A linear relationship is given in the table.
x y
4 11
2 7
0 3
−2 −1
What is the slope of the relationship?
(A)−3
(B)−2
(C)2
(D)3

The graph of a proportional relationship is simply a straight line that passes through the origin

Proportional relationships are used to relate variables that have equivalent ratios.

Using tables

Assume the variables are x and y.

To make use of tables, then the values of x and y must change at a constant rate.

Take for instance, the following table of values

x: 1, 2, 3

y: 2, 4, 6

Notice that, as x increases by 1; y increases by 2.

Such relationship is a proportional relationship

Using equations

A proportional relationship is represented by the following equation

Where k represents the proportionality constant, and k is not equal to 0

An example of such equation is

Using graphs

The graph of a proportional relationship is simply a straight line that passes through the origin, and does not have an undefined slope or a slope of 0

Therefore, The graph of a proportional relationship is simply a straight line that passes through the origin

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The Laplace transform of the ramp function is equal to -  [tex]\frac{m}{s^2}[/tex].

If a function has a finite number of breaks and does not blow up to infinity anywhere, it is said to be piecewise continuous. Assuming that f(t) is a piecewise continuous function, the Laplace transform is used to define f(t). Lf(t) or F is the symbol for a function's Laplace transform (s). When a differential equation is reduced to an algebraic issue, the Laplace transform aids in its solution.

Applying  Laplace transformation on function x(t)=mt,

[tex]L{[x(t)]=X(s)= \lim_{t \to \infty} [\int_0^Tmte^{-st}dx]\\\\\\[/tex]

[tex]X(s)=m \lim_{t\to \infty} [\int_0^Tte^{-st}dx] \\[/tex]

To solve the integration e use the parts method,

[tex]\int_0^Tudu=uv]_0^T-\int_0^Tv du\\[/tex]

Let u=t and [tex]dv=e^{-st}dt[/tex]

[tex]X(s)=m \lim_{n \to \infty} [te^{-st}/-s]_0^T-\int_0^Te^{-st}/-sdt]\\\\=m \lim_{n \to \infty} [\frac{Te^{-sT}}{-s}-0-\frac{e^{-sT}}{(-s)^2} +e^0/-s]\\\\\\X(s)=\frac{m}{s^2}[/tex]

The Laplace transform of the ramp function x(t) = mt, whose slope is the constant m- X(s)=  [tex]\frac{m}{s^2}[/tex].

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Answer:

B) 11.42

Step-by-step explanation:

Using the Law of Cosines:

[tex]c=\sqrt{a^2+b^2-2ab \cos C}=\sqrt{9^2+12^2-2(9)(12)\cos 64^{\circ}} \approx 11.42[/tex]

Answer:

[tex]15x^{5}y^{6}\\[/tex]

Step-by-step explanation:

First, we need to know that the area of a rectangle is length times width. Since we know both length and width, let's plug that into the formula for the area of a rectangle.

Area of a rectangle = length * width  

Area of a rectangle =[tex]3x^{3} y^{2}*5x^{2} y^{4}[/tex]

Now, we need to solve [tex]3x^{3} y^{2}*5x^{2} y^{4}[/tex]:

[tex]3x^{3} y^{2}*5x^{2} y^{4}\\15x^{5}y^{6}[/tex]

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Answer:

True

Step-by-step explanation:

If dividing polynomial P(x) by polynomial Q(x) produces a remainder of 0, then it means that Q(x) is a factor of P(x). This is because when we divide P(x) by Q(x), we are looking for a polynomial that, when multiplied by Q(x), will give us P(x). If the remainder is 0, it means that Q(x) is a factor of P(x) because it can be multiplied by Q(x) to give us P(x) exactly, with no remainder.

The Angle e = Angle a, as they are alternate angles,

Angle f = Angle c, as they are alternate angles,

Angles a, b, and c add up to 180° as they are on a straight line.

Therefore, angles e, f, and b also add up to 180°.

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

Given two lines are parallel and intersect by two transversal and they form a triangle between the lines,

from the diagram alternate angles are,

∠e and ∠a

∠f and ∠c

so ∠e = ∠a and ∠f = ∠c because they are alternate angles,

a straight line makes an angle of 180°

so the sum of Angles a, b, and c are 180°.

and the sum of the angles of a triangle is 180°

the sum of angles e, f, and b is equal to 180°.

