How do you make a graph compare two sets of data?

On solving the expression for (y), we get two possible values, one real and one complex as -

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}    -- Real

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}    -- Complex

Given is the expression as follows -

√{(x + c)² + y²} = x (a/c) + a

√{(x + c)² + y²} = xa/c + a

√{(x + c)² + y²} = a{x/c + 1}

√{x² + c² + 2xc + y²} = a{x/c + 1}

{x² + c² + 2xc + y²} = ± (a{x/c + 1})²

Now, we can write -

{x² + c² + 2xc + y²} = (a{x/c + 1})²              ...... (1)

and

{x² + c² + 2xc + y²} = - (a{x/c + 1})²                 ......... (2)

Solving (1) as -

{x² + c² + 2xc + y²} = (a{x/c + 1})²    

{x² + c² + 2xc + y²} = a²(x/c + 1)²

{x² + c² + 2xc + y²} = a²(x²/c² + 1 + 2x/c)

{x² + c² + 2xc + y²} = (a²x²/c² + a² + 2a²x/c)

y² = (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}

Solving (2) as -

{x² + c² + 2xc + y²} = - (a{x/c + 1})²                

y² =  - (a{x/c + 1})² - (x² + c² + 2xc)

y² = - {(a{x/c + 1})² + (x² + c² + 2xc)}

y = √- {(a{x/c + 1})² + (x² + c² + 2xc)}

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}

Therefore, on solving the expression for (y), we get two possible values, one real and one complex as -

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}    -- Real

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}    -- Complex

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â' in mathematics refers to the hexadecimal representation of the number 10.

In machine code and assembly programming languages, hexadecimal is widely utilised. It is frequently used to refer to memory addresses. It can be used to represent numbers kept in a CPU's registers or in main memory, as well as during the debugging phase of designing a computer programme.

Although there are six more digits to consider, counting in hex is very similar to counting in decimal. When a digit position exceeds "F," you roll that place over to "0" and increase the digit to the left by 1. And once you've reached 1F16, move on to 2016 and keep churning the right-most

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Answer:

-18a^3b^5

Step-by-step explanation:

First do -ab^2*-6ab^2=-6a^2b^4

Then multiply that by 3ab=-18a^3b^5

The degree of the polynomial √3 is 1.

Polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponents of variables. Polynomials are often used to solve problems in algebra, geometry, calculus and other branches of mathematics.

A polynomial is an expression made up of variables, constants, and exponents.

A polynomial is said to have a degree when the highest degree of any of its terms is known.

The degree of a polynomial is determined by the highest exponent of a given term. In the case of √3, the exponent is 1, making the degree 1.

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The product of (2x-3y)(2x+3y) is 4x^2-9y^2

Product= (2x-3y)(2x+3y)

Let the product of (2x-3y)(2x+3y) be P

P=2x(2x+3y)-3y(2x+3y)

P= 2x(2x)+2x(3y)-3y(2x)-3y(3y) {using distributive property of multiplication}

This property states that  multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a-b)(a+b) is equal to a^2 - b^2. This result is used as an identity.

P= 4x^2 +6xy - 6xy -9y^2

solving 6xy-6xy=0

P= 4x^2 - 9y^2

4x^2-9y^2 is the product of (2x-3y)(2x+3y).

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If his growth spurt continued at the same rate Andrew will grow 26/7 inches per month during that growth spurt.

To calculate someone's age, you would subtract their birth year from the current year. For example, if someone was born in 1995 and it is now 2020, their age would be calculated as 2020 - 1995 = 25 years old.

If you have a birthdate, you can use a date calculator to find the exact age in years, months and days.

It's also important to note that, if the person's birthday hasn't occurred yet in the current year, you would subtract the birth year from the current year minus one.

We can start by converting the mixed number 4 1/3 to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 4 x 3 + 1 / 3 = 13/3

To find out how much Andrew grew per month, we need to divide the total growth by the number of months.

