Find the domain and range of the relation: { ( 4 , − 4 ) , ( 3 , − 4 ) , ( 2 , − 4 ) , ( 1 , − 4 ) } . Then determine whether the relation is a function.

A hole in a graph appears as a break in the graph line, while a vertical asymptote appears as a line segment that the graph approaches but never crosses.

A hole in a graph appears as a break in the graph line; it's the point where the graph does not exist. Typically, the x-value of this point is the x-coordinate of the hole. To find out if there is a hole, you need to see if the graph is continuous and check to see if there is a break in the graph line.A vertical asymptote appears as a line segment that the graph approaches but never crosses. This occurs when the function value approaches positive or negative infinity. To find out if there is a vertical asymptote, you need to look at the function and see if it is undefined at any particular x-value. If it is, then there is a vertical asymptote.

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The graph of an inequality is shown below -

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which x-y pairings are the inequality's solutions.

Example -

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

Now, the graph becomes according to the slope-intercept form is:

Here we noticed that,

This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.

Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.

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A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

A function can have a "hole" if it is not defined at a certain input value. For example, consider the following function:

f(x) = 1/x

This function has a hole at x=0 because it is not defined at that value. If you try to evaluate the function at x=0, you will get an error or an undefined result.

To determine whether a function has a hole, you can consider the domain of the function, which is the set of all input values for which the function is defined. If there are any values in the domain for which the function is not defined, then the function has a hole at those values.

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Using the Poisson distribution and the exponential distribution, on average, there are (C) 2.25 consumers in line behind the person serving.

The Poisson point process, or a process in which events occur continuously and independently at a constant average rate, uses an exponential distribution to represent the probability distribution of the time between occurrences.

Statistics and probability theory both make use of this distribution.

So, we know that:

6 arrivals on average are made per hour (Poisson distribution).

It provides two services every fifteen minutes (exponential distribution).

Waiting line behind the person being served:

(15 / 6 * 2) + 1

(15 / 12) + 1

1.25 + 1

2.25

Therefore, using the Poisson distribution and the exponential distribution, on average, there are (C) 2.25 consumers in line behind the person serving.

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The nature of roots of the given quadratic equation is "real and unequal".

Nature of Roots:

Root type simply means the category to which the root belongs. Roots can be imaginary, real, unequal, or equal. If the discriminant is negative, the root is imaginary.

Depending on the value of the discriminant, we discuss the following cases for the nature of the root:

Case 1: D = 0

If the discriminant is zero (b2 – 4ac = 0), a, b, and c are real, and a≠0, the root of the quadratic equation is ax2 + bx + c = 0 is Real and equal. In this case the root is x = -b/2a. A graph of the equation is tangent to the x-axis at a point.

Case 2: D > 0

If the discriminant is greater than zero (b2 – 4ac > 0), then a, b, and c are real and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is real and not equal. The equation graph touches the x-axis at two different points.

Case 3: D < 0

If the discriminant is less than zero (b2 – 4ac < 0), a, b, and c are real, and a≠0, then the root of the quadratic equation ax2 + bx + c = 0 is Imaginary and not equal. Roots exist in conjugate pairs. The equation graph does not touch the x-axis.

Case 4: Perfect Square with D > 0

If D > 0 and Perfect Square, the roots of the quadratic equation are real, unequal, and rational.

Case 5: D > 0 and Not Perfect Square

If D > 0 and not perfect square, the roots of the quadratic equation are real, unequal, and irrational.

According to the Question:

The given quadratic equation:

2x²-4x-3 = 0

Here, a = 2, b = - 4 and c = -3

To Find: the nature of roots of the given quadratic equation.

∴ Discriminant, D = b²-4ac

= (-4)² - 4×2×(-3)

= 16 -8(-3)

= 16 + 24

=40

Since,

D = 40 > 0, the roots are real and unequal.

Hence, the nature of roots of the given quadratic equation is "real and unequal".

