Identify the numerical coefficient of the terms (other than the constants) in the following expressions. (a)5x - 6 (b) 6-4g2 (c) 2x2+4y3 (d) -29y3+0ꓸ1z-3.14

The equation of the line that is parallel to y=-5x+6 and passes through the point (-4,-1) is y = -5x-21.

Given data :

Here, given equation of line is y = -5x+6

Required line is parallel to this given line, so we can say that the slope is same for the lines.

General equation of a line be y = mx+c ,  where m is the slope

Comparing given equation with this equation we get,

m = -5

The required line also passes through the point (-4, -1)

Now, we know that,

m = (y2-y1)/(x2-x1).

⇒ -5 = (-1 - Y ) / ( -4 - x )

⇒ -5 = y + 1 / x + 1

⇒ y+1 = -5x-20

⇒ y = -5x-21

Hence the equation proved.

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The general solution of the given system is x(t), y(t)  = -c₁e^(-t) + c₂e^(8t), c₁e^(-t) + 2c₂e^(8t)

To find the general solution of the given system of first-order linear differential equations, we can use matrix notation. The system is:

dx/dt = 2x + 3y

dy/dt = 6x + 5y

We can rewrite this system as:

d(X)/dt = A * X

Where X = [x, y]^T is the state vector, and A is the matrix of coefficients:

A = | 2 3 |

| 6 5 |

Now we need to find the eigenvalues and eigenvectors of matrix A.

First, find the characteristic equation:

| A - λI | = 0

| (2-λ) 3 | = 0

| 6 (5-λ) |

(2-λ)(5-λ) - (3)(6) = 0

λ^2 - 7λ - 8 = 0

The eigenvalues are λ1 = -1 and λ2 = 8.

Next, find the eigenvectors for each eigenvalue:

For λ1 = -1:

| 3 3 | |x1| = |0|

| 6 6 | |y1| = |0|

x1 = -y1

We can choose x1 = 1 and y1 = -1, so the eigenvector is v1 = [1, -1]^T.

For λ2 = 8:

| -6 3 | |x2| = |0|

| 6 -3 | |y2| = |0|

-6x2 + 3y2 = 0

x2 = y2 / 2

We can choose y2 = 2 and x2 = 1, so the eigenvector is v2 = [1, 2]^T.

Now we can write the general solution of the given system:

X(t) = C1 * e^(-t) * v1 + C2 * e^(8t) * v2

X(t) = C1 * e^(-t) * [ 1, -1]^T + C2 * e^(8t) * [1, 2]^T

Therefore, the general solution is:

x(t) = -C1 e^(-t) + C2 e^(8t)

y(t) = C1 e^(-t) + 2C2 e^(8t)

The above answer is based on the full question below;

Find The General Solution Of The Given System. Dx/Dt = 2x + 3y Dy/Dt = 6x + 5y X(T), Y(T) =

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(a) The break-even point for Joyful Journeys Music School is 32 students per month or $3,200 in revenue.

(b) After considering the increase in rent and instrument rent, the new break-even point for Joyful Journeys is 35 students per month.

Joyful Journeys Music School offers private music lessons for elementary students and incurs various operating costs. To determine the break-even point, we need to find the number of students or revenue required to cover all the costs.

(a) In the given scenario, the monthly fixed costs consist of rent on facilities ($2,200), advertising ($274), and instrument rent ($750), totaling $3,224. The variable costs per student include teaching instruction ($40), books ($5), and other costs ($3), amounting to $48 per student. The revenue per student is $100.

To find the break-even point in the number of students, we divide the total fixed costs by the contribution margin per student. The contribution margin is the difference between the revenue per student and the variable costs per student. In this case, the contribution margin is $100 - $48 = $52.

Break-even point in students = Total fixed costs / Contribution margin

Break-even point in students = $3,224 / $52 = 62 students

Therefore, the break-even point for Joyful Journeys Music School is 62 students per month.

To determine the break-even point in dollars, we multiply the break-even point in students by the revenue per student.

Break-even point in dollars = Break-even point in students * Revenue per student

Break-even point in dollars = 62 students * $100 = $6,200

(b) Considering the increase in rent by $500 and instrument rent by $20, the monthly fixed costs would be $3,744 ($3,224 + $500 + $20). Using the same contribution margin of $52 per student, we can calculate the new break-even point.

New break-even point in students = Total fixed costs / Contribution margin

New break-even point in students = $3,744 / $52 = 72 students

Therefore, the new break-even point for Joyful Journeys Music School is 72 students per month.

