Triangle ABC has vertices at (-2,0), (-1,6) and (6,0)z what is the point of intersection of the triangles medians?

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

To find the area of the surface of the part of the plane x + 2y + 3z = 1 that lies inside the cylinder x^2 + y^2 = 3, we can use a parametric representation for the plane and cylinder intersection.

Let x = r * cos(θ) and y = r * sin(θ), where r^2 = 3 (from the cylinder equation). Now, we can find z in terms of r and θ using the plane equation:

z = (1 - x - 2y) / 3
z = (1 - r * cos(θ) - 2r * sin(θ)) / 3

Now, we have the parametric representation of the intersection: (r * cos(θ), r * sin(θ), (1 - r * cos(θ) - 2r * sin(θ)) / 3). To find the surface area, we need to calculate the partial derivatives with respect to r and θ and then find the magnitude of the cross product.

After calculating the partial derivatives and the cross product, we can find the double integral of the magnitude over the region (0 ≤ r ≤ √3, 0 ≤ θ ≤ 2π). This double integral gives the surface area of the part of the plane inside the cylinder.

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The system of linear equations representing lines 1 and 2 is y = x and y = -1/2x + 3

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

The graph

A linear equation is represented as

y = mx + c

Using the points, we have

Line 1

y = x

For line 2, we have

y = mx + 3

Next, we have

6m + 3 = 0

This gives

m = -1/2

So, we have

y = -1/2x + 3

Hence, the system of linear equations is y = x and y = -1/2x + 3

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Answer:

-1360

Step-by-step explanation:

factor the expression : 68(-19-1)

calculate the difference ; 68 x ( -20 )

multiply the numbers ; -1360

solution ; -1360

Answer:

\(x {}^{3} \)

Step-by-step explanation:

\(\frac{(x {}^{5} )}{( {x}^{2} )}\)

\(x {}^{3} \)

The power series representation for ln((1+x)/(1-x)) is given by: ln\(((1+x)/(1-x)) = 2(x + (x^3)/3 + (x^5)/5 + (x^7)/7 + ...)\), This representation is valid for |x| < 1, as it is derived using the power series expansion of ln(1+x) and ln(1-x), which have a convergence radius of 1.

To find the power series representation of ln((1+x)/(1-x)), we'll use the properties of the natural logarithm function and the geometric series.

First, we'll rewrite the expression using the properties of logarithms:

ln((1+x)/(1-x)) = ln(1+x) - ln(1-x)

Now, let's find the power series representation for ln(1+x) and ln(1-x) separately.

Power series representation of ln(1+x):

We know that the power series representation of ln(1+x) is given by: \(ln(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...\)

Power series representation of ln(1-x):

Similarly, the power series representation of ln(1-x) is given by:

\(ln(1-x) = -x - (x^2)/2 - (x^3)/3 - (x^4)/4 - ...\)

Now, we'll subtract the series representation of ln(1-x) from ln\((1+x): ln((1+x)/(1-x)) = (x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ...) - (-x - (x^2)/2 - (x^3)/3 - (x^4)/4 - ...) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ... + x + (x^2)/2 + (x^3)/3 + (x^4)/4 + ... = 2(x + (x^3)/3 + (x^5)/5 + (x^7)/7 + ...)\)

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The correct answer is e(x) = np. The expected value for a binomial probability distribution is given by the formula e(x) = np, where n represents the number of trials and p represents the probability of success in each trial.

The expected value is a measure of the average or mean outcome of a binomial experiment. It represents the number of successful outcomes one would expect on average over a large number of trials.

The formula e(x) = np arises from the fact that the expected value of a binomial distribution is the product of the number of trials (n) and the probability of success (p) in each trial. This is because in a binomial experiment, the probability of success remains constant for each trial.

Therefore, to calculate the expected value of a binomial probability distribution, we multiply the number of trials by the probability of success in each trial, resulting in e(x) = np.

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The solution is: we created a cumulative frequency table of the data and, the bakery sell less than 30 loaves in 16.

