What are the types of complex numbers?.

y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex]  is the rational function  that has a horizontal asymptote of y = 0.

When the denominator of a polynomial has a degree of at least 1, it is said to be a rational function. Or to put it another way, the denominator must contain a variable.

When p(x) and q(x) are polynomials and q(x) ≠ 0, the general form of a rational function is p(x)/q(x).

Asymptotes are lines that the function graph approaches but never crosses. Both the x and y axes are asymptotes in the parent function f(x)=1x. The parent function's graph will approach the asymptotes steadily but never actually touch them.

If the degree of the denominator > degree of the numerator, there is a horizontal asymptote at y = 0.

Here, only y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex] has the degree of the denominator > degree of the numerator.  

Thus, y = [tex]\dfrac{ x + 8}{x^2 + 3x + 2}[/tex]  is the rational function  that has a horizontal asymptote of y = 0.

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A binomial is an algebraic expression containing two different terms connected by addition or subtraction.

An algebraic expression containing only two terms is called a binomial expression. This is called a binomial polynomial. Also called the sum or difference of two or more monomials. This is the simplest form of polynomial. Binomials are classified into algebraic expressions based on the number of terms they contain, along with monomials, trinomials, quaternions, etc. In other words, two different monomials of different degrees connected by a plus or minus sign form a binomial. For example, consider two monomials 2x and 5x¹⁰. Adding these monomials gives the binomial given by 2x + 5x¹⁰.

2) For example, 2xy + 7y is binomial because it has two terms.

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Answer:

136 acres

Solution:

My way of doing this is by putting it in a fraction.

So,

0.2/100 × 68000/1 = x

Do the math and x = 136

The surface area of the rectangular prism, as a function of x, is given by:

A = 2*( (x - 2)*(x + 4) + (x + 4)*(2x + 1) + (x - 2)*(2x + 1))

For a prism whose dimensions are X, Y, and Z, the surface area is:

A = 2*(X*Y + X*Z + Z*Y)

In this case we know that the dimensions of the rectangular prism are:

X = x - 2

Y  =x + 4

Z = 2x + 1

Replacing that on the surface area equation we will get:

A = 2*( (x - 2)*(x + 4) + (x + 4)*(2x + 1) + (x - 2)*(2x + 1))

That equation gives the surface area as a function of x.

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The length of the side is greater than equal to 35 and less than equal to 46 such that the perimeter of square lies in the given range.

let the length of each side of square be x units

the perimeter of the square = x +x +x +x

=> 4x

so the boundation on the perimeter is given in the question

given:

138 < 4x < 186

138/4 < x < 186 /4

34.5 < x < 46.5

so the length of the side is greater than equal to 35 and less than equal to 46

The range of the possibel sides is [35 ,46]

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When you are skiing on a mountain with an altitude 12 meters and angle of depression is 21 degrees then you will ski down for a distance of 31.57 meters.

Solution:

Here we have ,

Height i.e altitude of mountain (h) = 12 meters

Angle of depression (∅) =21°

And let the distance coverd be (b)

Using theorm of trigonometery,

tan∅ = [tex]\frac{height}{base}[/tex]

       = [tex]\frac{12}{b}[/tex]

Therefore,

tan(21°) = [tex]\frac{12}{b}[/tex]

b = [tex]\frac{12}{tan(21)}[/tex]

b = [tex]\frac{12}{0.38}[/tex]

b = 31.57 meters

Hence ,

You will ski down 31.57 meters.

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Equivalent 4/5 is equals to 20/25 in fractions.

In mathematics, equivalent fractions are those with the same denominator but different numerators. For instance, since they both equal 1, 2/4 and 3/6 are comparable fractions. An element of the whole is a fraction. To represent identical components of the total, equivalent fractions are utilized.