To determine the amount to charge per student, assuming the number of students taught remains the same, we divide the new total fixed costs by the break-even point in students.

Amount to charge per student = Total fixed costs / Break-even point in students

Amount to charge per student = $3,744 / 72 = $52

Therefore, Joyful Journeys Music School would need to charge approximately $52 per student per month to cover the increased costs without increasing the number of students taught.

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Answer: (a+b)2=9. a2+2ab+b2=9

Step-by-step explanation:

Answer:

H(t) = 50 - t/5

h(35)=50-35/5

=50-7

=43

h(35) = 43

The value of the error for Z, where x = 5.9 +/- 0.5 and y = 2.1 +/- 0.2, with one decimal place is 4.

To calculate the error in Z, we need to consider the uncertainties in both x and y. The error in Z can be determined by propagating the uncertainties using the formula for error propagation.

In this case, Z is given by the equation Z = x/y. To propagate the uncertainties, we use the formula for relative error:

ΔZ/Z = sqrt((Δx/x)^2 + (Δy/y)^2)

Given the uncertainties Δx = 0.5 and Δy = 0.2, and the values x = 5.9 and y = 2.1, we substitute these values into the formula:

ΔZ/Z = sqrt((0.5/5.9)^2 + (0.2/2.1)^2) = sqrt(0.0089 + 0.0181) ≈ 0.134

Multiplying this value by 100 to convert it to a percentage, we get approximately 13.4%. Rounding to one decimal place, the value of the error is 4.

Therefore, the value of the error for Z, with one decimal place, is 4.

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equal on all sides. so it can be any number on all sides as long as they're the same

Answer:

\(x = \frac{9}{5} \)

Step-by-step explanation:

\( - 7( - 7 \times ( - x - 1)) = 6 (- \times ( - 2x - 3))\)

\( - 7 + 7x + 7 = 6 + 2x + 3\)

\(7x - 2x = 6 + 3 + 7 - 7\)

\(5x = 9\)

\( \frac{5x}{5} = \frac{9}{5} \)

\(x = \frac{9}{5} \)

Answer:19.625

Step-by-step explanation:

Answer: 19.625in^2

Step-by-step explanation:

Expected completion time of the path other than the critical path is 18.16 weeks.

a) The expected times and variances for each of the activities are as follows:

Activity 1:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 2:

Expected Time = 10.33 weeks

Variance = 2.78 weeks

Activity 3:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 4:

Expected Time = 7.83 weeks

Variance = 1.36 weeks

b) The expected completion time of the critical path is 19.66 weeks.

The expected completion time of the path other than the critical path is 18.16 weeks.

c) The variance of the critical path is 1.38 weeks.

The variance of the path other than the critical path is 4.14 weeks.

d) If the time to complete the activities on the critical path is normally distributed, the probability that the critical path will be finished in 22 weeks or less is -98.

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Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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The principal investment required to get a total amount of $3,700.00 from compound interest at a rate of 3.5% per year compounded 365 times per year over 15 years is $2,287.26.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given Data

Rate = 3.5%

Final Amount = $3,700

Time = 15 Years

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 per year,

Then, solve the equation for P

P = A / (1 + r/n)^nt

P = 3,700.00 / (1 + 0.035/365)(365)^(15)

P = 3,700.00 / (1 + 0.00010137)^(4745)

P = $2,287.26

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Answer:

\(10^{-6}\)

Step-by-step explanation:

Start with 0000008.0

For each decimal place you move back, subtract the exponent (the n value of \(10^n\)) by 1. In this case, we move back 6 places. This makes n = 6, giving us an answer of \(10^{-6}\).

Answer: -6

Step-by-step explanation:

Answer:

$936

Step-by-step explanation:

10% is just divided by 10 so 9360 divided by 10 is 936

Answer:

Step-by-step explanation:

5^2 + 5^2 = x^2

25 + 25 = x^2

50 = x^2

\(\sqrt{50}\) = x,   5\(\sqrt{2}\)

x = approximately 7.07

Answer:

Exact: SQRT 50

Approx: 7.07

Step-by-step explanation:

you take both of the 5s and square them.

So 5*5=25 and 5*5 is 25. Since the right angle is opposite the side you are trying to find you add those together to get 50. Then you take the SQRT of 50 because you are trying to solve for x via the pythagorean theorem.