Hence ∠e = ∠a and ∠f = ∠c,

the sum of Angles a, b, and c are 180°,

the sum of angles e, f, and b is equal to 180°.

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The number of cows equation he has is 40

A system of equations is any set of two or more equations that may be solved to get a single answer. The power of the equation must be in one degree. It is possible to employ a set of equations with variables for cows and chicks. Animals on the farm are consequently x+y=40. The legs of the farm are 4x+2y=100 as a result. A system of equations is a collection of two or more equations that use the same variables. The answer to a system of equations is a set of values for a variable that concurrently satisfy each equation.

h is the number of horses the farmer owns.

Now,h+5h=168

6h=168

h=168/6

h=28 horses.

5*28=140 cows.

28+140=168

168=168

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The piecewise function is defined as follows:

A piecewise function is a function that has different definitions, according to the input values assumed by the function.

The different definitions for the function in this problem are given as follows:

To the left of x = -2, the function is increasing with a slope 1, hence it would cross the y-axis at y = 1, and the definition is given as follows:

y = x + 1, x < -2.

At x = 2 and between x = 02 and x = 1, the function is constant.

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Answer:

You will have to pay 1/4 * $378.56 = $94.64 of the cost for the electric guitar on eBay

Answer: $94.64

Step-by-step explanation:

378.56 x 0.75 = 283.92

378.56 - 283.92 = $94.64

The probability of being either blood type a or blood type o is 5/8.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. A probability of 0.5, for example, means that an event has an equal chance of occurring or not occurring. The field of probability is used in many areas including statistics, mathematics, finance, and science to model and analyze uncertain events.

The probability of being either blood type A or blood type O is equal to the sum of the probabilities of being each blood type.

Probability of being blood type a + Probability of being blood type o = 1/8 + 1/2 = 5/8.

Hence, the chance of having either blood type A or O is calculated to be 5 out of 8.

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The number of different pizzas that can be made at the pizza shop is 1024.

This is because you have the option of choosing 10 toppings, and for each topping, we have two different choices: either include it or not. So, we have 2 choices for the first topping, 2 choices for the second topping

Step 1:

with the pizza topping or choose as many as topping as we want,

Total topping available = 10

The formula is given by,

1) with no topping option

2) with one topping option

3) with 2 topping options

4) with 3 toppings = option

Step 2:

5) with 4 topping

6) with 5 topping options

7) with 6 topping options

8) with 7 toppings

9) with 8 topping options

10) with 9 toppings option

11) with 10 toppings option

Step 3:

So the total number of different pizzas that can make at a pizza shop is = 1+10+45+120+210+252+210+120+45+10+1

So the total number of different pizzas that can be made at the pizza shop is 1024.

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Probability of obtaining at least 4 defectives in sample of 10 parts calculated 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)].

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.

Let's denote the number of defectives as X and the total number of parts as n = 10. The probability of obtaining k defectives in a sample of 10 parts can be calculated as:

P(X = k) = (10 choose k) * p^k * (1 - p)^(10 - k)

where (10 choose k) is the binomial coefficient, which can be calculated as 10! / (k! * (10 - k)!).

To find the probability of obtaining at least four defectives, we sum the probabilities of obtaining 4, 5, 6, 7, 8, 9, and 10 defectives:

P(X >= 4) = 1 - P(X < 4)

Probability of obtaining at least 4 defectives in sample of 10 parts calculated 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)].

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The value of x at which the minimum value of y occurs in [0, 1] is B) 1/8

Given y = 3x^(4/3) - 2x

We are asked to determine the value of x at which the minimum value of y occurs in [0, 1].

                                    Now, dy/dx = 0

                                     4x^(1/3) - 2 = 0

                                             x^(1/3) = 1/2

                                                     x = 1/8

Here, dy/dx = 0 when x = 1/8

So calculating y at x = 0, 1/8, 1

y(x = 0) = 0

y(x = 1/8) =3 (1/8)^(4/3) - 2/8 =  -1/16

y(x = 1) = 1

Hence, y has a minimum value of -1/16 at x = 1/8

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Answer:

Area of Triangle is 225 cm^2

Step-by-step explanation:

Let height of triangle be h

Let the base of triangle be b

It is given that the sum of base and height is 45

b + h = 45  ---------(1)

It is also given that the height is twice of base

2b = h ---------------(2)

by substituting (2) in (1)

b + 2b = 45

3b = 45

b = 15 cm

15 + h = 45

h = 30 cm

Area of triangle is given as

1/2 x b x h

= 1/2 x 15 x 30

= 225 cm^2

The area of the figure is 98 square meters.