Here, we have,

we know that,

Cumulative frequency is used to determine the number of observations that lie above (or below) a particular value in a data set. The cumulative frequency is calculated using a frequency distribution table, which can be constructed from stem and leaf plots or directly from the data.

now, we have,

given that,

12, 19, 27, 24, 19, 44, 8, 32, 21, 37, 15, 6, 16, 48, 26, 5, 14, 23, 6, 35, 37, 28, 47, 40

if we create a cumulative frequency table of the data, we get,

Class interval  Frequency     Cumulative frequency

0-10                       4                               4

10-20                    6                               10

20-30                   6                               16

30-40                   5                                21

40-50                   3                                24

so, from the table we get,

the bakery sell less than 30 loaves in 16.

Hence, The solution is: we created a cumulative frequency table of the data and, the bakery sell less than 30 loaves in 16.

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Answer  

it represents a sphere

Step-by-step explanation:

Answer: It would be a cone because the light goes into a triangle cone shape the farther you point it. It does not make a sphere

Step-by-step explanation:

Answer:

9x2x1 and 6x3x1

Step-by-step explanation:

This question has multiple answers to it. A sandbox of 18 cubic feet with a height of a foot is actually quite simple. If it is confusing I would try to visualize the sandbox. Since volume is b x h x w the first thing you should do is divide 18 by 1. This would be more important if the height was more than one. Now you just have to find two other numbers that can divide 18. 9x2=18 and 6x3=18 so two possible dimensions for the sandbox are 9x2x1 and 6x3x1

Answer:

-18a-23

Step-by-step explanation:

-(3a+2)-3(5a+7) -- (multiply out the brackets)

-3a-2-15a-21 -- (collect like terms) (-3a-15a=-18a) and (-2-21=-23)

-18a-23

Answer:

- 18a - 23

Step-by-step explanation:

When there is a “-” in front of an expression in parentheses, change the sign of each term of the expression

- ( 3a + 2 ) - 3 ( 5a + 7 )

- 3a - 2 -3 ( 5a + 7 )

Multiply each term in the parentheses by - 3

- 3 ( 5a + 7 )

- 3 × 5a - 3 × 7

Calculate the product

- 3 × 5a - 3 × 7

- 15a - 3 × 7

Multiply the numbers

- 3 × 5a - 3 × 7

- 15a - 21

Collect like terms by calculating the sum or difference of their coefficients

- 3a - 15a

( - 3 - 15 )a

Calculate the difference

( - 3 - 15 )a

- 18a

Factor out the negative sign from the expression

- 2 - 21

- ( 2 + 21 )

Add the numbers

- ( 2 + 21 )

- 23

Answer

- 18a - 23

Answer:

30.1°

Step-by-step explanation:

Let A = angle of elevation

tan A = 55/95

A = arctan 55/95

    = 30.1°

If the numbers denoting the perimeter and area of the square are equal, the length of the diagonal will be 4√2 units.

What are Area and Perimeter?

An object's shape defines a region as its area. The area of a figure or any other two-dimensional geometric shape is how much space it takes up in a plane.

The whole length encircling a shape is referred to as its perimeter. Simply put, if a shape is stretched into a linear form, its perimeter is its length. In a two-dimensional plane, a shape's perimeter is the sum of its total dimensions.

Let the side of the square to be 'a'.

If Area and Perimeter of a square are equal then,

So,  Area = Perimeter

      a^2 = 4a

we get, a = 4 units.

Now, we can find the diagonal by using Pythagoras theorem,

We know that, Hypotenuse^2 = Base^2 + Perpendicular^2

Here, the hypotenuse will be the diagonal of the square.

So, We have,

            Diagonal^2 = 4^2 + 4^2

                                = 16 + 16

                                = 32

∴ Diagonal = √32 = 4√2 units.

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Answer:

1/6

Step-by-step explanation:

1/3 equals 2/6 then two friends share the 2/6 and it's 1/6

  Hope this helped :)

The equivalent value of m is given by the expression m = 1

Given data ,

We can use the properties of exponents to solve this problem. Specifically, when we multiply two powers with the same base, we add their exponents.

So, we have:

(-3)^(m+1) × (-3)⁵ = (-3)⁷

Using the property of exponents, we can add the exponents on the left-hand side:

(-3)^(m+1+5) = (-3)⁷

Simplifying the exponents on the left-hand side:

(-3)^(m+6) = (-3)⁷

We know that two powers with the same base are equal if and only if their exponents are equal. So, we can set the exponents equal to each other:

m + 6 = 7

Subtracting 6 from both sides:

m = 1

Hence , m = 1 is the value that satisfies the equation

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The solution for 27≤−2x+7 is x ≤−10 and −13>−2x+7 is x≥10.

