A square has an unknown side length, 2x. Write a simplified expression for its perimeter (distance around the
outside of an object. Remember, side plus side plus...)

The simplification of all the given algebra fractions are;

1) a/c

2) (a - b)/(a - 1)

3) (x + 1)/(x - 4)

An algebraic fraction is defined as a fraction whose numerator and denominator are algebraic expressions.

1) (abc + ab²)/(b²c + bc²)

Factorizing numerator and denominator gives;

ab(c + b)/bc(b + c)

b(b + c) will cancel out to get; a/c

2) (a² - b²)/(a² - a + ab - b)

Factorizing numerator and denominator gives;

[(a + b)(a - b)]/[a(a - 1) + b(a - 1)]

= [(a + b)(a - b)]/(a + b)(a - 1)

(a + b) will cancel out to get;

(a - b)/(a - 1)

3) (x² - 2x - 3)/(x² - 7x + 12)

Expanding the numerator and denominator gives;

(x² - 3x + x - 3)/(x² - 4x - 3x + 12)

= ((x + 1)(x - 3))/((x - 3)(x - 4)

(x - 3) will cancel out to get;

(x + 1)/(x - 4)

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Area of the convex polygon whose vertices are the centroids of these 7 triangles is 184.

What is a convex polygon?

A polygon that forms the edge of a convex set is said to be convex polygon. This indicates that the union of the interior and the boundary of the polygon has the line segment connecting two points of the polygon.

Given,

 AB = CD = EF = GH = 10

 BC = DE = FG = HA = 11

 Triangles of side length 6,8,10 is cut from corners 23×27 rectangle.

Using the above information, we marked the position of A,B,C,D,E,F,G,H and J, taking the upper left corner of rectangle as origin.

The centroid of a triangle can be found using the formula,

 Centroid = [tex](\frac{x_{1} + x_{2}+x_{3}}{3} , \frac{y_{1} +y_{2}+y_{3}}{3})[/tex]

For ΔJAB,

[tex]C_{1}[/tex] = (8/3 , -35/6)

For ΔJBC,

[tex]C_{2}[/tex] = ( 9 , -23/6)

For ΔJCD,

[tex]C_{3}[/tex] = ( 46/3, -35/6)

For ΔJDE,

[tex]C_{4}[/tex] = ( 18 , -23/2)

Area of convex polygon = [tex]\frac{1}{2} [x_{1} y_{2} + x_{2}y_{3}+.........+x_{n}y_{1}] - [y_{1}x_{2}+y_{2}x_{3}+......+y_{n}x_{1}][/tex]

From figure we find the area of C₁C₂C₃C₄C₈, where C₈ = (8/3 , -23/2)

Area =

[tex]\frac{1}{2} [8/3 (-23/6 )+ 9(-35/6)+46/3(-23/2)+18(-23/2)+8/3(-35/6)] - [(-35/9)9+(-23/6)46/3+(-35/6)18+(-23/2)8/3+(-23/2)8/3][/tex]

= 184 / 2

Therefore total area of convex polygon = 2 × 184/2 = 184 sq. units

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Answer: To find an equation for a parabola that passes through three specific points, we can use the method of algebraic manipulation.

Since the parabola is symmetric about the y-axis, the equation of the parabola will have the form y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Given three points (-2,7), (1, 10), and (2,27), we can use the vertex form of the equation and substitute the x, y values of the three points to find the values of a, h and k

y = a(x-h)^2 + k

Since it is passing through (-2,7), we can substitute the values of x and y in the equation and get

7 = a(-2 - h)^2 + k

It passing through (1, 10), we can substitute the values of x and y in the equation and get

10 = a(1 - h)^2 + k

It passing through (2,27), we can substitute the values of x and y in the equation and get

27 = a(2 - h)^2 + k

Now we have three equations with three variables, we can solve it using any of the techniques such as substitution, elimination or matrix. But the final equation will be in the form of y= a(x-h)^2 + k

Here, x= (-2, 1, 2) and y = (7, 10, 27) . Therefore it has a unique parabola passing through these points.

Step-by-step explanation:

The solution to the differential equation y'' + y = sin2x is y = -2sin2x + (Acos2x + Bsin2x).

This differential equation can be solved by the method of variation of parameters. This method involves finding two arbitrary functions, U and V, such that U' = V and V' = -U + sin2x, so that the general solution of the differential equation is y = U + V. Solving the two equations yields U = Acos2x + Bsin2x and V = -2sin2x, where A and B are arbitrary constants. Substituting U and V into the general solution of the differential equation yields the final solution y = -2sin2x + (Acos2x + Bsin2x).

