How do you find the vertical and horizontal asymptotes of a function using limits?

The lines y = -4x and y = x are neither parallel nor perpendicular.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given equations of line are,

y = -4x and y = x,

The graph of the equations y = -4x and y = x are shown below.

Since, the slope of the line y = -4x is = -4.

And the slope of the line y = x is 1

For the parallel lines, the slope should be equal.

And for the perpendicular lines, the multiplication of slopes should be equal to -1.

In the given equations of line, the slope is neither same nor multiplication is -1.

Therefore, the lines are neither parallel nor perpendicular.

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A =  [tex]s^{2}[/tex]  or A = side x side is the formula of [tex]s^{2}[/tex] .

  When calculating a square's area, you are determining the size of its surface. You can think of it as counting the number of square units that make up the surface as a whole. The formula for calculating the area of a square is A = [tex]S^{2}[/tex], or A = side x side. They are pretty basic animals, squares.

They have four equal sides and four right angles at their intersections, making them two-dimensional shapes. Four equal sides and four equal angle make up the closed, two-dimensional object known as the square. At the vertices, the square's four sides correspond to its four angles. A square's perimeter is equal to the sum of the lengths of all of its sides, and the amount of space it takes up in total is equal to its area.

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Question :

What is the formula  [tex]S^{2}[/tex] of square represents ?

The function 4x+7 does not have a horizontal asymptote.

The horizontal asymptote of a function is a horizontal line that the graph of the function approaches as the x-values get larger or smaller.

In this case, the function 4x+7 does not have a horizontal asymptote. This is because the function is a linear function (a function of the form y = mx + b) and all linear functions have a slope (in this case, the slope is 4) but no horizontal asymptotes.

If you are given the graph of a function and you want to find its horizontal asymptotes, you can look at the degree of the function (the highest exponent of the variable). If the degree of the function is less than the degree of the denominator of the function, then the function will have a horizontal asymptote at y = 0.

If the degree of the function is equal to the degree of the denominator, then the function will have a slant asymptote (a line that the graph approaches as the x-values get larger or smaller). If the degree of the function is greater than the degree of the denominator, then the function will not have any horizontal or slant asymptotes.

--The question is incomplete, answering to the question below--

"What is the horizontal asymptote of y = 4x+7?

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The mean of given numbers is 4.

To find: mean of given numbers.

Given data : 2, 3, 4, 5, 6

Average is the arithmetic mean. also called as mean .

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here, sum of observations =20

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data

Total number of observations=5

The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset.

Substituting values in above formula,

Mean=[tex]\frac{20}{5}[/tex]=4

Therefore, the mean is 4.

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Answer:Taking into account the definition of weigth, the correct answer is option A: the mass of the object is 50 kg.First, you  have to know that mass is an indicator of the amount of matter that makes up a body. Its unit in the International System is the kilogram (kg).The mass of an object will always be the same, no matter where it is located.On the other side, bodies are subjected to the action of forces, such as the force of gravity or electromagnetic forces. So, weight is the action exerted by the force of gravity on the body. That is, weight is a measure of how much force gravity exerts on the mass of an object.The weight of an object is measured in Newton (N) and will vary according to the force of gravity that acts on it.The expression for the calculation of the weight is:P= m×gwhere:P is the weight of a body.m is its mass.g is the gravity or acceleration with which bodies fall.In this case, you know that:P= 980 Nm= ?g= 19.6 Replacing in the expression for the calculation of the weight:980 N= m× 19.6 Solving:m= m=50 kgFinally, the correct answer is option A: the mass of the object is 50 kg

Step-by-step explanation:

The formula that represents the defined sequence is  [tex]4 (-6)^{n-1}[/tex]

The given recursive formula are:

[tex]a _{1} = 4[/tex]

[tex]a _{n} = -6 a _{n-1}[/tex]

Considering n = 2 ,

[tex]a _{2} = -6(a _{2-1})\\ a _{2} = -6(a _{1})\\a _{2} = 4(-6)[/tex]