The numerator and denominator of each fraction can be multiplied by the same integer to determine the equivalent fraction. Equivalent fractions are those that, despite visible differences, signify the same value. For instance, if you take a piece of cake, divide it into two equal pieces, and then eat one of them, you will have consumed half of the cake.

= 4/5 ( multiply by 5/5)

= 4/5 * 5/5

= 20/25

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Correct Question:

What is 4/5 as an equivalent fraction?.

Answer:

the requisite answer for this question is 10 meter.

Step-by-step explanation:

the analysis for this question's answer is as follows:

since, he has a 50 meter long role of cable, correct to the nearest meter,with him and also he uses 10 meter of that role each time during his job to the nearest meter.

therefore, if he does four jobs then the maximum amount of cable that could be left with him would be;

he took (40-m) to finish the entire work,

this simplifies, 50-(10×4) which is equal to 50-40 which in turn is equal to 10

hence, the solution to the afore-mentioned problem is 10 meters.

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The mirror image of (4,5) is (4,-5) or (-4,5)

The term mirror image in math is defined as a reflected duplication that appears identical but in reverse.

Here we need to find the mirror image of (4,5).

As we all know that the rule used here is written as the image of (x, y) in the y-axis is (–x, y).

Then according rule here the given that the mirror image of (4,5) along x axis is written as (4,-5).

Then as per the point lies in fourth quadrant.

Then the another form of the mirror image of ( 4,5) along y axis is written as (-4,5) and then the point lies in second quadrant.

Complete Question:

What is the mirror image of the coordinate (4,5)?

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The equation of the function shown in the provided graph is y = 1

                                                                                                         (x+3)²  

The parent function is f(x) =  1

                                              x²

Graph can be defined as a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things

How horizontal shifting of the graph takes place

If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+k) where k>0

Since the graph is shifted towards the negative x-axis by 3 units

So, the parent function f(x) will become f(x+3)

 f(x)=  1

         x²

f (x+3)= 1    

           (x+3)²

So, the equation of the function will be y = 1    

                                                                       (x+3)²  

Therefore, The equation of the function shown in the provided graph is  

y = 1

    (x+3)²                                          

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Angles 1 and 5 are called corresponding angles.

Corresponding angles refer to angles that occur on the same side of the transversal line. Corresponding angles are equal in size and can both be obtuse or acute. In other words, corresponding angles are any pair of angles which occur on the same side of the parallel lines which are cut by another line. As shown in the given figure, a transversal line intersects two parallel lines which produces eight angles. It contains four pairs of corresponding angles, i.e., 1 and 5, 2 and 6, 3 and 7, and 4, and 8. Corresponding angles are congruent angles. All angles possess the same position in reference to the parallel lines and the transversal are corresponding pairs.

Note: The question is incomplete. The complete question probably is: In the given figure, what are angles 1 and 5 called?

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The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

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The equivalent expressions are

(3x² + 21x + 18) / (x² - 7x - 8)
3 (x + 6) (x + 1) / (x + 1) (x - 8)

Options A and E are the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(3x² + 21x + 18) . x² - 7x - [tex]8)^{-1}[/tex]

This can be written as,

(3x² + 21x + 18) / (x² - 7x - 8) ______(A)

Now,

Solve for (3x² + 21x + 18).

(3x² + 21x + 18)

3 (x² + 7x + 6)

3 (x² + (6 + 1)x + 6)

3 (x² + 6x + x + 6)

3 (x (x + 6) + 1 (x + 6))

3 (x + 6) (x + 1)

Solve for (x² - 7x - 8).

x² - (8 - 1)x - 8

x² - 8x + x - 8

x (x - 8) + 1 (x - 8)

(x + 1) (x - 8)

Now,

(3x² + 21x + 18) / (x² - 7x - 8)

= 3 (x + 6) (x + 1) / (x + 1) (x - 8) _____(B)

Thus,

From (A) and (B),

(3x² + 21x + 18) / (x² - 7x - 8)  and 3 (x + 6) (x + 1) / (x + 1) (x - 8) are the equivalent expressions.

