Write an equation in Point-Slope Form that passes through the points (2,-3) & (4,7)

Answer:

93.5

Step-by-step explanation:

trust meee

Step-by-step explanation:

one side.

as each tile is guaranteed an equilateral triangle, all sides are equally long. measuring 1 side clarifies therefore the overall size of the tile.

the angles are the same in any case, as every equilateral triangle (no matter its size) has only angles of 60°.

so, if any side has the same length as the side lengths of the other triangles, then the checked triangle is congruent with the others.

1. The graph opens downward.

2. The graph has a maximum value.

4. The maximum height is approximately 22.704 yards.

5. Increasing the coefficients makes the parabola narrower and steeper, while decreasing them makes it wider and flatter.

1. The graph of the quadratic function y = -0.0352x² + 1.4x + 1 opens downwards. This can be determined by observing the coefficient of the squared term (-0.0352), which is negative.

2. The graph of the quadratic function has a maximum value. Since the coefficient of the squared term is negative, the parabola opens downward, and the vertex represents the maximum point of the graph.

3. To graph the quadratic function y = -0.0352x² + 1.4x + 1, we can plot points and sketch the parabolic curve. Here's a rough representation of the graph:

Graph of the quadratic function

The x-axis represents the distance (in yards) the football is kicked (x), and the y-axis represents the height (in yards) the football reaches (y).

4. To find the maximum height of the football, we can determine the vertex of the quadratic function. The vertex of a quadratic function in the form y = ax² + bx + c is given by the formula:

x = -b / (2a)

In this case, a = -0.0352 and b = 1.4. Plugging in the values, we have:

x = -1.4 / (2 * -0.0352)

x = -1.4 / (-0.0704)

x ≈ 19.886

Now, substituting this value of x back into the equation, we can find the maximum height (y) of the football:

y = -0.0352(19.886)² + 1.4(19.886) + 1

Performing the calculation, we get:

y ≈ 22.704

Therefore, the maximum height of the football is approximately 22.704 yards.

5. If the coefficients of the "2" and "a" terms were increased, it would affect the shape and position of the graph. Specifically:

Increasing the coefficient of the squared term ("2" term) would make the parabola narrower, resulting in a steeper downward curve.

Increasing the coefficient of the "a" term would affect the steepness of the parabola. If it is positive, the parabola would open upward, and if it is negative, the parabola would open downward.

On the other hand, decreasing the coefficients would have the opposite effects:

Decreasing the coefficient of the squared term would make the parabola wider, resulting in a flatter downward curve.

Decreasing the coefficient of the "a" term would affect the steepness of the parabola in the same manner as increasing the coefficient, but in the opposite direction.

These changes in coefficients would alter the shape of the parabola and the position of the vertex, thereby affecting the maximum height and the overall trajectory of the football.

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Answer:

Graph in the image above

Step-by-step explanation:

Answer:

26% tip

Step-by-step explanation:

213.90 / 1.15 = 186

213.90 + 20 = 233.9

233.9 / 186 = 1.26

26% tip

Answer:

\(s = 76\)

Step-by-step explanation:

Given

\(TU=s\)

\(VX = s -38\)

See attachment for triangle

Required

Solve for s

From the triangle, we have:

\(\triangle UTW\) similar to \(\triangle XVW\)

Such that

\(TW = 2 XW\)

\(UW = 2 VW\)

This implies that:

\(TU = 2 VX\)

Substitute: \(TU=s\)  and \(VX = s -38\)

\(s = 2 * [s - 38]\)

\(s = 2 s - 76\)

Collect like terms

\(s - 2 s =- 76\)

\(-s =- 76\)

Divide by -1

\(s = 76\)

Answer:

The answer is C.

Step-by-step explanation:

ur welcome

9514 1404 393

Answer:

  x = 44.5

Step-by-step explanation:

The angles defined by x will be supplementary when the lines m and n are parallel.

  (x +4) +(3x -2) = 180

  4x +2 = 180

  4x = 178

  x = 44.5 . . . . will make m and n parallel

Answer:

250

Step-by-step explanation:

y=50x+200

Once you graph the line with the slope above than you should be able to find it on the graph.