Area is the amount of area occupied by an object's flat (2-D) surface or shape.

A figure is given.

To find the area of the figure:

We will find the area in separate terns.

The area = 4 x 2 + (8+4) x 4 + (8 + 4 + 2) x 3

The area of the figure = 8 + 48 + 42

The area of the figure = 98 square meters.

Therefore, the area is 98 square meters.

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The only function [tex]z=e^{y}(ycosx - xsiny)[/tex] satisfies the equation and is considered a harmonic function.

The equation ∂^2.z/∂x^2 + ∂^2.z/∂y^2 = 0 is known as Laplace's equation, and it is used to determine if a given function is a harmonic function. In this case, we have two functions

=>[tex]z=e^{y}(ycosx - xsiny)[/tex] and

=> [tex]z=e^y(ycosx - xsinx)[/tex], and we need to determine which of these functions, if any, satisfies Laplace's equation.

The first step in this process is to calculate the partial derivatives of the functions.

After calculating the partial derivatives, we can then substitute them into Laplace's equation to see if the equation is satisfied.

In this case, only function[tex](1) z=e^y(ycosx - xsiny)[/tex] satisfies Laplace's equation, which makes it a harmonic function.

Function [tex](2) z=e^y(ycosx - xsinx)[/tex]does not satisfy Laplace's equation and is therefore not a harmonic function.

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if a and b are invertible n×n matrices, then the inverse of a+b is a−1+b−1. Let W be the inverse of AB. Then WAB = I and (WA)B = l. Therefore, matrix B is invertible by part (j) of the IMT by letting C = WA.

We have A and B are two n × n matrices and AB is invertible. We have to prove that B is invertible by showing a valid reason given by one of the four options:

The first option is not valid proof. since W is the inverse of A B would imply WAB = I, as multiplying a matrix by its inverse will produce the identity matrix of the corresponding order. Here stated that WAB = B, which is invalid.

It is true that AB invertible implies  is invertible but this does not imply B is invertible (not a valid statement).

A B is invertible does not mean . Since  implies AB = I, but AB need not be only the identity matrix. So these statements are invalid.

W being inverse of AB, this gives WAB = I

(WA) B = I since matrix multiplication is associative.

WA is the inverse of B, as multiplying WA by B produces the identity matrix I. Hence, this is valid proof to show that B is invertible.

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The value of Trigonometric function is

sin Q = 5/13

cos Q = 12/13

tan Q = 5/12

sin S = 12/13

cos S = 5/13

tan S = 12/5

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

RS = 5

RQ = 12

QS = 13

Using Trigonometry

sin Q = P/H

         = 5/13

and, cos Q = B/H

         = 12/13

and, tan Q = P/B

                  = 5/12

and, sin S = P/H

                 = 12/13

and, cos S = B/H

                  = 5/13

and, tan S = P/B = 12/5

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The length of FG is sqrt(84) and the radius of the circle is sqrt(21).

Let's call the radius of the circle "r".

The area of the shaded sector can be expressed as a fraction of the total area of the circle:

Area of sector = (m∠ GFH / 360°) * πr^2

Since the area of the shaded sector is given as 14π, we can write:

(m∠ GFH / 360°) * πr^2 = 14π

Solving for r:

r^2 = 14 / (m∠ GFH / 360°)

r = sqrt(14 / (m∠ GFH / 360°))

Plugging in m∠ GFH = 140°:

r = sqrt(14 / (140 / 360°))

r = sqrt(14 / (2 / 3))

r = sqrt(21)

Finally, the length of FG can be found by multiplying the radius by 2:

FG = 2 * r = 2 * sqrt(21) = sqrt(84).

So, the length of FG is sqrt(84) and the radius of the circle is sqrt(21).

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Complete question.

In circle F, m∠ GFH=140°

and the area of the shaded sector = 14π. Find the length of FG

FG finds the radius of the sector area

5.7(26 - 3.82x) = 5.7(26) - 5.7(3.82x) = 149.2 - 21.534x

Answer:

5.7(26-3.82x)

(5.7*26) + (5.7*-3.82x)

148.2 + -21.774x

Step-by-step explanation:

According to the problem the algebra tile shape is 13.