Considering n = 3 ,

[tex]a _{3} = -6(a _{3-1})\\ a _{2} = -6(a _{2})\\a _{3} = -6 (4(-6))\\a _{3} = 4(-6)^2[/tex]

Considering n = 4 ,

[tex]a _{4} = -6(a _{4-1})\\ a_4}= -6(a _{3})\\a _{4} = -6 (4(-6)^{2} )\\a _{4} = 4(-6)^3[/tex]

So, the formula that represents the defined sequence is  [tex]4 (-6)^{n-1}[/tex]

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Answer:

Answer explained in picture (8.75)

So after doing the division and getting the answer we multiply 8.75 by 4 we will get 35

Using multiplication we get, 4 times 8.75 is about 35.

Here, we have,

given that,

4 times what number is about 35

now, let, the number be x.

so, we get,

4 times x is = 35

or, 4 × x = 35

or, x= 35/4

or, x = 35÷4

or, x = 8.75

Hence, Using multiplication we get, 4 times 8.75 is about 35.

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Therefore , the cube of the number is three times of its  multiplication where as square is two times its multiplication.

A number's square root is the result of multiplying it by itself, which yields the original number. Examples of exponents include squares and square roots. Imagine the number nine. Additionally, this can be expressed as 3x3.

Here,

The original number can be obtained by multiplying the square root of a number by itself,

and the cube root of a number by multiplying it by itself three times.

Therefore , the cube of the number is three times of its  multiplication where as square is two times its multiplication.

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The Multiplicative Inverse of number 5 is "1/5" .

The Inverse (Multiplicative) is defined as the number which when multiplied by the original number give the product as 1 .

In simple words , the product of the number and its multiplicative inverse is 1 .

the number is given to be 5 .

let the multiplicative inverse of 5 be = "x" ;

So , 5×(x) = 1 ;

dividing both sides by 5

5x/5 = 1/5 ;

Simplifying further ,

we get ;

x = 1/5   , and the product of 5 and 1/5 is 1 .

Therefore , the multiplicative inverse is 1/5 .

The given question is incomplete , the complete question is

What is the Multiplicative Inverse of 5 ?

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Answer:

24

Step-by-step explanation:

You need to work out 16% of 150

10% of 150 = 15

1% 0f 150 = 1.5

so, 6% of 150 = 1.5 x 6 = 9

16% = 10% + 6%

so, 16% = 15+9

24 = 16%

Therefore there are 24 left handed students in Year 9.

Answer:-96

Step-by-step explanation:

The temperature in a town is 12°C, then the temperature in degrees Fahrenheit is 53.6°F.

The Fahrenheit temperature scale, named after German physicist Daniel Gabriel Fahrenheit, is the most commonly used temperature measurement in the United States (and its associated territories) and several Caribbean nations. Water freezes at 32°F and boils at 212°F on a Fahrenheit scale (at sea level).

The Celsius temperature scale—originally known as centigrade before being renamed after Swedish astronomer Anders Celsius—is used almost everywhere else in the world. Water freezes at 0 degrees Celsius and boils at 100 degrees Celsius on the Celsius scale (at sea level).

To convert degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.

In the question, the temperature in a town in 12°C .

by applying the equation F=1.8C+32

                                            =1.8×12+32

                                            =53.6°F

Hence, The temperature in a town is 12°C, then the temperature in degrees Fahrenheit is 53.6°F.

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Utilize the standard normal curve to calculate probability as follows:

(A) Go to the row that contains the first two digits of your z score.

(B) Go to the column with the third digit of your z-score.

(C) Find the value at the row and column intersection of the previous stages.

The horizontal axis is approached by the standard normal curve as it stretches continuously in both directions without ever being touched by it.

The center of the bell-shaped, z=0 standard normal curve.

Between z=3 and z=3, almost the entire region under the standard normal curve is located.

Find the z-score of the data value and use a Z-Score Table to find the area under the normal curve in question.

A Z-Score Table is a chart that displays the percentage of values (or area percentage) on a standard normal distribution that is to the left of a specified z-score.

To determine probability, use the ordinary normal distribution.

(A) Go to the row that has your z score's first two digits.

(B) Cross over to the column that has your z score as the third digit.