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Amelie needed 335 cups of flour for the recipe.

Given data :

She is making 2 1/2 or 2.5 times the original recipe.

Cups in original recipe= 134 cups

cups Amelie will need= 2.5 × 134

                                     = 335 cups

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Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

3x-3y=-6 implies 3(x-y)=3(-2), so x-y=-2.

-----------------------------

x-y=-2

3x+y=10

---------------

4x=8

x=8/4=2

2-y=-2

y=2-(-2)=2+2=4

Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility test for three.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

add all number

9+9+0 = 18

and 18/3 = 6

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On solving the provided question, we can say that in this triangle 2x-6 = 3 => 2x = 9 => x = 9/2 and 2z = 4 => z = 2

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in this triangle

2x-6 = 3

2x = 9

x = 9/2

2z = 4

z = 2

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a) 7 examples are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

b) Fabric Larry will have left after using [tex]2\frac{2}{3}[/tex] yard out of [tex]5\frac{5}{6}[/tex] yard to make a bag for his computer is: [tex]3\frac{3}{6} yard[/tex]

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

7 examples of mathematical expression are:

[tex]2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z[/tex]

For the second part of the question:

Larry had 5 3/6 yards of fabric. He used 2 2/3 yards to make a bag for his computer. Write an expression that will show how much of the fabric Larry will have left.

The mathematical expression that represents the amount of fabric Larry has left is:

5 3/6 - 2 2/3 = 2 7/18

You can simplify this further:

2 7/18 = 2 1/6

The amount of fabric Larry will have left is 2 1/6 yards.

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The solution is given by the equation A = how many diet sodas there are in the fridge compared to how many regular sodas

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the equation will be

The ratio of cows to pigs on a farm could be 1 to 3

So , the proportion is 1 : 3

Now , The ratio of chocolate chips to raisins in a cookie could be 5 to 9

So , the proportion is 5 : 9

Now , the number of diet sodas there are in the fridge compared to number of regular sodas is also a proportion

Hence , the proportion is number of diet sodas to number of regular sodas

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A rectangle is a four-sided geometric shape where opposite sides are parallel and congruent. The diagonals of a rectangle are two lines that connect the opposite corners of the rectangle, and they bisect each other at 90 degrees.

Briefly defined, what is rectangle?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Given the sides of rectangle WXYZ are WY = 14x + 10 and XZ = 11x + 22. We can find the length of the diagonals using the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the diagonal of the rectangle) is equal to the sum of the squares of the other two sides (the sides of rectangle)

Diagonal WX: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)

Diagonal YZ: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)

So, the lengths of the diagonals of rectangle WXYZ are √(317x^2 + 940x + 584) units.

Note that the diagonals of a rectangle are congruent and the value of x is not a known, the diagonal of rectangle is the value of the square root of the expression.

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Answer: 66

Step-by-step explanation:

I skipped it to see the answer hope this helps

Answer:

2A/h - b2= b1

Step-by-step explanation:

The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the G.C.F. defines the greatest factor present between any given pair of two or more numbers.

LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).

The highest common factor (HCF) between two or more numbers is two or more. The LCM, on the other hand, is the lowest common multiple that exactly divides these two figures. The greatest common factor between any two numbers is also known as HCF. Between two or more numbers, LCM is also known as Least Common Divisor.

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Answer:

Refer to the attached image.

Step-by-step explanation:

The simplified ratio that compares 5 meters to 100 centimeters is 5: 1 .Option A

Ratio is simply described as the non equal comparison of two numbers, variables, or events.

It shows how many times a number or variable contains another.

The comparison is also based on size.

From the information given, we have;

5 meter to 100 centimeters

It is important to note that;

100 centimeters = 1 meters

Also, 1 meter= 100 centimeters

5 meters = x centimeters

cross multiply

x = 100(5)

Multiply the values

x = 500 centimeters

Then,

5 meters = 1 meter

Hence, the ratio is 5:1

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So x = 2.1 is the only possible value of x that makes the equation true.

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.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The equation is given as follows:

-3x + 6.3 = 0

To find the value of x, we need to isolate x on one side of the equation. We can do this by adding 3x to both sides:

-3x + 3x + 6.3 = 0 + 3x

6.3 = 3x

Now we can divide both sides by 3:

x = 6.3/3

x = 2.1

So x = 2.1 is the only possible value of x that makes the equation true.