Algebra is a branch of mathematics that uses symbols to represent numbers and operations. It helps us to solve problems by using equations and formulas. Algebra is used in many fields, including science and engineering. It is used to solve equations, simplify expressions, and graph functions. Algebraic equations can be used to describe and analyze relationships among different variables. Algebra is also used in applications such as financial planning, engineering, and computer programming. Algebraic equations can be used to solve real-world problems, such as calculating the area of a triangle or finding the maximum profit in a business.

The algebra tile shape at right can be represented as follows:

(x + 1)(x + 2)

The perimeter of the shape can be calculated by adding up the lengths of the four sides. The expression for perimeter is therefore:

Perimeter = 2x + 3

For x = 5, the perimeter is:

Perimeter = 2(5) + 3 = 13

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On simplifying the equations and using mathematical operations, 203 $1 bags were sold,

Mathematical operations can be made more simpler by using the right order of operations. Exponents, terms in parentheses, multiplying, division, addition, and ultimately subtraction are the right order of operations. You can use the acronym PEMDAS to help you remember this.

Pricing times units sold equals revenue, thus if N is the total amount of $3 bags sold, then 307 - N must represent the amount of $1 bags sold (total sales)

3(N) + 1(307-N) = 515 simplify

3N + 307 - N = 515

2N + 307 = 515 Take 307 off both sides.

Divide both sides by 2 if 2N = 208.

The overall amount of $3 bags sold is N = 104.

203 $1 bags were sold, which is 307 - 104.

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Answer:

  (c)  6x − y < −3

Step-by-step explanation:

You want to know which inequality has shading above the dashed line through (0, 3) and (1, 9).

The first given point is the y-intercept of the boundary line: 3. The two points together can be used to find the slope:

  m = (y2 -y1)/(x2 -x1)

  m = (9 -3)/(1 -0) = 6

This means the slope-intercept equation of the line is ...

  y = mx +b

  y = 6x +3

Rearranging to standard form, this is ...

  6x -y = -3

The fact that the boundary line is dashed means the inequality symbol will not include the "equal to" case. It will be one of < or >.

The shading above the line with positive slope is the same as shading to the left of that line. That is, x-values in the solution set will be less than x-values on the line. The inequality will be ...

  6x -y < -3

__

Additional comment

You can determine line type and shading by looking at the inequality symbol and a variable with a positive coefficient. In the above inequality, x has a positive coefficient, so that is the one we considered when looking at shading. X-values less than those on the line means the relation shown in the inequality will be ...

  x <

Shading above the line would look like ...

  y >

In our equation for the boundary line, the coefficient of y is negative. Multiplying this inequality by -1 would give ...

  -y <

Hence the inequality 3x -y < -3 is consistent with a dashed line having shading above and to the left.

If the symbols are < or >, the line is dashed. If they are ≤ or ≥, the line is solid.

The Fourier transform of x(t) = 2sin(2πf0t)cos(2πf0t) is π/2)δ(f - f0) + (π/2)δ(f + f0).

A Fourier transform (FT) is a mathematical operation that separates functions into frequency components. The output of the transform is shown as a function of frequency. The most frequent transformations include functions of time or space, and the function that results depends on the frequency of the input variable (either time or space). Analysis is the name given to the process.

The Fourier transform of x(t) = 2sin(2πf0t)cos(2πf0t) is,

                                     X(f) = (π/2)δ(f - f0) + (π/2)δ(f + f0),

where δ is the Dirac delta function.

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Answer:

y-12=-32

Step-by-step explanation:

no explanation needed

Answer:

13

Step-by-step explanation:

Standard form is a convenient approach to effortlessly record extremely big or extremely small values.

Ax + By= C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x + 3y = 5. Finding both intercepts of an equation in this format is rather simple (x and y). When resolving systems of two linear equations, this form is also incredibly helpful.

Here,

Standard form is a convenient approach to effortlessly record extremely big or extremely small values. Ax + By = C is the formula for a linear equation. You must place the x and y on the same side of the equal sign and the constant on the other side in order to convert an equation in slope-intercept form (y=mx+b) to standard form. Terms can be moved using inverse procedures.

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The complete question is "What is standard Form and how to write the equation in standard from ?"

Answer:
56.25

Step-by-step explanation:

2.25/4= 0.5625
0.5625 to a percentage:
0.5625 x 100 =
56.25