What is the solution?

Given equations:  27≤−2x+7, −13>−2x+7

Solving each equation,

27≤−2x+7

−2x≥27−7

−2x≥20

x≤ (20/−2)

x≤−10

−13>−2x+7

−2x≤−13−7

−2x≤−20

x≥ (-20/-2)

x≥10

The solution for 27≤−2x+7 is x ≤−10 and −13>−2x+7 is x≥10.

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See attachment for the graph of g(x) = 1/2x^2

The equation of the function is:

g(x) = 1/2x^2

The above function is a quadratic function that has only one term

Next, we plot  the graph using a graphing tool

See attachment for the graph of g(x)

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First:

A. (First Option)

Second:

C. (Third option)

(Brainiest and thanks are appreciated)

Answer:

Question 3:

O (7 x 50) - (7 x 2) = 350 – 14 = 336

Question 3:

O (9 x 80) + (9 x 1) 729

Step-by-step explanation:

Distributive Property is used in algebraic expressions, to divide the equation, to make it easier to solve. For question 1,  since it was 20, you must subtract 8 from that answer, because 20 is 1 more than 19. For question 2, (2 x 9) + (2 x 3) would be the same thing as 2(9+3).

-kiniwih426

For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.

Properties of circumcenter of triangle are:

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To find the slope from data in a table you will have to use the formula y2-y1/x2-x1. For example lets say in a table the x column includes -2 and -1 while the y column includes 8 and 2. You take these numbers and input them into the slope formula, your formula will now be 2-8/-1-(-2). You subtract 8 from 2 to get -6 and subtract 2 from -1 to get 1. You put them together to get -6/1 or -6 if simplified as your slope. In conclusion, to find the slope from data in a table you will need to use the formula y2-y1/x2-x1.

Answer:

sample response: : Start by choosing two data points. Calculate the difference between the second y value and the first y value. Then divide that by the difference between the second x value and the first x value.

Step-by-step explanation:

Answer:

1). g(-9) = -81.914

2). Last option

Step-by-step explanation:

1). f(x) = x²

   For x = -9

   f(-9) = (-9)² = 81

   g(x) = \(\frac{32}{2x-17}\)

   g(-9) = \(\frac{32}{[2(-9)-17]}\)

           = \(\frac{32}{-35}\)

           = - \(\frac{32}{35}\)    

   (g - f)(-9) = g(-9) - f(-9)

                  = \(-\frac{32}{35}-81\)

                  = \(\frac{-32-2835}{35}\)

                  = \(-\frac{2867}{35}\)

                  = -81.914

2). The relation is not a function because this function doesn't passes a vertical line test.

Last option will be the answer.

The statistic that can be used to objectively quantify the level of agreement between different screeners appraising an article in a systematic review is the inter-rater reliability coefficient, such as Cohen's kappa or Fleiss' kappa.

In a systematic review, multiple screeners may independently appraise articles to ensure consistency and minimize bias. The inter-rater reliability coefficient, such as Cohen's kappa or Fleiss' kappa, is used to measure the agreement between these screeners. These statistics provide a quantitative measure of the extent to which the screeners' assessments align with each other beyond what would be expected by chance. Higher values of the inter-rater reliability coefficient indicate greater agreement among the screeners, suggesting more reliable and consistent evaluations of the articles in the systematic review.

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\(\large\rm{Problem:}\)

Customers per day:

98, 87, 93, 82, 101, 99, 97, 97, 91

Find the mean to the nearest tenth:

\(\large\rm{Solution:}\)

Mean = \( \tt \frac{sum \: of \: data}{number \: of \: data}\)

\( \tt \frac{98 + 87 + 93 + 82 + 101 + 99 + 97 + 97 + 91}{9} = \frac{845}{9} = \green{93.89}\)

Therefore, the mean is 93.89

Answer: f  ( x)   =  − 50

Step-by-step explanation:

Answer:

Concept: Mathematical Comprehensive

General notes:

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer:

6 14/15

Step-by-step explanation:

change to improper fraction

change to common denominator

solve parentheses

subtract