13/3 inches / 3 1/2 months = (13/3) / (7/2) = (13/3) x (2/7) = 26/7 inches/month.

So, Andrew grew 26/7 inches per month during that growth spurt.

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well, what's 230% of $480?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{230\% of 480}}{\left( \cfrac{230}{100} \right)480}\implies \text{\LARGE 1104}[/tex]

No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.

The sum of the angles of a triangle must always add up to 180 degrees. To determine if a set of angles can form a triangle, add the angles together. If the sum is 180, the angles can form a triangle. In this case, 30 + 60 + 90 = 180, which does not equal 180. Therefore, these angles cannot form a triangle.

No, the sum of the angles of a triangle must add up to 180 degrees. 30 + 60 + 90 = 180, so these angles cannot form a triangle.

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The equation of line passes through the point (2, 3) will be;

⇒ y = 1/2x + 2

And, Graph of this equation of line is shown in figure.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (2, 3).

And, The perpendicular line is,

⇒ y - 4 = - 2 (x + 3)

⇒ y -  4 = - 2x - 6

⇒ y = - 2x - 2

Now,

Since, The equation of line passes through the point (2, 3).

So, We need to find the slope of the line.

Since, The product of slope of the perpendicular line is - 1.

Hence, Slope of the given perpendicular line is,

⇒ y = - 2x - 2

m = dy/dx = - 2

m = - 2

So, The slope of line is,

⇒ m₂ = - 1/m

         = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - 3 = 1/2 (x - 2)

⇒ y - 3 = 1/2 (x - 2)

⇒ y - 3 = 1/2x - 1

⇒ y = 1/2x - 1 + 3

⇒ y = 1/2x + 2

Therefore, The equation of line passes through the point (2, 3) will be;

⇒ y = 1/2x + 2

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To solve complex fractions there are two methods -

1 - Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator and then simplify further if necessary.

2 - Multiply the numerator and denominator of the overall complex fractions and then simplify further if necessary.

What is a complex fraction?

A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction.

There are two ways to solve a complex fraction -

Method 1 : Take an example - (1/3-1/4)/(1/8+1/2)

Step 1 - If necessary, combine the denominator and numerator into a single fraction.

Add the numerator -

=1/3-1/4

=(4-3)/12

=1/12

Add the denominator -

=1/8+1/2

=(1+4)/8

=5/8

Combine back to form a complex fraction -

=(1/12)/(5/8)

Step 2: Multiply the numerator by the denominator's reciprocal, then divide the result by the denominator.

Step 3: Simplify the rational expression if necessary.

=(1/12)×(8/5)

=8/60

=2/15

Method 2: Take an example - [(2x+1)/(x^2-25)]/[(4x^2-1)/(x-5)]

Step 1 - Divide the LCD of the smaller fractions by the numerator and denominator of the total complex fractions.

(x^2-25)=(x+5)(x-5)

The denominator of the denominator’s fraction  has the following factor -

(x-5)

Using the highest exponent and combining all the other factors, we arrive at the LCD shown below for all the little fractions -

(x+5)(x-5)

By multiplying the LCD by the numerator and denominator -

=[{(2x+1)/(x+5)(x-5)}×(x+5)(x-5)]/[{(2x+1)(2x-1)/(x-5)}×(x+5)(x-5)]

=(2x+1)/(2x+1)(2x-1)(x+5)

Step 2 - Simplify the rational expression if necessary.

=(2x+1)/(2x+1)(2x-1)(x+5)

=1/(2x-1)(x+5)

Therefore, there are two methods to solve complex fractions.

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The value of x and y in triangles AEB and BCD is 40° and 50°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is 180°.

Therefore, In ΔAEB,

(2x + 5)° + 50° + 45° = 180°.

2x + 100° = 180°.

2x = 180° - 100°.

2x = 80°.

x = 40°.

Now, ΔBCD,

x + y + 90° = 180°.

40° + y + 90° = 180°.

y = 180° - 130°.

y = 50°.

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The age group that falls between two standard deviations is 20 to 28.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.