The expected loss per game is approximately -$0.31.

The terms we need to consider in this problem are: standard 52-card deck, face cards, and expected gain or loss.
To find the expected gain or loss per game, follow these steps:

1. Determine the probability of drawing a face card.
There are 12 face cards (Kings, Queens, and Jacks) in a standard 52-card deck. So the probability of drawing a face card is \(\frac{12}{52}\), which simplifies to \(\frac{3}{13}\).

2. Determine the probability of drawing a non-face card.
There are 40 non-face cards in the deck (52 cards - 12 face cards). So the probability of drawing a non-face card is \(\frac{40}{52}\), which simplifies to \(\frac{10}{13}\).

3. Calculate the expected gain or loss per game.
Expected gain or loss = (Probability of drawing a face card x gain from drawing a face card) + (Probability of drawing a non-face card x loss from drawing a non-face card)

4. Simplify the equation.
Expected gain or loss = \((\frac{3}{13} (2))  +  (\frac{10}{13} (-1))\)
Expected gain or loss = \(\frac{-4}{13}\)

Your expected loss per game is approximately -$0.31 (rounded to two decimal places).

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Answer:

Exactly 3 factors

Step-by-step explanatin

The number 1001 is a composite number because 1001 can be divided by one, by itself and at least by 7, 11 and 13. A composite number is an integer that can be divided by at least another natural number, besides itself and 1, without leaving a remainder (divided exactly).

The factorization or decomposition of 1001 = 7•11•13. Notice that here, it is written in exponential form.

The prime factors of 1001 are 7, 11 and 13. It is the list of the integer's prime factors.

The number of prime factors of 1001 is 3.

Answer: if you insert each x and y coordinate into the equations you will be able to figure out that option A will give you an answer of 10=16 and 1=3 which isn't correct. And so we do this for B and C until D is correct and matches with 6=6 and 3=3.

Answer:

im on the same question too

Step-by-step explanation:

honestly i am 80% sure the answer is c

The transformations that move figure A onto figure B and then onto figure C is B. Reflection, translation.

Shape transformation is a type of geometric transformation that involves changing the shape of an object. It is a type of transformation that changes the size, orientation, and position of the object while preserving its overall structure. Some examples of shape transformations include scaling, rotation, reflection, shearing, and dilation.

Shape transformation is used in a variety of applications, including computer graphics, image processing, and computer-aided design (CAD). By applying shape transformations, it is possible to modify the appearance of an object or image, to correct distortions or errors, or to generate new versions of the original object or image.

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Image transcribed and completed:

These figures are congruent. Identify the transformations that move figure A onto figure B and then onto figure C.

A. Translation, translation

B. Reflection, translation

C. Rotation, translation

D. Reflection, reflection

The given operational problem relates to production or manufacturing, with decision variables representing the quantities of the two products to be produced and an objective function representing the specific goal to be achieved (such as maximizing profit or minimizing costs).

Based on the information provided, it appears that the given scenario relates to a production or manufacturing problem. The problem involves the production of two different products, Product 1 and Product 2, and requires specific quantities of different resources or components.

Decision Variables:

The decision variables in this operational problem could include the quantities or amounts of each product to be produced. For example, let's denote the quantity of Product 1 as x and the quantity of Product 2 as y.

Objective Function:

The objective function represents the goal or objective of the problem. In this case, the objective could be to maximize or minimize a certain aspect, such as profit, production efficiency, or resource utilization. The specific objective function would depend on the specific goal of the problem. For example, if the objective is to maximize profit, the objective function could be expressed as a linear combination of the quantities produced and the associated costs and revenues.

Since the specific objective function is not provided in the question, it is not possible to determine it accurately. However, it could involve maximizing profit, minimizing production costs, or maximizing resource utilization efficiency, among other possibilities.

In summary, the given operational problem relates to production or manufacturing, with decision variables representing the quantities of the two products to be produced and an objective function representing the specific goal to be achieved (such as maximizing profit or minimizing costs).

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Answer:

The same thing to both sides.