(C) Find the value at the point where the preceding steps' row and column overlap.

Therefore, utilize the standard normal distribution to calculate probability as follows:

(A) Go to the row that contains the first two digits of your z score.

(B) Go to the column with the third digit of your z-score.

(C) Find the value at the row and column intersection of the previous stages.

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Answer:

Therefore x is either 6 or 5.

The expression given in question can be written in an equation form and hence, we determine the unknown variable x.

An expression is a combination of terms and operator. The terms contain two or more numbers or both numbers and variables. An expression describes a mathematical concept or system of mathematical operation in a symbolic form. The expression which has an equal sign to express the equality among the terms is called equation. So, the only difference between equation and expression is the equal sign =.

The above is a mathematical expression that contains two numbers 1,3 and one variable x along with a subtraction sign, -.

The number 1 is called constant number and number 3 is called the coefficient of x.

In order to do the problem, we can put any real value of x such as x= 0, 1, 2, 3, 4, 5, 6, 7 or -1, -2, -3, -4, 5 and so on.

For each value of x, we get a result either positive or negative.

3×0 -1, when x=0

-1

3×1 -1, when x=1

the result is 2

We can also write the expression in the form of equation by putting an equal sign such as 3x-1 = 0

from the equation, we can easily get the value of x.

3x -1 =0

3x = 1

x =1/3

this is the result.

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The inverse formula is [tex][(f o f^{-1}) (x) ] =[( f^{-1} o f ) (x)] = x[/tex]

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The factor of 6x² 11x 3 is 6x(x + 3).

The factor is a number that can be multiplied by itself to produce a specific result. It is used in mathematics and science to determine the relationship between two or more variables. For example, the factor of 4 is 2 because 2 multiplied by 2 is 4. Factors can also be used to determine the probability of an event occurring or the likelihood of a given outcome. In these cases, the factor is a measure of the degree of influence that one variable has on the other.

The factor of 6x² 11x 3 is 6x(x + 3).

This can be determined by factoring out the greatest common factor (GCF) of the expression.

The GCF of 6x² 11x 3 is 6x, and the remaining factors are x + 3.

Therefore, the factor of 6x² 11x 3 is 6x(x + 3).

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Complete questions as follows-

Factorise: 6x 2+11x+3

Answer:

The coordinate of the midpoint is (\frac{11}{2},\frac{-13}{2}  )\\ with endpoints B(9,−8) and C(2,−5)

Step-by-step explanation:

The equation of the line that passes the points (1, - 6) and (- 5, - 3) is - (1 / 2) · x - 11 / 2.

According to Euclidean geometry, a line can be constructed by setting two points on a plane. By analytical geometry, lines are described by polynomials of the form:

y = m · x + b

Where:

The slope can be found by means of secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

If we know that (x₁, y₁) = (1, - 6) and (x₂, y₂) = (- 5, - 3), then the equation of the line is:

m = [- 3 - (- 6)] / (- 5 - 1)

m = 3 / (- 6)

m = - 1 / 2

b = y - m · x

b = - 6 - (- 1 / 2) · 1

b = - 6 + 1 / 2

b = - 11 / 2

The equation of the line is - (1 / 2) · x - 11 / 2.

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Answer:

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

8% of 575 is 46

Answer:

60

Step-by-step explanation:

Adding [tex]72[/tex] to both sides yields [tex]t=72-12=60[/tex].

Answer:

[tex] \sf \: a) \: 60[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of t.

The equation is,

→ t - 72 = -12

Then the value of t will be,

→ t - 72 = -12

→ t = -12 + 72

→ [ t = 60 ]

Hence, the value of t is 60.

The idea is to find the sum of integers between 1 and 100 using the n×(n+1)/2 where n is the array’s size and subtract the actual sum of array

Python is a popular computer programming language used to create software and websites, automate processes, and analyze data. Since Python is a general-purpose language, it may be used to develop a wide range of applications and isn't tailored for any particular issues.

