2x + 3y = 12
2x - y = 4

Answer:

14.728

Step-by-step explanation:

m³ + n if m = 1.2 and n = 13

= (1.2)³ + 13

= 1.728 + 13

= 14.728

The vertical asymptote is at x = -2

The horizontal asymptotes are at y =0.

First, the vertical asymptote, it happens when the denominator becomes zero, then we need to solve:

-x - 2 = 0

x = -2

The vertical asymptote is at x = -2

For the horyzontal asymptotes we need to check the limit as x tends to ±∞, in both cases because x is only in the denominator, the function will tend to zero.

So we have two horizontal asymptotes at y = 0.

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The simplified form of a rational equation [x + 1 / (x - 2)] / [x² / (x - 2) + 1] is equivalent to (x - 1) / (x + 2).

In this problem we need to determine the simplified form of a rational equation, whose form is:

R(x) = P(x) / Q(x)

Where:

The simplification process can be done by means of algebra properties. First, write the rational equation:

[x + 1 / (x - 2)] / [x² / (x - 2) + 1]

Second, expand the numerator and the denominator:

[(x² - 2 · x + 1) / (x - 2)] / [(x² + x - 2) / (x - 2)]

Third, simplify the fraction by algebra properties:

[(x² - 2 · x + 1) · (x - 2)] / [(x² + x - 2) · (x - 2)]

(x - 1)² / [(x + 2) · (x - 1)]

(x - 1) / (x + 2)

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The equations are solved using graphing, elimination, substitution methods.

A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.

The systems of equations are given below are given below,

(a) -2x + 3y = 1(using elimination method)

     2x+6y= 2

     eliminating x term we get,

     9y = 3

     ⇒y=3.

(b)  y = x + 4 ---(1)(using substitution method)

     x = -3y---(2)

     Substitute (2) in (1) we get,

     y = -3y+4

     ⇒4y=4 ⇒y=1

(c)   3x - y = 7 (using graphing method)

      y = 3x - 2

     This system has no intersection point

     So this system has no solution.

    ( The graph is attached below.)

(d)   x + 2y = 1-----(1) (using elimination method)

      3x + 5y = 8-----(2)

     For eliminating x we have to the multiply equation(1) by 3,

      we get 3x+6y=3

      eliminating 3x we get, y=-5/3 substitute y in (1) we get x=49 /3

Hence, the equations are solved using graphing, elimination, substitution methods.

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Answer:

1. b = [tex]\sqrt{20}[/tex]

2. c = [tex]\sqrt{2[/tex]

3. b = [tex]\sqrt{105}[/tex]

4. c = [tex]\sqrt{113}[/tex]

5. c = [tex]\sqrt{52}[/tex]

6. b = [tex]\sqrt{80}[/tex]

7. b = [tex]\sqrt{130}[/tex]

8. a = [tex]\sqrt{48}[/tex]

9. c = [tex]\sqrt{149[/tex]

10. c = [tex]\sqrt{5}[/tex]

Example:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]8^{2}[/tex] + [tex]b^{2}[/tex] = [tex]12^{2}[/tex]

64 + [tex]b^{2}[/tex] = 144

64 + [tex]b^{2}[/tex] = 144 - 64

[tex]b^{2}[/tex] = 80

[tex]\sqrt{b}[/tex] = [tex]\sqrt{80}[/tex]

Answer: 21.6

Step-by-step explanation:

length X height

4(5.4)=21.6

25 mcg is equal to 0.025 mg. both are unit of measurement of weight.

The prefix "mcg" stands for microgram, which is a unit of measurement in the metric system that is one millionth of a gram (10⁻⁶ g). On the other hand, "mg" stands for milligram, which is one thousandth of a gram (10⁻³ g). Therefore, to convert from mcg to mg, you need to divide the value in mcg by 1000.

In this case, 25 mcg divided by 1000 equals 0.025 mg. It's important to be mindful of the units when dealing with measurements, as confusion between different units of measurement can lead to incorrect calculations and dosing errors.

Overall, when converting from mcg to mg, you can easily make the conversion by dividing the value in mcg by 1000, as the prefix "milli" represents a factor of 1000 in the metric system.