Step-by-step explanation:

To find (f o g)(-4), we substitute -4 into g(x) to get -4, and then substitute -4 into f(x) to get -11.

The question asks us to find (f o g)(-4), where f(x) = 3x + 1 and g(x) = x. To find (f o g)(-4), we need to substitute -4 into g(x) and then take that result and substitute it into f(x).

First, let's find g(-4) by substituting -4 into g(x):
g(-4) = -4

Now, let's substitute g(-4) into f(x):
f(g(-4)) = f(-4)

Substituting -4 into f(x):
f(-4) = 3(-4) + 1
       = -12 + 1
       = -11

Therefore, (f o g)(-4) = -11.

In mathematics, a function is an expression, rule, or law that specifies a connection between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical connections in the sciences.

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To use the tangent ratio in a triangle, you need to know the lengths of two sides or the measures of two angles in the triangle. The tangent ratio relates the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle.

The tangent ratio is a trigonometric ratio that relates the length of one side of a right triangle to the length of another side. It is defined as the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle.

In order to use the tangent ratio, you must have knowledge of the triangle's sides or angles. If you know the lengths of two sides of a right triangle, you can use the tangent ratio to find the measure of one of the acute angles in the triangle. Conversely, if you know the measure of one of the acute angles, you can use the tangent ratio to find the ratio of the lengths of the sides in the triangle.

Essentially, to apply the tangent ratio, you need to have sufficient information about the triangle to identify the sides or angles involved in the ratio calculation. This information can be provided in terms of lengths of sides or measures of angles, allowing you to use the tangent ratio to solve for missing values or determine specific relationships within the triangle.

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ANSWER:

hope this helps

Step-by-step explanation:

this what we know So the arc right here give us one new point this point should mark. The radius so we don't want to draw any jokes over there. Once we have this new point over here we use the same radius

Constructing a parallel through a point - Rhombus method

Place the compasses on point R and set its width to a little more than the distance to the line PQ. ...

Draw a wide arc from the right of R around so it crosses the line PQ at two points.

Answer:

ok, the correct answer should be R(1.5)=R(2)!

Step-by-step explanation:

I did this my class before!

Answer:

multiply vertically

Step-by-step explanation:

The logical statement that defines the relation (⊂) in terms of (∈) is:

A ⊂ B if every element of A is an element of B.

To prove that (A-B) ∩ (B-A) = ∅,

follow the steps below:

Step 1: To begin, assume that x ∈ (A-B) ∩ (B-A)

Step 2: This means that x is an element of both A-B and B-A.

Step 3: Since x ∈ A-B, x ∈ A, but x ∉ B.

Step 4: Since x ∈ B-A, x ∈ B, but x ∉ A.

Step 5: Since x ∈ A and x ∉ B, it is impossible for x to be in both A and B.

Step 6: Therefore, x cannot be in (A-B) ∩ (B-A).

Step 7: This means that (A-B) ∩ (B-A) is an empty set, or ∅.

Step 8: Thus, (A-B) ∩ (B-A) = ∅.

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Answer:

Step-by-step explanation:

The Pythagorean theorem is sqrt(a^2 + b^ 2) = c, so:

sqrt(22^2 + 8^2) = c

sqrt(548) = c

23.41 = c

The expression  aₙ > 0 and lim n → [∞] aₙ + 1 is true.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.

And we need to check whether the given statement is true or not.

While we looking into the given question, we have identified the following expression,

=> lim n → [∞] aₙ + 1

Here we have also know that the value of aₙ > 0.

When we equate the given expression with zero, we have get the following expression,

=> lim n → [∞] aₙ + 1 = 0

=>  lim n → [∞] aₙ = -1

Here we have given the condition that,  aₙ >0, so

=> lim n → [∞] aₙ = 0

Therefore, the expression is zero.

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a) Diagonal matrix equivalent to A is $ \begin{pmatrix} 2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\\ \end{pmatrix} $.

b) Diagonal matrix equivalent to A is $ \begin{pmatrix} 2 & 0 & 0\\ 0 & 3 & 0\\ 0 & 0 & 2\\ \end{pmatrix} $.

a) Here, we are given the matrix A = $ \begin{pmatrix} 1 & 2 & 2\\ 2 & 3 & 6\\ 2 & 6 & 6\\ \end{pmatrix} $ which is symmetric.