Python code for computing sum

Find the missing number in a given array

def getMissingNumber(arr):

  # get the array's length

  n = len(arr)

  # actual size is `n+1` since a number is missing from the list

  m = n + 1

  # get a sum of integers between 1 and n+1

  total = m * (m + 1) // 2

 # the missing number is the difference between the expected sum and

  # the actual sum of integers in the list

  return total - sum(arr)

if __name__ == '__main__':

  array_input = input("Enter a list of integers separated by spaces: ")

  array = [int(x) for x in array_input.split()]

  print('The missing number is', getMissingNumber(arr))

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Answer:

4

Step-by-step explanation:

For each kilogram of mass, [tex]0.2+4(0.1)=0.6[/tex] milligrams are needed.

Thus, [tex]0.6(10)=6[/tex] milligrams are needed.

This is equal to 4 mL

Answer:

  4 ml

Step-by-step explanation:

You want to know how many mL of medicine is needed for 5 days when the dose is 0.1 mg/kg per day and the concentration is 1.5 mg/mL. The dose on the first day is double that for the rest of the days.

The dose on the first day is equivalent to the dose for 2 days, so we can simply add 1 day to the time period: 5 +1 = 6 days of 0.1 mg/kg/day.

The total amount required will be ...

  (0.1 mg/kg/day) × (10 kg) × (6 days) = 6.0 mg

At a concentration of 1.5 mg/mL, the quantity required is ...

  (6.0 mg)/(1.5 mg/mL) = 4.0 mL

For 5 days, the dog will need 4.0 mL of medicine.

__

Additional comment

Each day except the first, the dog should receive 2/3 mL of medicine. On the first day, the dog should get 4/3 mL.

Sets are the term used in mathematics which means the collection of any objects or collection.

Now, According to the question:

Let's know:

What is sets?

Any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.

What is sets in real life?

We all have a group of some objects, collection of our favorite things, sets of books, a list of cities and countries in our life. These all are sets, and we come to their usage in our daily life.

Examples of sets in daily life:-

1. Kitchen is the most relevant example of sets. Our mother always keeps the kitchen well arranged. The plates are kept separate from bowls and cups. Sets of similar utensils are kept separately.

2.School bags of children is also an example. There are usually divisions in the school bags, where the sets of notebooks and textbooks are kept separately.

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Answer:

q alguien me explique y pueden ser español

As per the distance formula, the work done by the tractor in 1s is 5000m or 5 km

The term distance in math refers the length along a line or line segment between two points on the line or line segment

Here we have given that a tractor pulls a 20 km at a speed of 4 m/s.

And we need to determine the work done by the tractor in 1 s.

While we looking into the given question, we have given that the following values are given,

Distance = 20km

Speed = 4m/s

Here we have to convert the km into m then we get,

=> 1 km = 1000 m

Then 20km = 20000m

Therefore, in 4m/s it pulls 20000m.

Then in 1s the work done is calculated as,

=> 20000/4

=> 5000

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He will have to mix 3 pounds of cashews and 7 pounds of peanuts .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Let c be denoted as cashew and p be denoted as peanuts

c + p = 10  ⇒ (1)

5.6c + 2.3p = 3.29*10 ⇒ (2)

Multiply eq(1) by 560

Multiply eq(2) by 100

560c + 560p = 5600

560c + 230p = 3290

Subtract and solve for "p":

330p = 2310

p = 7  (amt. of peanuts needed)

substitute  the value of p in eq(1)

c + 7 = 10

c = 3  (amt. of cashews needed)

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The ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.

To use a congruence criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.

In this case, the ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.

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The question is -

Which congruence theorem can be used to prove EB = BD, AE = CB, ∠ A = ∠ C = 90°?

Exponents that are positive go to the right. Exponents with negative signs shift to the decimal to the left. A result is stated in scientific notation when it is a power of ten multiplied by a number that is greater than or equal to one but less than ten.

One approach is to fully write out each number after it has been converted from scientific notation, then calculate the total of the two values and translate the result back into scientific notation.

Therefore, The 2, 4, 5, and final 0 in the number 0.2540 are all significant because they come after the decimal point and follow numbers. Scientific notation does not consider exponential digits to be significant; 1.12106 has three significant digits, 1, 1, and 2.

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