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The main difference between a true solution and a colloidal solution is the particle size of the dispersed substance. In a true solution, the particles are so small that they cannot be seen with the human eye, while in a colloidal solution, the particles are intermediate in size and are visible under microscope.

A true solution is a homogeneous mixture of two or more substances where one substance is completely dissolved in the other. The particles of the dissolved substance, called solute, are so small that they cannot be seen with the human eye and are evenly distributed throughout the solution. A true solution is transparent, and the particles of the dissolved substance do not scatter light, thus not visible under a microscope. Examples of true solutions are sugar dissolved in water, and salt dissolved in water.

On the other hand, a colloidal solution is a type of mixture where one substance is dispersed throughout another substance in small particles that are not large enough to settle out but are large enough to scatter light. The particles of the dispersed substance, called the dispersed phase, are intermediate in size between those of a true solution and a suspension. The particles are visible under microscope, but not to the human eye, and the mixture is usually cloudy or opaque. Examples of colloidal solutions are milk, fog, and blood.

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The slope of the line is a measure of the rate of change between two points and is calculated by dividing the change in y-values by the change in x-values. In this case, the slope is -6, which means that for every 1 unit increase in x, there is a 6 unit decrease in y.

The slope of the line is a measure of the rate of change between two points. It is calculated by dividing the change in y-values by the change in x-values. To find the slope of the line represented by the table of values, we need to first identify two points on the line. We will use the points (x1, y1) and

(x2, y2).

We can choose any two points, but for this example, we will use

(x1, y1) = (-7, 9) and (x2, y2) = (8, -15).

The slope of the line is then calculated by finding the difference between the y-values

(y2 - y1 = -15 - 9 = -24)

and the difference between the x-values

(x2 - x1 = 8 - (-7) = 15)

and dividing these two values:

-24/15 = -6.

This means that for every 1 unit increase in x, there is a 6 unit decrease in y.

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Yes, AB ≅ DE, EF ≅ DE, then AB ≅ EF. The property of congruence illustrated in the question is the transitive property.

The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.

In the statement "If AB ≅ DE, EF ≅ DE, then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.

The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.

--The given question is incorrect; the correct question is

"Is AB ≅ DE, EF ≅ DE then AB ≅ EF? explain"--

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Answer:5 pieces

Step-by-step explanation:

4/0.8=5

After solving, the slope of equation 3x + y = -3 is -3.

In the given question, we have to find the slope for 3x + y = -3.

The given equation is 3x + y = -3.

The general equation of line is y = mx + c, where m = slope of line and c is the y-intercept of line.

To find the slope we have to convert the given equation in the form of general equation.

To convert in general form we have to isolate the y.

3x + y = -3

Subtract 3x on both side, we get

y = -3x - 3

Now comparing with y = mx + c, we get

m = -3

Hence, the slope of equation 3x + y = -3 is -3.

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The complete question is:

What is the slope for 3x + y = -3?

The total amount of tips that the waiters collected that night is $1,622.60.

To find the total amount of tips, you can multiply the mean tip by the number of waiters.

In this case, the mean tip is $115.90 and there are 14 waiters, so:

$115.90 x 14 = $1,622.60

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The first waiter with $60 tips share $15 dollar to the second waiter and the second waiter with $80 share $20 to the first waiter.

As per data given is two different earned from tips, there will be two different amount of share from each. For a waiter that earned $60 from tip, the share will be:

First waiter share = tips earned x 1/4

First waiter share = $60 x 1/4

First waiter share = $60 x 0.25

First waiter share = $15

The share of the second waiter that earned $80 from tip will be:

Second waiter share = tips earned x 1/4

Second waiter share = $80 x 1/4

Second waiter share = $80 x 0.25

Second waiter share = $20

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The number of students that were surveyed where 7 out 8 students own a bike is equal to 96.