We have to find an orthonormal basis in which A diagonalizes. Firstly, let us find eigenvalues of the matrix A. Characteristic polynomial of A is given by $(t-2)^2(t-3)$.So, we have two eigenvalues 2 and 3.

Now, let us find eigenvectors corresponding to the eigenvalues.

For eigenvalue 2: For this, we need to solve the equation $(A-2I)X=0$.

So, $ \begin{pmatrix} -1 & 2 & 2\\ 2 & 1 & 6\\ 2 & 6 & 4\\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z\\ \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0\\ \end{pmatrix} $. On solving this, we get the eigenvector $\begin{pmatrix} -2 \\ 1 \\ 0\\ \end{pmatrix}$ or $\begin{pmatrix} -2\sqrt{5}/5 \\ \sqrt{5}/5 \\ 0\\ \end{pmatrix}$.

Similarly, we can find the eigenvector corresponding to eigenvalue 3 which is $\begin{pmatrix} 2 \\ 0 \\ -1\\ \end{pmatrix}$ or $\begin{pmatrix} 2\sqrt{5}/5 \\ 0 \\ -\sqrt{5}/5\\ \end{pmatrix}$.

Now, we normalize these eigenvectors to obtain the orthonormal basis.

So, we get $\frac{1}{\sqrt{5}}\begin{pmatrix} -2 \\ 1 \\ 0\\ \end{pmatrix}$, $\frac{1}{\sqrt{5}}\begin{pmatrix} 2 \\ 0 \\ -1\\ \end{pmatrix}$, $\frac{1}{\sqrt{5}}\begin{pmatrix} 1 \\ 2 \\ 0\\ \end{pmatrix}$ as an orthonormal basis in which A diagonalizes.  

Diagonal matrix equivalent to A is $ \begin{pmatrix} 2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\\ \end{pmatrix} $ .

b) Here, we are given the matrix A = $ \begin{pmatrix} 1 & 2 & 2\\ 2 & 3 & 6\\ 2 & 6 & 6\\ \end{pmatrix} $ which is symmetric. We have to find an orthonormal basis in which A diagonalizes.

Firstly, let us find eigenvalues of the matrix A.

Characteristic polynomial of A is given by $(t-2)^2(t-3)$.

So, we have two eigenvalues 2 and 3. But this time, we have only one eigenvector corresponding to eigenvalue 2.

For eigenvalue 2: For this, we need to solve the equation $(A-2I)X=0$. So, $ \begin{pmatrix} -1 & 2 & 2\\ 2 & 1 & 6\\ 2 & 6 & 4\\ \end{pmatrix} \begin{pmatrix} x \\ y \\ z\\ \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0\\ \end{pmatrix} $.

On solving this, we get the eigenvector $\begin{pmatrix} -2 \\ 1 \\ 0\\ \end{pmatrix}$ or $\begin{pmatrix} -2\sqrt{5}/5 \\ \sqrt{5}/5 \\ 0\\ \end{pmatrix}$.

Now, we normalize this eigenvector to obtain the orthonormal basis.

So, we get $\frac{1}{\sqrt{5}}\begin{pmatrix} -2 \\ 1 \\ 0\\ \end{pmatrix}$ as an orthonormal basis in which A diagonalizes.

Diagonal matrix equivalent to A is $ \begin{pmatrix} 2 & 0 & 0\\ 0 & 3 & 0\\ 0 & 0 & 2\\ \end{pmatrix} $ .

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Answer:

27

Step-by-step explanation:

here we remark that we have a proportional relationship Between the number of seeds and the number of flowers

Let x be the number of seeds we need in order to guarantee that 45 flowers grow.

8 seeds ————————-> 5 flowers

x seeds ————————-> 45 flowers

in order to find x ,We have to solve this equation :

\(\frac{x}{8}=\frac{45}{5}\)

⇔ x/8 = 9

⇔ x = 8×9 = 72

“how many seeds did not grow” : 72 - 45 = 27

In linear equation, 54 is the value of x.