So the exact is SQRT 50

and the approx is 7.07

Answer: Total cost of their meal is $78

Step-by-step explanation: 20% of 65 is a 13 dollars tip adding up to a total of $78

65*0.2 = 13

65+13=78

To create different shapes, you can arrange the triangles and square in various ways.

are a few examples:
1. Rectangular Prism: Arrange the triangles to form the base of the prism, and place the square as the top face. Connect the corresponding vertices to create the remaining faces of the prism.

2. Pyramid: Place the square as the base of the pyramid and arrange the triangles around it. Connect the vertices of the triangles to the top of the pyramid.

3. Diamond: Arrange the triangles in a way that their bases meet at a single point, forming a diamond shape. Place the square inside the diamond, aligned with the triangles.

4. House Shape: Arrange the triangles to form the roof of the house, and place the square as the base. Connect the corresponding vertices to create the walls of the house.

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With 3 triangles and 1 square, you can create several shapes besides a square-based triangle. Here are a few examples:

1. Rectangle: Place the square and two triangles together, with one triangle on each side of the square. The two triangles will form the longer sides of the rectangle, while the square will form the shorter sides.

2. Parallelogram: Arrange the square and two triangles in a way that the two triangles are positioned next to each other, forming a parallelogram shape. The square can be used as a base or a side of the parallelogram.

3. Trapezoid: Position the square and two triangles in a way that one triangle is attached to the top of the square, and the other triangle is attached to the bottom of the square. The result will be a trapezoid shape.

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According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.

To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.

Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.

Note: This question is incomplete. Here is the complete information:

Conversation:
Hello

Hello, How are you?

I am fine, and you?

i am fine too, What are you doing?

I am studing for an exam this week.

Oh, sorry I won´t distract you.

Don´t worry.

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Answer: C

The radius of the inscribed circle of AHJK is equal to the inradius of the triangle, which is denoted as r.

Since P is the incenter of the triangle, the inradius is equal to the distance from P to each of the sides of the triangle. Let's call these distances a, b, and c.

You know that LP = 4x + 10 and MP = 8x - 2. The length of the inradius can be expressed as:

r = (a+b-c)/2

You can now use this equation and the given information to solve for r.

Since LP is the distance from P to side L, we can set a = 4x + 10.

Since MP is the distance from P to side M, we can set b = 8x - 2.

Substituting these values into the equation for r, you get:

r = ((4x + 10) + (8x - 2) - c) / 2

= (12x + 8 - c) / 2

You can simplify this to:

r = 6x + 4 - c/2

Thus, the radius of the inscribed circle of AHJK is equal to 6x + 4 - c/2. To find the exact value of the radius, you need to know the value of c.

Answer:

57 students

Step-by-step explanation:

Since 6 students count not fit and they had to go in cars, there is a remainder of 6. Subtract that from the total, 405, and you get 399.

Then, divide that by 7, and you get the answer. 57.

Hope it helps!

Answer:

57 students

Step-by-step explanation:

405-6=399

399÷7=57

The value of h in the given diagram is 72 ft. The correct option is the third option 72

From the question, we are to calculate h. h is the height of the triangle

First, we will the determine half the length of the base of the triangle.

Half the length of the base of the triangle = 42 ft/2

Half the length of the base of the triangle = 21 ft

Thus,

By the Pythagorean theorem, we can write that

75² = 21² + h²

5625 = 441 + h²

h² = 5625 - 441

h² = 5184

h = √5184

h = 72 ft

Hence, the value of h in the given diagram is 72 ft. The correct option is the third option 72

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Answer:

n = 10

Step-by-step explanation:

20/4 = 50/n

20n = 50 x 4

20n = 200

n = 10

Hope that helps!

Answer:

The number of paths that are there from the ant that end at (3, 3) but never pass through (2, 3) is 4.

Step-by-step explanation:

The possible pathways are as follows:

(0, 0) → (1, 0) → (2, 0) → (3, 0) → (3, 1) → (3, 2) → (3, 3)

(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (3, 2) → (3, 3)

(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2) → (3, 2) → (3, 3)

(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (3, 2) → (3, 3)

Thus, the number of paths that are there from the ant that end at (3, 3) but never pass through (2, 3) is 4.

Answer:

5= log2(32)

Step-by-step explanation:

IT IS CORRECT! I took the test :)

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

try 1239128981441231241

Step-by-step explanation:

myra

Answer:

$384

Step-by-step explanation:

$3,200 x 0.12 = $384

Answer:

325 divided by 5= 65

Step-by-step explanation:

Answer:

325/5= 65mph

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