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The standard form of linear equation in two variables is Ax + By = C.

The standard form of linear equation in two variables is Ax + By = C, where A, B and C are constants and A and B are not both zero. This equation can be used to represent a line on a graph, which can be found by plotting any two points that satisfy the equation.

To calculate the equation of a line in standard form, first identify two points on the line. For example, point (x1, y1) and point (x2, y2). Then, calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1). The slope determines the constants A and B for the equation. A = m and B = -1. Finally, calculate the constant C by substituting one of the two points into the equation. C = Ax1 + By1.

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Answer:

1.1 s

Step-by-step explanation:

The mass ( 30 g ) is not needed for this

d = 1/2 at^2

6 = 1/2 ( 9.8)(t^2

t= 1.1 s

3.5% percent does the number of Salmonella cells increase each minutes when y = a(4.7[tex])^{t/45}[/tex].

Given that,

The number of y of Salmonella cells on an egg after t minutes is

y = a(4.7[tex])^{t/45}[/tex]

Here,

y is the number of salmonella cells.

a is the initial number of cells.

t is the time in minutes.

We have to find what percent does the number of Salmonella cells increase each minutes.

We know that,

Take the original function,

y = a(4.7[tex])^{t/45}[/tex]

Take the power of proportionality

y = [a(4.7[tex])^{1/45}]^{t}[/tex]

Evaluating the power

y = [a(4.7[tex])^{1/45}]^{t}[/tex]

y = a(1.035[tex])^{t}[/tex]

y = a(1-0.035[tex])^{t}[/tex]

Therefore, 3.5% percent does the number of Salmonella cells increase each minutes when y = a(4.7[tex])^{t/45}[/tex].

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The slope of the function may be found by differentiating it. Finding the derivative's maxima will show where the function is rising at the fastest pace as slope is defined as the rate of change.

The slope of the function may be found by differentiating it. Finding the derivative's maxima will show where the function is rising at the fastest pace as slope is defined as the rate of change.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

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An asymptote of a function is a line that the graph of the function gets closer and closer to, but never touches. It is an approaching line that has a fixed slope.

An asymptote of a function is a line that the graph of the function gets closer and closer to, but never touches. It is an approaching line that has a fixed slope. Asymptotes are used to determine the behavior of a function as it approaches infinity or negative infinity. They can be used to help visualize the behavior of the function in the large and small limits. Asymptotes can be either horizontal or vertical. A horizontal asymptote is a line that the graph of the function approaches as it approaches positive or negative infinity, and a vertical asymptote is a line that the graph of the function approaches as it approaches either the positive or negative x-axis. Asymptotes can also be used to describe the behavior of a function near a local minimum or maximum. Asymptotes can be found by looking at the degree and leading coefficient of a polynomial, or by analyzing the behavior of the function at different points.

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Answer:

A. The graph is nonlinear.

D. The graph is a function

E. The graph is increasing in two intervals.

Step-by-step explanation:

        We will review each answer choice to decide on our answer to this question.

✓ A. The graph is nonlinear.

             Since the graph has a change in it's rate of increase, it's nonlinear.

✗ B. The function increases at the same rate.

             As stated below, the rate increases after x = 2 so the function is not increasing at the same rate.

✗ C. The rate decreases after x = 2.

             No, the rate increases after x = 2.

✓ D. The graph is a function.

             Yes, there is only one output for every input, so this is a function.

✓ E. The graph is increasing in two intervals.

             The graph is only increasing in two intervals. These intervals change at x = 2.

Answer:

Hence, three equivalent ratios of 8: 6 are 16: 12, 24: 18, and 32: 24.

Step-by-step explanation:

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The general solution of the given non homogeneous

equation is

y(t)=c₁[tex]e^{-t}[/tex] +c₂[tex]e^{t}[/tex] - t

A non-homogeneous system of equations is a system in which the vector of constants on the right-hand side of the equal sign is non-zero.

