2x + 3y = 12
what is the slope​

The slope of the line of image 1 is 2

The slope of the line of image 2 is 5/2

The slope of the line of image 3 is 2/5.

The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.

The slope of the line of image 1 is:

The line is passing through the points (6, 10 and (2, 2)

So,

Slope=(y₂-y₁)/(x₂-x₁)

m=(2-10)/(2-6)

m=8/4

m=2

Therefore, the slope of the line for image 1 is 2.

Hence, option A is correct.

The slope of the line for image 2 is:

The line is passing through the points (3, 4) and (7, 14)

Slope=(y₂-y₁)/(x₂-x₁)

m=(14-4)/(7-3)

m=10/4

Therefore, the slope of the line for the image 2 is 5/2.

Hence, option F is correct.

The slope of the line for image 3 is:

The line is passing through the points (2, 1) and (7, 3)

Slope=(y₂-y₁)/(x₂-x₁)

m=(3-1)/(7-2)

m=2/5

Therefore, the slope of the line for the image 3 is 2/5

Therefore, option D is correct.

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Answer:

3

Step-by-step explanation:

72/9 = 8 ( The quotient of 72 and 9)

8-5 = 3 (Decrease by 5)

The number of hours in a week a student played basketball is \(11\frac{3}{8}\).

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.

Also given that 1/4 of the exercise of a student came from playing basketball.

Therefore, Time playing basketball is one-fourth of the total time exercised which is,

= (3 + 1/4)×(1/4).

= (13/4)×(1/4).

= (13/8).

Therefore, In a week the student played (13/8)×7.

= 91/8.

= \(11\frac{3}{8}\).

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

33/90 is the answer

Step-by-step explanation:

exactly what you have there is the procedure

Answer:

He will read 92 pages in an hour going by the current rate at which he reads

Step-by-step explanation:

The complete question is as follows;

Jamil found that he reads 1/5 of his 115 - page book in 1/4 of an hour. At this rate how many pages does he read in an hour

We proceed as follows;

If he reads 1/5 of 115 in 1/4 hour

1/5 of 115 pages refer to 1/5 * 115 = 23 pages

This means that he reads 23 pages in quarter of an hour

So in an hours the number of pages he will read will be 23 * 4 = 92 pages

Answer:

X=-2.5+3

Step-by-step explanation:

2x + 5y = 6

2X=-5Y+6

X=-2.5Y+3

User involvement throughout the number of systems project is essential in the successful development of business information systems.

User involvement throughout the systems project is essential in the successful development of business information systems.The process of gathering user requirements and feedback is an important part of the development process. User involvement helps to ensure that the system meets the users needs and is aligned with the overall business objectives.

User involvement throughout the number of systems project is essential in the successful development of business information systems.

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The value of beta considering the standard deviation of the market is equal to 0.8419 or 1.1581

Tracking Error Volatility is defined as the standard deviation of the difference in returns between an investment and its benchmark.The extent to which the returns on a portfolio deviate from those of a benchmark is known as tracking error. It's also known as the active risk of a portfolio.It's typically expressed as a percentage and is computed as the standard deviation of the portfolio's active returns divided by the expected portfolio return or average benchmark return.

Beta (β) is a measure of a security or portfolio's volatility in comparison to the entire market. Beta compares the volatility of a security to that of the overall market, which has a beta of 1.0.The market, typically represented by an index such as the S&P 500, has a beta of 1.0. A beta of less than 1.0 indicates that the security is less volatile than the market, whereas a beta of more than 1.0 indicates that the security is more volatile than the market.As a result, beta is a measure of the systematic risk of a security or portfolio.

To calculate the possible value(s) for Beta, we have to use the following formula:

σ TE2=(1−β) 2 σ m2 +σ ε2

Here is the solution:

σ TE2=(1−β) 2 σ m2 +σ ε23.5²

= (1 - β)² × 20² + 1.5²12.25

= (1 - β)² × 400 + 2.25(1 - β)²

= 10/400

= 0.025

Taking the square root of both sides, we get:

1 - β = 0.1581 or -0.1581β

= 0.8419 or 1.1581

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Why the solution for an absolute value equation or inequality typically result in a pair of equations or inequalities?

Because the absolute value equations behave differently in the different ranges.

For a given absolute value equation (or inequality)

| x - a| = b

We get two equations or inequalities:

x - a = b

x - a = - b

And this is why the solution leads to two equations, this originates in the fact that the parent absolute value function:

f(x) = |x|

Behaves differently if x is positive or negative.

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Yes, the two cones are congruent because they have the same radius, height, and volume, indicating that they share the same shape and size. Their identical properties provide clear evidence of their congruence.