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No solution is when a system of equations has no solution. This means that the equations are inconsistent, and there is no set of values that can make the equations true.

For example, if the system of equations is 2x + 3y = 4 and 2x + 3y = 5, then there is no solution. This is because no matter what values are chosen for x and y, the equations cannot both be true. This means that the system of equations is inconsistent, and there is no solution.

To symbolically represent no solution, you can use the following notation:

2x + 3y = 4, 2x + 3y = 5   No solution

This notation is used to indicate that the equations are inconsistent and that there is no solution.

Complete question: What is the solution to the equation 2x + 3y = 4 and 2x + 3y = 5?

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The scale factor of the two rectangles is 1.5

According to Euclidean Plane Geometry, a rectangle is a quadrilateral with equal opposed sides and four right angles. In other words, a rectangle is a parallelogram with a right angle of 90 degrees or an equiangular quadrilateral (i.e., 360°/4 = 90°). A rectangle is referred to as a square if its four sides are all the same length.

The ratio of the matching side lengths of two comparable figures is known as the scale factor. We know that the ratio of the respective side lengths of the two rectangles equals equivalent to r since Rectangle A and Rectangle B are similar to one another by the scale factor r.

We can set up the following ratio to determine the scale factor if the lengths of rectangles A and B are 1.5r+2.25 units and 3 units, respectively.

(1.5r+2.25) / 3 = r

Solving for r, we get:

r = (1.5r + 2.25) / 3

multiply both sides of the equation by 3

3r = 1.5r + 2.25

Subtract 1.5r from both sides

1.5r = 2.25

divide both sides by 1.5

r = 2.25/1.5

r = 1.5

Therefore, the scale factor of the two rectangles is 1.5.

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Answer:

6.3

Step-by-step explanation:

This is a right triangle, so in order to solve you can use the Pythagorean theorem; which is a² + b² = c² (The hypotenuse, or the longest side, equals C.  A and B equal the legs, or the shorter sides.)  So once you plug in the values, your equation should look like this:

3² + b² = 7²

Square each side, or in other words multiply it by itself.  

9 + b² = 49

Subtract 9 from both sides.  

b² = 40

Take the square root of 40 and your done!

b = 6.3

I hope this helped you!  :)

So, y = ab^x and y = ac^x are the exponential functions to represent the spread of Ben's and Carter's social media posts respectively.

An exponential function has the form y = ab^x, where a and b are constants and x is the independent variable (in this case, time).

For Ben's social media posts:

y = ab^x

For Carter's social media post:

y = ac^x

Please note that the value of a, b, and c will be different for Ben and Carter's post, as it will depend on the number of shares, likes, views, etc., and the rate of spread of the post.

This is an exponential function that represents the spread of Ben's social media posts and  Carter's social media post.

Complete Question:

1. Write an exponential function to represent the spread of Ben's social media post 2. Write an exponential function to represent the spread of Carter's social media post. 3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology. 4. Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers 5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is   . How does this graph compare with the original graph of Amber's photo share? 6. Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions? 7. If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions

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The correct answer of expression 's+3' is (c) Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class. She used the sign "+" instead of "x" or any other notation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression is (Number/variable, Math Operator, Number/variable)

The answer here should be Option C, as she used the sign "+" instead of "x" or any other notation. She wanted to add something.

And as it is very clear that she wanted to write the information about two classes, so that makes the second term for second class and first term for first class.

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The complete Question is:

Teresa wrote this expression (s+3) to describe the total distance she was going to swim during two swim classes. Which situation could be described by this expression?

A. Teresa wasn't sure how far she would swim during the first class. She would swim 3 fewer laps during the second class.

B. Teresa wasn't sure how far she would swim during the first class. She would swim the same distance for 3 classes.

C. Teresa wasn't sure how far she would swim during the first class. She would swim 3 laps during the second class.

D. Teresa wasn't sure how far she would swim during the first class. She would swim 3 times farther during the second class.

Answer:

70⁰

Step-by-step explanation:

We need to use the knowledge of trigonometry to find the indicated angle. Given the information in relation to the angle we have the opposite and the hypotenuse.

we therefore use Sine in this calculations

Sin ? = opposite/ hypotenuse

= 16/17

= 0.9412

to get the angle we get the sine inverse

Sine inverse of 0.9412 = 70.25⁰

= 70⁰

Answer:

? ≈ 70°

Step-by-step explanation:

using the sine ratio in the right triangle

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 70° ( to the nearest degree )

The answer to 7^2 is 49. This means that 7 is multiplied by itself two times. To solve the given problem following steps should be followed :

Step 1: To calculate the value of 7 power 2, we need to use the exponentiation operator (^).