Given:-General solution for the equation: [tex]y^{"} - y^{'} = t[/tex], [tex]y_{p} (t) = - t[/tex]

Explanation:-Consider the equation [tex]y^{"} - y^{'} = t[/tex] . The corresponding homogeneous equation has the associated auxiliary equation [tex]r^{2} -1 =0[/tex]   which has [tex]r^{} =-1[/tex]  and [tex]r^{} =1[/tex]  as solutions.

The solution of an n-order differential equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.

Hence the general solution for a homogeneous equation is

y(t) = [tex]-t[/tex]+[tex]c[/tex]₁[tex]e^{t}[/tex]+[tex]c[/tex]₂[tex]e^{-t}[/tex]

Combining the general solution [tex]y(t)=c[/tex]₁[tex]e^{t}+c[/tex]₂ [tex]e^{t}[/tex]  with the particular solution of  [tex]y_{p} (t) =-t[/tex] of [tex]y'-y"=t[/tex], we find that the general solution to[tex]y"-y'=t[/tex]  is [tex]y(t)=c[/tex]₁[tex]e^{-t}+c[/tex]₂[tex]e^{t}[/tex]

The general solution of the given non homogeneous equation is

y(t)=c₁[tex]e^{-t}[/tex] +c₂[tex]e^{t}[/tex] - t

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a. The probability that a randomly selected home run was hit to right field is 0.286.

b. The probability that a randomly selected home run was hit to left field is 0.031.

c. Yes it was unusual for this player to hit a home run to left field.

From the information, the baseball player hit 63 home runs in a season. Of the 63 home runs, 18 went to right field, 25 went to right center field, 9 went to center field, 9 went to left center field, and 2 went to left field.

The probability that a randomly selected home run was hit to right field is:

= 18 / 63

= 0.286.

The probability that a randomly selected home run was hit to left field is:

= 2 / 63

= 0.031.

It was unusual for this player to hit a home run to left field as the chance is 3%.

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The perimeter of the figure as shown in the diagram is 60.84 m.

Perimeter is the total distance around an object.

To calculate the perimeter of the figure, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the perimeter of the figure is 60.84 m.

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Option B. It represents a nonlinear function because its points are not on a straight line.

What is linear and non-linear functions?

When plotted on a graph, a linear function produces a straight line. Therefore, any non-linear functions are those that are functions. The quickest way to tell if a function is linear or non-linear is probably by graphing it, but we can also tell if a function is linear by looking at its input/output table or equation.

If A(0, 0), B(1, 0) and C(2, 4).

We know that,

If point A,B and C are on a straight line then the slope of AB must be equal to the slope of AC

The formula to calculate the slope between two points is equal to

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Find the slope AB

A(0, 0) and B(1, 0)

[tex]m = \frac{0-0}{1-0} = 0[/tex]

Find the slope AC

A(0, 0) and C(2, 4)

[tex]m = \frac{2-0}{4-0} = \frac{1}{2}[/tex]

Slope of AB ≠ Slope of AC

Points A, B and C are not on a straight line.

Hence, it represents a nonlinear function because its points are not on a straight line.

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The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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The value of x in the equation 5/3x + 1/3x = 13⅓ + 8/3x is calculated as: x = -20.

To solve an equation is to find the value of the variable by isolating it in such a way that it is moved to one side of the equation.

Given the equation, 5/3x + 1/3x = 13⅓ + 8/3x, to solve this equation, we need to find the value of x by isolating the variable x to one side.

Follow the steps below:

5/3x + 1/3x = 40/3 + 8/3x

2x = 40/3 + 8/3x

Substract both sides by 8/3x:

2x - 8/3x = 40/3 + 8/3x - 8/3x

-2/3x = 40/3

Multiply both sides by -3/2:

-2/3x × -3/2 = 40/3 × -3/2

x = -120/6

x = -20

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In slope intercept form, Equation 14x-20y=-13 can be written as 13 + 4y/20 = y.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Given,

Equation

14x-20y=-13

In slope intercept form

13 + 4x = 20y

13 + 4y/20 = y

In slope intercept form, Equation 14x-20y=-13 can be written as 13 + 4y/20 = y.