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Answer:

22.5%

Step-by-step explanation:

45×50/100 gives you the answer using BODMAS

10 ml is equal to 2 teaspoons. This is because 1 teaspoon is equal to 5 ml. To calculate the number of teaspoons in 10 ml, you must divide 10 ml by 5 ml. 10 ml divided by 5 ml equals 2 teaspoons.

To convert milliliters to teaspoons, you must use the conversion factor of 1 teaspoon = 5 ml. This means that for every 1 teaspoon, there are 5 milliliters. To figure out the number of teaspoons in 10 ml, you must take 10 ml and divide it by 5 ml. This will give you the number of teaspoons in 10 ml.When converting from milliliters to teaspoons, it is important to use the correct conversion factor. If you use the wrong conversion factor, you will end up with incorrect results. For example, if you use 1 teaspoon = 4 ml instead of 1 teaspoon = 5 ml, you will end up with an incorrect result.In addition to using the conversion factor, it is also important to keep in mind that a teaspoon is a measure of volume, not weight. This means that the amount of liquid in a teaspoon may vary depending on the density of the liquid. For example, a teaspoon of water will contain more liquid than a teaspoon of honey.

In conclusion, 10 ml is equal to 2 teaspoons. To convert milliliters to teaspoons, you must use the conversion factor of 1 teaspoon = 5 ml. It is important to remember that a teaspoon is a measure of volume, not weight, and the amount of liquid in a teaspoon may vary depending on the density of the liquid.

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The height of the cylindrical concrete pillar is approximately 153.2 centimeters.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

We are given that;

Length of prism=8.8cm

Height=4.4cm

Volume=271.04 cubic centimeters.

Now,

We can use the formula for the volume of a cylinder to find the height of the pillar. The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

First, we need to find the radius of the pillar. The diameter of the pillar is given as 10 centimeters, so the radius is half of that:

r = 10/2 = 5 centimeters

Now we can substitute the given volume and radius into the formula and solve for the height:

12,042 = π(5)^2h

Divide both sides by π(5)^2:

h = 12,042 / (π(5)^2)

h ≈ 153.2 centimeters (rounded to one decimal place)

Therefore, by the given volume the answer will be 153.2 centimeters.

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Using mathematical operators, the value of the expression is 23

Simplification of an expression is the process of reducing a mathematical expression to its simplest form while retaining the same value. This is done by using various rules and techniques, such as combining like terms, using the distributive property, and applying the order of operations.

The goal of simplification is to make the expression easier to work with and understand. It also helps to avoid errors when solving problems or simplifying more complex expressions.

In this expression given;

3(x + 2y) - 2x + 10 = ?

x = 1, y = 2

3(1 + 2(2)) - 2(1) + 10 = 23

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The equivalent perimeter expression is 3 * 3

From the question, we have the following parameters that can be used in our computation:

Side lengths = 3m, 3m and 3m

The perimeter of the triangle is the sum of the side lentths

So, we have

perimeter = 3 + 3 + 3

Using the distributive property, we have

Perimeter = 3 * 3

Hence, the perimeter expression is 3 * 3

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Complete question

The lengths of the sides of a triangle are represented by 3m, 3m and 3m.

6 cmAnswer:

Step-by-step explanation:

The centroid of this triangle is located at the point (6, 3).

The centroid of a triangle is the point where the three medians of a triangle intersect. Medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side.

The centroid is the "center of mass" or the "balance point" of the triangle. In other words, if the triangle were made of a solid material and suspended by a string attached to the centroid, it would balance.

To find the coordinates of the centroid of a triangle, we will use the following formula:

G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3

Where G is the centroid, and (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the triangle's vertices.

So for the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0), we have:

G = (2 + 6 + 10)/3, (5 + 5 + 0)/3

G = (18/3, 10/3)

G = (6, 3.333...), which we can round to (6, 3)

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The answer is:

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Answer:

To show that 3 divided by 1/4 is equal to 3x4 on a number line:

1. Draw a number line starting from 0 and mark every 1/4 division.

2. Label 3 divisions with the corresponding value '3'.

3. Move 4 divisions in the same direction as that of 3 divisions.

4. Mark the point at 4 divisions and label it as ’12’.

5. From the starting point to the point labelled ‘12’, there are 7 divisions.

6. Since each division represents a quantity of 1/4, dividing 3 by 1/4 (or multiplying by 4) will result in a total of 12, or 3x4.