Congruence means that two objects have the same shape and size. In this case, the cones have the same radius, height, and volume, which are all key properties that determine their shape and size.

To demonstrate their congruence, we can examine the relationships between these properties. Since the cones have the same radius, their circular bases are identical in size. The height of the cones is also the same, meaning their slant heights and lateral surfaces are equal.

Additionally, the volume of a cone is calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height. Given that the volumes of the two cones are equal, it implies that their radii and heights are proportional.

Considering all these factors, we can confidently conclude that the two cones are congruent. Their identical radii, heights, and volumes provide substantial evidence that they share the same shape and size, satisfying the criteria for congruence.

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Nevertheless, it appears that the question is not fully formed; the appropriate request should be:

Answer:

-2640

Step-by-step explanation:

5³ = 125

11³ = 1331

16³ = 4096

125 + 1331 = 1456

1456 - 4096 = -2640

a. Φ(t)= P.D.\(P^{-1}\) is the fundamental matrix of the homogeneous system.

b. \(P^{-1}\)= 1/√5 || 1 2 || || -2 1 || is the inverse

c. x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).\(x_0\)

d. The solution to the system is x(t)= || e-t/√5 (1-e2t)/2√5 - (2e2t -3)/2√5 || || 1/√5 e-t/√5 +2/√5 (e2t-1)/2√5 ||

In this problem, we will solve the nonhomogeneous system.

Firstly, we will write a fundamental matrix for the associated homogeneous system 1 1 2 0.

a) Fundamental matrix for the homogeneous system

The homogeneous system of equations can be written as:

X'=AX

Here, X is the vector of unknowns, and A is a matrix of constants.

For the given homogeneous system of equations, we have:

1 1 2 0X1' X2'= 1 2 X1X2

X'= AX

Thus, the matrix A can be written as:

A= 1 2 1 0

Now, let us solve the eigenvalue problem for matrix A as follows:

| A - λI |= 0

⇒| 1 - λ 2 || 1 || λ - 0 || 1 || 2 || 0 - λ || 0 |

⇒ (1-λ)(0-λ)-2⋅1=0

⇒ λ2 - λ - 2 = 0

On solving, we get:

λ1 = -1 and λ2 = 2

Thus, the eigenvectors corresponding to these eigenvalues are:

For λ1 = -1, A - (-1)I= 2 2 || x || = 0 1 || y ||

⇒2x+2y = 0y = -2x

Thus, the eigenvector corresponding to λ1 is:

x1= || 1 || and x2 = || -2 ||

The normalized eigenvector corresponding to λ1 is:

x1= || 1/√5 || and x2 = || -2/√5 ||

For λ2 = 2, A - 2I= -1 2 || x || = 0 -2 || y ||

⇒-x+2y = 0y = 1/2x

Thus, the eigenvector corresponding to λ2 is:

x1= || 2 || and x2 = || 1 ||

The normalized eigenvector corresponding to λ2 is:

x1= || 2/√5 || and x2 = || 1/√5 ||

Thus, the matrix P of eigenvectors is:

P= || 1/√5 -2/√5 || || 2/√5 1/√5 ||

Hence, the fundamental matrix of the homogeneous system is:

Φ(t)= P.D.\(P^{-1}\)

where D= diagonal matrix of eigenvalues= || -1 0 || || 0 2 ||and \(P^{-1}\) is the inverse of matrix P.

We will now find the inverse of matrix P.

b) Computation of inverse of matrix P

The inverse of matrix P is:

\(P^{-1}\)= 1/√5 || 1 2 || || -2 1 ||

c) Multiplication by and integration

Multiplying Φ(t) by e

At, we have:e AtΦ(t)= PeDt.

\(P^{-1}\).eAt= P.|| e-1t 0 || || 0 e2t ||.\(P^{-1}\)

The solution to the system is:

x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).\(x_0\)

where b(t) is the vector of inhomogeneous terms, and \(x_0\) is the initial condition.

d) Solution to the system

The nonhomogeneous system of equations can be written as:

X'=AX + b

where b= 1 \(e^{-t}\)

The solution to the system is:

x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).x0= P.|| e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.P-1 .|| 0 || || 1 ||+ P.|| 1/√5 -2/√5 || || e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.P-1 .|| -1/√5 || || 2/√5 ||= || 1/√5 -2/√5 || || e-t/√5 (1-e2t)/2√5 || || (e2t-3)/2√5 e-t/√5 ||.|| 0 || || 1 ||+ || 1/√5 -2/√5 || || e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.|| -1/√5 || || 2/√5 ||
The final answer is: x(t)= || e-t/√5 (1-e2t)/2√5 - (2e2t -3)/2√5 || || 1/√5 e-t/√5 +2/√5 (e2t-1)/2√5 ||

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The cost of the product as a function of the price p is (2/25)\sqrt{100-p}+ 600\\.

