therefore, limN→[infinity] RN = 400

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Answer:

7

Step-by-step explanation:

Answer:
7

If this help please set brainliest.

Step-by-step explanation:

To find the length between Point A (-3,4) and Point B (4,4), we can use the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates, we get:

distance = √((4 - (-3))^2 + (4 - 4)^2)

Simplifying this, we get:

distance = √(7^2 + 0^2)

Simplifying further, we get:

distance = √49

So the distance between Point A and Point B is approximately 7.

The regular price of the soda is $1.59

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

Number of bottles = 5

Total cost = 5.20

Coupon = 0.55

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

Total cost = Number of bottles * (Regular price - Coupon)

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

5 * (Regular price - 0.55) = 5.20

So, we have

Regular price - 0.55 = 1.04

Add 0.55 to both sides

Regular price = 1.59

Hence, the regular price is 1.59

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Answer:

Here is a table to organize the information given:

Type of Bug Number of Bugs Number of Legs

Ants x 2x

Spiders 54 - x 350 - 2x

We are trying to find the value of x, which is the number of ants that Angelica has. We know that the total number of legs is 350 and the number of legs on the ants is 2x, so we can set up the equation:

350 = 2x

To solve for x, we can divide both sides by 2:

x = 350 / 2

= 175

Therefore, Angelica has 175 ants in her collection. The number of spiders in her collection is 54 - x = 54 - 175 = -121. This is not possible, because it is not possible to have a negative number of bugs. This means that the initial assumption that x represents the number of ants is incorrect, and there must be a different solution.

Alternatively, we could assume that x represents the number of spiders in Angelica's collection. In this case, the equation would be:

350 = (54 - x) * 8

Solving for x, we find that x = 27, so Angelica has 27 spiders in her collection. This is a valid solution, because it is possible to have 27 spiders and 27 ants in a collection of 54 bugs.

Step-by-step explanation:

The numerical length of BD is 16 units

as given in the question,

There is a line segment BD

and a point lies on the line segment BD which is point C

but we don't know the exact position where the point C lies on the line segment BD

from the details given

The distance between C and B is x

the distance between B and D is 2x

the distance between C and D is 8

let the point C be a arbitrary point in the line segment BD

now ,

BC + CD = BD

x + 8 = 2x

x = 8

now  BD is 2x that is 2( 8) is 16

The length of BD is 16.

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The numerical length of [tex]\overline{bd}[/tex] is 16 units.

Using the formula for the length of a line segment, we can calculate the length of segment BD. The formula is

Length = [tex]√((x2-x1)^2+(y2-y1)^2)[/tex]

We know that BD = 2x so x2 = 2x and x1 = 0. We also know that CD = 8 and BC = x so we can calculate y2 and y1. y2 = 8 - 2x and y1 = x - 0.

Therefore, plugging in these values we get:

Length =[tex]√((2x-0)^2+(8-2x)^2)[/tex]

Solving for the length of BD we get:

Length = [tex]√(4x^2 + 64)[/tex]

Substituting in the value of x = 8, we get:

Length = [tex]√(4*8^2 + 64)[/tex]

Length = [tex]√(256 + 64)[/tex]

Length = [tex]√320[/tex]

Length = 16 units.

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