Let the number of students surveyed be [tex]x[/tex] .

According to the question,

When 8 students were surveyed 7 owned a bike. So, when [tex]x[/tex] students were surveyed,

               Number of students who own bikes = [tex]\frac{7}{8} x[/tex]

                Number of students who don't own bike = [tex]\frac{1}{8} x[/tex]

 In question, it is given that:

                             [tex]\frac{7}{8} x - \frac{1}{8}x = 72\\\\\frac{6}{8} x = 72\\\\6x = 576\\x= 96[/tex]

Hence, the number of students that were surveyed is 96.

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Answer:

x = 8, y = 9

-3x + 44 - x = 12

-3x - x = 12 - 44

-4x = -32

x = 8

-3(8) + 4y = 12

-24 + 4y = 12

4y = 12 + 24

4y = 36

y = 9

I have left 6 mangoes after I got 5 extra from father and mother ate 2

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating how many mangoes I have after I got 5 from my father:

No. mangoes 1 = Have + got

No. mangoes 1 = 3 mangoes + 5 mangoes

No. mangoes 1 = 8 mangoes

Calculating how many mangoes I have after my mother ate 2 mangoes:

Final No. mangoes = No. mangoes 1  - eat

Final No. mangoes = 8 mangoes - 2 mangoes

Final No. mangoes = 6 mangoes

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The value of the equation on x = 2 is 5. Thus, Option D is the correct answer.

Given Quadratic equation,

[tex]=\frac{1}{2} x^{4} - \frac{3}{4}x^{2}[/tex]

Put the value of x = 2 in the above equation and we get

[tex]=\frac{1}{2} x^{4} - \frac{3}{4}x^{2}[/tex]

[tex]=\frac{1}{2}* 2^{4} - \frac{3}{4}*2^{2}[/tex]

= 8 - 3

= 5

Therefore, the value of the equation on x = 2 is 5.

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Answer:

Step-by-step explanation:

1 st Q:  answer is -2 (choice C)

2nd Q:  answer is (8,1)  (choice D)

The solution is where the 2 lines intersect

Triangle ABC and triangle DEF are not congruent.

What does a math congruent mean?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

The measure of angle A and angle D are both 40 degrees, but the measure of angle B and angle F are not equal. The measure of angle B is 20 degrees, while the measure of angle F is 120 degrees.

In a triangle, the sum of all three angles is 180 degrees. So in triangle ABC, the measure of angle C is 180-40-20 = 120 degrees.

In triangle DEF, the measure of angle E is 180-40-120 = 20 degrees.

Therefore, angle B and angle E are not congruent, so the triangles are not congruent.

In order for two triangles to be congruent, they must have corresponding sides and angles of the same measure. Since the measure of angle B and angle E are not equal, then triangle ABC and triangle DEF are not congruent.

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We can calculate it by using a long multiplication method where you multiply every digit of 12 by 12. 144 = 1 x 12 + 4 x 1 = 12 + 4 = 16. So, the value of 144 is 16

Calculating the value of 144 is a simple mathematical operation that can be done in several ways. The most straightforward method is to multiply 12 by 12, as 144 = 12 x 12. Another way to calculate the value of 144 is to find the square of 12, as 144 = 12^2. An alternative method is to use long multiplication where you multiply every digit of 12 by 12. The result of this will be 144 = 1 x 12 + 4 x 1 = 12 + 4 = 16.

In summary, the value of 144 is 16, regardless of the method you choose to calculate it. It is a well-known fact and can be easily looked up in mathematical tables as well.

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Gallons of gas used 40 gallons.

The given equation, m = pace / 40g, represents the distance in miles (m) that a car can travel using a certain number of gallons (g) of gas. The variable "pace" represents the miles per gallon (mpg) of the car. To find the number of gallons used, we need to solve for g in the equation.

Here are the key steps:

Finally, we can solve for g and we get the answer that the car used 40 gallons of gas.

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