What is the most effective way to explain linear equations?

An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). A linear equation is an algebraic equation of the form y=mx+b.

                          In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.

Angle at the top is equal to angle at the bottom

2x + 2 = 3x - 52

3x - 2x = 2 + 52

x = 54

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The Markov Chain Model is the best model to predict what activity people will do in two days based on the current weather. It is suitable for predicting outcomes based on probabilities over time, and it considers only the current weather conditions and the probabilities of the different activities.

To predict what activity people will do in two days based on the current weather, I would use a Markov Chain Model. This model is suitable for predicting outcomes based on probabilities over time. In this case, the model would use the current weather (sunny) and the probabilities of the different activities (going for a walk, shopping, or staying home and cleaning) to predict the probability of each activity in two days. The Markov Chain Model assumes that the probability of an activity depends only on the current weather, and not on any previous or future weather conditions.

A Markov Chain Model is the most appropriate model to predict what activity people will do in two days based on the current weather. This model is suitable for predicting outcomes based on probabilities over time, and it would use the current weather (sunny) and the probabilities of the different activities (going for a walk, shopping, or staying home and cleaning) to predict the probability of each activity in two days. The Markov Chain Model assumes that the probability of an activity depends only on the current weather, and not on any previous or future weather conditions.

In conclusion, the Markov Chain Model is the best model to predict what activity people will do in two days based on the current weather. It is suitable for predicting outcomes based on probabilities over time, and it considers only the current weather conditions and the probabilities of the different activities. By using this model, we can make accurate predictions about what people are likely to do in the future, based on the current weather conditions.

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Answer:

-2

Step-by-step explanation:

We are given that R is a random variable with the probability density function (PDF) given

We have, f(r) = 3/4 (1 − (6 − r)² if 5 ≤ r ≤ 7 and f(r) = 0 otherwise.

Area of the circular region: \($A = \pi r^2$\)

For a continuous random variable X with probability density function f(x), the expected value of a function g(X) is given by the following integral:

\($E[g(X)] = \int_{-\infty}^\infty g(x)f(x)dx$\)

Here, our function is the area of the circular region, which is given by A = πR2.

Therefore, we have g(R) = πR².

Substituting this into the formula above, we get:

\($E[\pi R^2] = \int_{-\infty}^\infty \pi R^2f(R)dR$\)

However, f(R) is only non-zero for values of R between 5 and 7. Therefore, we can simplify the above expression as follows:

\($E[\pi R^2] = \int_{5}^7 \pi R^2f(R)dR$\)

Using the given pdf, we can substitute f(R) as follows:

\($f(R) = \begin{cases} \frac{3}{4}(1 - (6 - R)^2) & \text{if } 5 \leq R \leq 7 \\ 0 & \text{otherwise} \end{cases}$\)

Substituting this into the above integral, we get:

\($E[\pi R^2] = \int_{5}^7 \pi R^2\cdot\frac{3}{4}(1 - (6 - R)^2)dR$\)

Expanding the square and simplifying, we get:

\($E[\pi R^2] = \int_{5}^7 \pi R^2\cdot\frac{3}{4}(2R - R^2 - 35)dR$\)

\($E[\pi R^2] = \frac{3\pi }{4}\int_{5}^7 (2R^3 - R^4 - 35R^2)dR$\)

Evaluating the integral, we get:

\($E[\pi R^2] = \frac{3\pi }{4}\left[\frac{1}{2}R^4 - \frac{1}{5}R^5 - \frac{35}{3}R^3\right]_{5}^{7}$\)

\($E[\pi R^2] = \frac{3\pi }{4}\left[\left(\frac{7^4}{2} - \frac{7^5}{5} - \frac{35\cdot7^3}{3}\right) - \left(\frac{5^4}{2} - \frac{5^5}{5} - \frac{35\cdot5^3}{3}\right)\right]$\)

\($E[\pi R^2] = \frac{3\pi }{4}(468.67)$\)

Therefore, the expected area of the resulting circular region is approximately 1101.38 square meters (rounded to four decimal places)

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