Obtain the general solution to the equation. StartFraction dy Over dx EndFraction equals StartFraction y Over x EndFraction plus 3 x plus 1 The general solution is ​y(x)equals nothing​, ignoring lost​ solutions, if any.

Step-by-step explanation:

11x+4y+13

Hope it helps you

Answer:

thanks for your support of the personal information on the direction of economics class

The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.

Then the surface area of the triangular prism will be

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (h x b) + (L₁ + L₂ + L₃) x W

The dimension of the triangle is 13 feet, 5 feet, and 12 feet. And the width of the rectangle is 6 feet.

The surface area of the triangular prism will be given as,

Surface area = 5 x 12 + (5 + 12 + 13) x 6

Surface area = 60 + 180

Surface area = 240 square feet

The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.

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Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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\((\stackrel{x_1}{6}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{j}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{j}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{6}}} \implies \cfrac{j -9}{2}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{-7}\implies j-9=-14\implies j=-5\)

Answer:

13.375 miles

Step-by-step explanation:

Hope this helps :)

Answer:

true

Step-by-step explanation:

True the table top can go on forever without touching the floor.

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Given,

The points which the line passes, (x₁, y₁) = (7, 6)

Slope of the line, m = 0

We have to find the equation of the line:

We know that,

y - y₁ = m(x - x₁)

So,

y - 6 = 0(x - 7)

y - 6 = 0

y = 6

That is,

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

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Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer: BC = 24

Step-by-step explanation:

Given:

AB = x+33

AC = 3x - 15

BC = x

<B = <C

Solution:

Because <B = <C, you can say the corresponding sides AB and AC are equal as well

AB = AC

x + 33 = 3x -15  

48 = 2x

x = 24

Since x = BC

BC = x

BC = 24

Answer:

20x

Step-by-step explanation:

It is as simple as mutiplying number of exhibits (20) by number of staff members required for each exhibit.

Answer:

length-x

width-x-4

area-- length* width

192=X*(X-4)

x^2-4x-192=0

x^2-16x+12x-192=0

X(x-16)+12(x-16)=0

(x-16),(X+12)

X= 16 because X cannot be negative like (-12)

the dimensions of the classroom will be

length = 16

width = 12

I hope this will help everyone

Answer:

-7/3

Step-by-step explanation:

Rise/Run = -4-3/1--2

= -7/3

Answer: The first one.

Step-by-step explanation:

Since 1.5 + 2.5 = 4, and the only graph that has an arrow pointing to 4 is the first one, then the first number line is the correct answer.

Hope this helps :)

The number line shows the correct total, which is 4. The others don't have the correct sum. 1.5 + 2.5 will always equal 4. Therefore, Number line A represents 1.5 + 2.5.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

Step-by-step explanation:

4(30+5)

4(30)+4(5)

120+20

140

Answer:

They are both the same

Step-by-step explanation:

(ratio of brown eyes to blue eyes)

Ms. Abbott's class- 18:12

Ms. Downey's class-  15:10

if you simplify both of the ratio's you'll get 3:2 for both of them. Therefore both classes have the same ratio of brown eyes to blue eyes.

The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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The location which is in the region for plants receiving the maximum amount of water is "(-3,-1)". The Option A is correct.

Water flows into the open pore spaces in the soil by gravity, and the size and spacing of the soil particles determine how much water can flow in. Because coarse soils have larger pore spacing at the soil surface, they have a higher infiltration rate than fine soils.

Based on the graph, we observed that the point of location in which is in the region for plants receiving the maximum amount of water is the point (-3,-1). Therefore, we agree that Option A is correct.

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Answer:

For the Broadway actors acting in their first role on Broadway, mean: 0.184, Standard Deviation: 0.063.

For the proportion of smokers, mean = 0.167, standard deviation = 0.068

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers.

This means that \(p = 0.184, n = 38\)

What are the mean and standard deviation for the sampling distribution of p^?

Mean:

\(\mu = p = 0.184\)

Standard deviation:

\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.184*0.816}{38}} = 0.063\)

Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.

This means that \(n = 30, p = 0.167\)

What is the mean and the standard deviation of the sampling distribution of p^ ?

Mean:

\(\mu = p = 0.167\)

Standard deviation:

\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.167*0.833}{30}} = 0.068\)

Answer:

I don't understand what the problem is saying... 2124...95...

Step-by-step explanation:

Answer:

Step-by-step explanation:

We shall find the solution of this problem with the help of vector notation of i , j , which show east and  north direction .

The first displacement can be represented by the following

D₁ = - 3 cos 45 i + 3 sin45 j = - 3 / √2 i + 3 / √2 j

The second  displacement can be represented by the following

D₂ = - 5 cos 45 i - 5 sin45 j = - 5 /√2 i - 5 /√2 j

The third  displacement can be represented by the following

D₃ =  4 cos 45 i + 4 sin45 j =  4 /√2 i + 4 /√2 j

Total displacement D =

D₁ +D₂ + D₃

= i ( -3 -5 + 4 ) / √2 + j ( 3 - 5 + 4 ) / √2 j

= - 4  / √2 i + 2 / √2 j

D = - 2.8288 i + 1.414 j

Magnitude of D

= √ ( 2.8288² + 1.414² )

= 3.16 miles

For direction we calculate angle with X axis

Tanθ = 1.414 / 2.8288

θ = 26 °

As x is negative and Y is positive ,

the direction will be north of west .

Answer:

12 apples is the answer because 1/2 divided by 6 is 12

Step-by-step explanation:

if /sqrt equals this \(\sqrt{21}\) then the answer lies between 4-5