Answer:

8.1

Step-by-step explanation:

100%= 45

1%= 45÷100

= 0.45

18%= 0.45×18

= 8.1

Answer:

3v + 14w + 13

Step-by-step explanation:

The expression can be simplified as follows:

(3v + 8w + 19) + (6w - 6)

Combining like terms, we have:

(8w + 6w) and (19 - 6)

3v + 14w + 13

So the simplified expression is equal to 3v + 14w + 13.

The price of each ticket is given as follows:

The prices for each type of ticket are obtained via a system of equations, for which the variables are given as follows:

On the first day of ticket sales the school sold 12 senior citizen tickets and 6 student tickets for a total of $252, hence:

12x + 6y = 252

2x + y = 42 (simplifying by 6).

y = 42 - 2x.

The school took in $98 on the second day by selling 6 senior citizen tickets and 1 student ticket, hence:

6x + y = 98

y = 98 - 6x.

Equaling the two equations, the value of x is obtained as follows:

42 - 2x = 98 - 6x

4x = 56

x = 56/4

x = 14.

Then the value of y is of:

y = 98 - 6(14)

y = 14.

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Answer:

Step-by-step explanation:

its 3.02

Answer:

Step-by-step explanation:

You need the area.

If this is a square - it is 54 × 54 = 2916 inches squared

The weight of the object is 79.461 newtons.

The standard value for the acceleration due to gravity is approximately 9.81 m/s^2 near the Earth's surface.

To find the weight of an object with a mass of 8.1 kg, we can use the formula:

Weight = mass x acceleration due to gravity

So, the weight of the object is:

Weight = 8.1 kg x 9.81 m/s^2

Weight = 79.461 N (newtons)

Hence, the weight is 79.461 newtons.

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Answer: $20.10

Step-by-step explanation: If you multiply 3.90 by 4 and add 4.50 you get 20.10

Answer:

!20.1

Step-by-step explanation:

I got here by multiplying $3.90 by four and adding $4.50. This equals $20.1

Hence the answer is: She will earn $20.1

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There are 50 calories per cup of popcorn and 16 per ounce of soda.

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

Let's represent x be the number of calories per cup of popcorn

And let's represent y be the number of calories per ounce of soda.

The two equations are based on the given details:

2x + 7y = 212 ....(i)

1x + 11y = 226 ....(ii)

From equation (ii), we have

x + 11y = 226

x = 226 - 11y

Substitute the value of x = 226 - 11y in equation (i), and solve for y:

y = 16

Substitute the value of y = 16 in equation (ii), and we get

x = 50

Thus, the number of calories per cup of popcorn is 50 and the number of calories per ounce of soda is 16.

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There are 1000 cubic centimetres in a litre (cm3). This is so because one cubic centimetre (cc) equals one millilitre (ml), and one litre (l) equals 1000 ml.

1000 ml make up 1 litre (L).

ml (millilitres) = cm3

1000 ml = 1000 cm3

1 L = 1000 cm3

One litre is equal to one thousand cubic centimetres (cm3). This is because one cubic centimetre is equivalent to one millilitre (ml), and one litre is equal to 1000 millilitres (ml). The subsequent actions can be conducted in order to calculate this. Initially, one litre (L) equals one thousand millilitres (ml). Second, one cubic centimetre is equivalent to one millilitre (cm3). Thus, one millilitre is equivalent to one hundred cubic centimetres. Last but not least, one litre equals one thousand cubic centimetres, or 1 L = 1000 cm3. Anybody wishing to translate between the two different volume measures will find this information valuable. For instance, if a recipe calls for a certain amount of an ingredient in litres, it is simple to convert that amount to cubic centimetres if necessary.

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Answer: 6x^2-x-1

Step-by-step explanation:

(3x+1)(2x-1) = 6x^2 - 3x + 2x -1

6x^2-x-1

Answer:

a. Elena has fewer roses than Lin. Lin has 6 roses and Elena has x roses.

Step-by-step explanation:

Answer:

a= 77, b= 77, c= 103.

Step-by-step explanation:

a= 77 (vertically opposite)

b= a= 77 (corresponding angles)

c= 180-77

 = 103 (angles on a straight line)