We have given that

the price of the product p in terms of the quantity sold x is,

p= (- 1/4)x+100, 0\leq x\leq 400

⇒(p-100)=(- 1/4)x

⇒x=400-4p

The cost of production is

c=\sqrt{x} /25  + 600

substituting the value of x

⇒c=  \sqrt{400-4p}/25 +600

  c= (2/25)\sqrt{100-p} + 600

Therefore the cost c as a function of the price p is                                     c= (2/25)\sqrt{100-p}+600

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Answer: $1.25 Per Roll

Step-by-step explanation:

(14,17.50) and (16,20)

Answer:

(2 , 72) and (5 , 180)

Step-by-step explanation:

Options A (2 , 72) and C (5 , 180) will be the correct options.

An equation is an expression that shows the relationship between two or more numbers and variables.

we are Given equation representing the relation between two variables 'x' and 'y' is,

y = 36x

Here, y = yards and x = inches

Now Satisfy this equation with each point given in the question;

Option A. (2, 72)

72 = 36 × 2

72 = 72

This is True

Option B. (4, 40)

40 = 36 × 4

40 = 144

This is False

Option C. (5, 180)

180 = 36 × 5

180 = 180

This is True

Option D. (40, 4)

4 = 36 × 40

4 = 1440

This is False

Option E. (72, 2)

2 = 36 × 72

2 = 2592

This is False

Option F. (180, 5)

5 = 36 × 180

5 = 6480

This is False

Therefore, Options (A) and (C) will be the correct options from all the other

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The answer is true. When a function is invoked with a list argument in Python, the reference to the list is passed to the function.

This means that any changes made to the list within the function will affect the original list outside of the function as well.

Here's an example to illustrate this behavior:

def add_element(lst, element):

   lst.append(element)

my_list = [1, 2, 3]

add_element(my_list, 4)

print(my_list)  # Output: [1, 2, 3, 4]

In this example, the add_element function takes a list (lst) and an element (element) as arguments and appends the element to the end of the list.

When the function is called with my_list as the first argument, the reference to my_list is passed to the function.

Therefore, when the function modifies lst by appending element to it, the original my_list list is also modified. The output of the program confirms that the original list has been changed.

It's important to keep this behavior in mind when working with functions that take list arguments, as unexpected modifications to the original list can lead to bugs and errors in your code.

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The volume of the finely shredded paper that will be needed to completely fill the box with bowling balls to prepare for shipping is 2341 cubic inches.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

We have cubic box with edge length 17 inches

Volume of the cube = (side)³ = 17³ = 4913 cubic inches

As given, the bowling balls that are packaged are all the same size and are tangent to each other and the sides of the box

The radius of each ball will ball:

r = 17/4 inches

Volume of each(ball) sphere:

\(\rm V = \dfrac{4}{3}\pi r^3\)

\(\rm V = \dfrac{4}{3}\pi (\dfrac{17}{4})^3\)

V = 321.55  cubic inches

Volume for the 8 balls:

V = 8×321.55  = 2572.4 cubic inches

The total volume of finely shredded paper is:

V(s) = 4913 - 2572.4  = 2340.60 ≈ 2341 cubic inches

Thus, the volume of the finely shredded paper that will be needed to completely fill the box with bowling balls to prepare for shipping is 2341 cubic inches.

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The probability that the flower picked by the customer is not a rose is 0.75, or 75%. can be calculated by dividing the number of flowers that are not roses by the total number of flowers in the inventory.

In this case, the inventory has 2525 roses, and the total number of flowers in the inventory is the sum of the different types of flowers: 2525 + 1515 + 3030 + 2020 + 1010 = 10100.

To find the number of flowers that are not roses, we subtract the number of roses from the total number of flowers: 10100 - 2525 = 7575.

Therefore, the probability that the flower picked by the customer is not a rose is 7575/10100, which simplifies to 3/4 or 0.75.

So, the probability that the flower picked by the customer is not a rose is 0.75, or 75%.

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Answer:

Russia won 22 medals. Germany won 29 medals.

Step-by-step explanation:

Let's let R denote the amount of medals Russia won and G denote the amount of medals Germany won.

We know that Russia won 7 fewer medals than Germany. In other words, however many medals Germany won, we subtract 7 to get the amount Russia won. In an equation, this is:

\(R=G-7\)

We also know that the two countries won a total of 51 medals. So:

\(R+G=51\)

This is a system of equations. We can solve by substitution.

Let's substitute our first equation into the second. This yields:

\((G-7)+G=51\)

Combine like terms:

\(2G-7=51\)

Let's add 7 to both sides. The left side cancels:

\(2G=58\)

Divide both sides by 2:

\(G=29\)

So, Germany won 29 medals.