Step 2: The operator is written as 7^2, which is read as "seven to the power of two".

Step 3: We can calculate the value of 7 power 2 by multiplying 7 by itself 2 times.

Step 4: 7 × 7 = 49

Therefore, 7 power 2 = 49.

An expression known as "power" is defined as the process of repeatedly multiplying a value or integer. An is often a power where n is the exponent and an is the base.

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Therefore , the solution of the given problem of ratio comes out to be

lim C(p) as p->19 = 152900.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Here,

a) To find the cost of removing 90% of the impurities, we can substitute 90 for p in the equation:

C(p) = 8100p / (100-p)

C(90) = 8100(90) / (100-90)

C(90) = 729000

So the cost of removing 90% of the impurities is Rs. 729000.

b) To find the limit of C(p) as p approaches 19, we can substitute 19 for p in the equation:

lim C(p) as p->19 = 8100(19) / (100-19)

lim C(p) as p->19 = 152900

The value of the limit of C(p) as p approaches 19 means that as the percentage of impurities approaches 19, the cost of purification approaches Rs. 152900.

c) It is not possible to purify completely as the percentage of impurities approaches 100. It's because as the percentage of impurities becomes closer to 100, the denominator of the fraction becomes smaller, thus the value of the cost of purification becomes larger, and it is impossible to pay an infinite amount of money.

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The solution of the inequality is,

⇒ x > - 5

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ - 4x + 3 < 23

Now,

Since, The inequality is,

⇒ - 4x + 3 < 23

Solve as;

⇒ - 4x < 23 - 3

⇒ - 4x < 20

⇒ - x < 5

⇒ x > - 5

Thus, The solution is,

⇒ x > - 5

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The the wind speed of a tornado with Beaufort number 9 is 51.3 miles per hour.

What is speed?

Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in meters per second (m/s) in this example because the distance is measured in meters (m) and the time is measured in seconds (s).

Given:

The Beaufort Scale measures the intensity of tornadoes. For a tornado

with Beaufort number B, the formula [tex]v = 1.9B^\frac{3}{2}[/tex] may be used to

estimate the tornado's wind speed in miles per hour.

We have to estimate the wind speed of a tornado with Beaufort number 9.

Plug B = 9 in the formula [tex]v = 1.9B^\frac{3}{2}[/tex]

⇒

[tex]v = 1.9(9)^\frac{3}{2} \\v = 1.9(27)\\v = 51.3[/tex]

Hence, the the wind speed of a tornado with Beaufort number 9 is

51.3 miles per hour.

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The speed of the Bike is 5 meters per second

Speed is a scalar quantity that describes how fast an object is moving . It is defined as the distance an object travels divided by the time it takes to travel that distance. The units of speed are typically meters per second (m/s) or kilometers per hour (km/h).

To find out how fast you are traveling on your bike, you can use the formula:

Speed = [tex]\frac{Distance}{Time}[/tex]

In this case, the distance is 340 meters and the time is 68 seconds. So, you can plug these values into the formula and get:

Speed = 340 meters / 68 seconds

Speed =  [tex]\frac{340 meters}{68 seconds}[/tex]  =   5 meters per second

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this is a question of set of equations and solution is as follows,

Williamston Daily newspaper started printing newspaper.

Three years ago they had 5900 subscribers.

every month there is an increase of 66 new subscribers.

n is the number of months the paper has been printed.

so, the linear model will be  

B= early subscriber + number of month × increments

B= 5900 + n × 66

B= 66 n + 5900

Example - subscribers after 3 months,

n = 3

= 66 x 3 +5900

= 198 + 5900

= 6000

set of equations

A system of equations is a set or collection of equations that you deal with all together at once. Linear equations are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.

Linear equations

Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.

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Answer:(-2,-2)

Step-by-step explanation:

The radical has a value of 0 when x = -2. At that point, the function value is ...

 f(-2) = √(-(-2)-2) -2 = √(0) -2

 f(-2) = -2

On observing the provided question we can say that - the function f(x) = a^x is Range : (−∞,∞) or all real numbers

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the number and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The answer to the question is that all real numbers or (−∞,∞)

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