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Answer:

“If none of the input values are repeated, the relation is a function” because one input must have one output.

The required equation in the slope-intercept form is y = 2/3x - 4.

Y = MX + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form.

We can see that the slope of the line in our equation, y = 6x + 2, is 6.

So, we have the equation:

2x − 3y = 12

To represent the equation in the slope-intercept form:

First, remove 2x from both sides of the equation to move the independent variable (x) to the right side of the equation.
2x − 3y − 2x = 12 − 2x

− 3y = 12 − 2x

The dependent variable is the only component of the left side of the equation, as seen in the generic equation of a line in slope intercept form, whereas the independent variable and constant are both present on the right side of the equation.

The result of multiplying by 1 and dividing by 3 into both sides of the equation is:

-1 * -3y/3 = -1 * (12 - 2x)/3

y = 2/3x - 12/3

y = 2/3x - 4

Therefore, the required equation in the slope-intercept form is y = 2/3x - 4.

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What kind of line is Y =- 3?

Answer:

This is a horizontal line occurring at y = -3 meaning there is no slope.

Answer:

B

Step-by-step explanation:

Answer: B, √60 .

Step-by-step explanation: Irrational numbers are numbers that can not be written in the form of a/b. To further explain, this includes any decimals that go on forever and are non-repeating, such as pi 3.14159... Numbers that have repeating numbers like 5.5555555 are rational, so don't get confused between the two! The square root of 60 is 7.74596669 making it the only irrational number here.

Part (a)

Company A has the most variability because it has the m greatest range.

Part (b)

Company B has the lowest salaries on average since they have the smallest mean salary.

Answer: City fans = 33,264 fans

because City fans percentage = 100% - 37% = 63%

Multiplier = 0.63 (63/100)

So City fans = 0.63 x 52800 = 33,264

Hope this helps!

Answer:

Step-by-step explanation:

To find out how many fans at the match support City, we first need to find out how many fans support Rovers. We can do this by multiplying the total number of fans by the percentage of fans who support Rovers:

Total fans supporting Rovers = 52800 fans * 37% = 19296 fans

Since the total number of fans at the match is 52800, and 19296 of those fans support Rovers, then the number of fans who support City is:

Total fans supporting City = 52800 fans - 19296 fans = 33504 fans

Therefore, there are 33504 fans at the match who support City.

An asymptote function is called such because it is a line that a curve approaches but never touches, or "asymptotically" approaches.

An asymptote is a line that a curve approaches but never actually touches. It is called an asymptote because the word comes from the Greek asymptōtos, which means "not falling together." Asymptotes are used in mathematics to describe curves that approach a particular line without ever intersecting it. For example, in a graph of a function, an asymptote is a line that the graph of the function approaches, but never intersects with, as it approaches infinity. Asymptotes are also used to describe straight lines in a plane that approach each other at a certain angle, but never meet. In both cases, the idea is that the line or curve approaches the asymptote, but never actually touches it, thus the name asymptaote.

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Answer:

12x -15

Step-by-step explanation:

-3(-4x + 5)

Distribute the -3 to each term inside the parentheses

-3 * -4x + -3 *5

12x -15

The probability that Tara first paints her bedroom green is 1/16.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

In this case, Tara picks out 4 paint colors (beige, blue, green, and gray) to paint 4 rooms in her house (living room, dining room, main bedroom, and kitchen).

The probability of painting bedroom = 1/4

The probability of picking green = 1/4

Therefore, the probability that Tara first paints her bedroom green is:

P(bedroom) × P(green)

= 1/4 × 1/4

= 1/16

The probability is 1/16.

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