Since Russia won 7 fewer medals, Russia won 29 - 7 or 22 medals.

And we're done!

Answer:

\(4.6\ \text{cm}\)

Step-by-step explanation:

Perimeter of the pentagon = 20.5 cm

Length of 4 sides = \(x\)

Length of the other side = 2.1 cm

Perimeter of the pentagon will be

\(x+x+x+x+2.1=20.5\\\Rightarrow 4x+2.1=20.5\\\Rightarrow 4x=20.5-2.1\\\Rightarrow 4x=18.4\\\Rightarrow x=\dfrac{18.4}{4}\\\Rightarrow x=4.6\ \text{cm}\)

The value of \(x\) is \(4.6\ \text{cm}\).

Answer:

OPTION 2

Step-by-step explanation:

The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular  x   value. The   y   value of a point where a vertical line intersects a graph represents an output for that input  x   value. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that   x   value has more than one output. A function has only one output value for each input value.

--------------------------------------------------------------------------

HOW TO: GIVEN A GRAPH, USE THE VERTICAL LINE TEST TO DETERMINE IF THE GRAPH REPRESENTS A FUNCTION.

1.Inspect the graph to see if any vertical line drawn would intersect the curve more than once.

2.If there is any such line, the graph does not represent a function.

3.If no vertical line can intersect the curve more than once, the graph does represent a function.

(The 2nd pic represents a graph that has a function)

The central limit theorem (CLT) states that as sample size increases, "The correct answer is C - both A and B". The shape of the distribution of sample means tends to be normal if the population from which the samples are obtained is normal and the sample size is n-30 or more.

the distribution of sample means will approach a normal distribution regardless of the shape of the population distribution, provided that the sample size is large enough. Therefore, the answer to this question involves both the conditions of the CLT and the nature of the population distribution.

Condition A states that the population from which the samples are obtained must be normal. This means that the population distribution is symmetrical and bell-shaped, with most of the observations clustered around the mean, and the tails of the distribution taper off towards plus and minus infinity. If the population is not normal, then the sample mean distribution may not be normal, regardless of sample size.

Condition B states that the sample size should be n-30 or more. The rule of thumb is that if the sample size is greater than or equal to 30, the distribution of sample means will be approximately normal, regardless of the population distribution. This is because as sample size increases, the sample means will tend to cluster around the population mean, and the standard error of the mean will decrease. This, in turn, will result in a narrower and more symmetrical distribution of sample means.

Therefore, both conditions A and B must be satisfied for the distribution of sample means to be normal. If either of these conditions is not met, the distribution of sample means may not be normal.

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The length of the garden is 99 m.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the area of the rectangle is 8811 \(m^{2}\) and the width is 89 m. Substituting these values into the formula, we get:

8811 \(m^{2}\) = Length x 89 m

To solve for the length, we can divide both sides of the equation by 89 m:

Length = 8811 \(m^{2}\) / 89 m

Simplifying, we get:

Length = 99 m

Therefore, the length of the garden is 99 m.

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Answer:

a. The given equation is d = -75·t + 275 is a function

b. f(t) = -75·t + 275

c.  275 km

d. The situation does not makes sense for t > 11/2 hours.

Step-by-step explanation:

a. Given that a relation is a functional relation if for each input of a member in the relation, there is only one output for the other member, therefore;

The given equation is d = -75·t + 275 is a function

As when t = 1, d = 200 km

b. The equation written in functional notation, f(t) is f(t) = -75·t + 275

c. At the start of the journey, t = 0

Therefore;

f(0) = -75×0 + 275 = 275 km

d. The values of t that do no make sense in the function are given as follows

0 = -75×t + 275

t = 275/75 = 11/3 = 3.67 hours

For times above 3.67, the distance becomes negative

Therefore, the situation does not makes sense for t > 11/2 hours.

Answer:

infinite

Step-by-step explanation: pi is a never ending number with no patterns

Answer:

On Thursday, G00gle announced that one of its employees, Emma Haruka Iwao, had found nearly 9 trillion new digits of pi, setting a new record. Humans have now calculated the never-ending number to 31,415,926,535,897 (get it?) — about 31.4 trillion — decimal places.

Answer: In mathematics, the reciprocal of a number is 1 divided by that number. So the reciprocal of 7/9 is 1/(7/9) which can be simplified to 9/7.

Therefore, 9/7 is the number that when multiplied by 7/9 will result in the product of 1.

Another way of arriving at the same solution is to remember that the product of a number and its reciprocal is always 1. In this case, the number is 7/9, and its reciprocal is 9/7.

Step-by-step explanation:

Answer:

i don't know I don't have ideas about it