Given, The average age of a university student was found to be 24 with a standard deviation of 2.

Therefore, age group is within 2 standard deviations of the mean is,

24 + 2×2 = 24 + 4 = 28,

And 24 - 2×2 = 24 - 4 = 20.

So, The age group between 20 to 28 falls within 2 standard deviations of the mean.

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Ken should leave a $3.59 tip.

We will discuss algebra, a branch of mathematics that deals with symbols and the rules for manipulating them, in the context of algebra word problem worksheets.

They represent variables or quantities without set values. Our abilities to construct and solve equations must be combined in order to solve algebraic word problems.

It is crucial to start by converting verbal descriptions into algebraic formulas before tackling word issues.

To find the amount of tip he should give, we note that 15% is equal to 0.15 as a decimal.

23.95 * 0.15= 3.5925≈3.59 (approximately)

Therefore, Ken should leave a $3.59 tip.

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Answer:

2(3n^2-4) and 6n^2-8

Step-by-step explanation:

There are two different answers but try at least both of them.

To find the unknown part of a right triangle, you can use the Pythagorean theorem or the trigonometric ratios.

A right triangle is a triangle that has one angle measuring exactly 90 degrees, this angle is called the right angle.

To find the unknown part of a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (the hypotenuse). The formula is:

a² + b² = c²

Where c is the length of the hypotenuse and a and b are the lengths of the legs.

You can use this theorem to find the length of a missing side, if you know the length of the other two sides. For example, if you know the lengths of the two legs (a and b) and you need to find the length of the hypotenuse (c), you can use the formula:

c = √(a² + b²)

Alternatively, if you know the length of the hypotenuse (c) and one leg (a), you can use the formula to find the length of the other leg (b):

b = √(c² - a²)

Another way to find the unknown part of a right triangle is the use of trigonometric ratios. As you know, in a right triangle, there are three main ratios: sine, cosine, and tangent. These ratios are defined as follows:

Sin(A) = a/c

Cos(A) = b/c

Tan(A) = a/b

Where A is one of the acute angles of the triangle, and a,b,c are the sides of the triangle. By using the known side and the known angle you could find the unknown side.

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The number √2 is called an irrational number because the value of √2 = 1.41421356... and the the value is non terminating and non repeating .

What are Irrational Numbers ?

The Numbers whose vales are Non Repeating and Non Terminating are called as Irrational Numbers ,

also the numbers that cannot be expressed on the form of [tex]\frac{p}{q}[/tex] are called as Irrational Numbers .

the number is given as √2 ;

we know that the values of √2 is = 1.41421356... ,

we see that the the value is non terminating and the numbers after decimal point are non repeating ,

Therefore  , the number √2 is an irrational number .

The given question is incomplete , the complete question is

Why the number √2 is called a Irrational Number ?

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Equation that will determine the amount of last year’s budget

Two or more expressions with an Equal sign is called as Equation.

Given that a school plans to spend twice the amount it did last year on its winter dance , less the cost of the disco ball which was $150 since they have it from last year

A total of $1,500 is being spent this year.

We need to find the equation which determine the amount of last year’s budget

2a-150=1500

When a is the amount of last year’s budget

Hence, 2a-150=1500 is the equation that will determine the amount of last year’s budget

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The score of Larry is 32 points.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Ervin scores half as many points in a game as Larry.

If Larry scored x points,

then the points of Ervin are x/2 points.

Here, x = 16,

So,

Ervin's points = Larry's points

The equation is,

16 = x/2

x = 16(2)

x = 32 points

Therefore, 32 points are the score of Larry.

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Since the tallest man is a lone individual, he can only take a seat in the center. The four other men can sit in 4! = 24 different positions.

We'll take pictures of five people standing in a row, all of varying heights. The tallest individual must be in the middle, so. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The likelihood that an event will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely alternatives that result in a given occurrence. Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. If we throw a coin into the air,

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Answer:

-25, -19, -15, -4, 5, 7, 22

Step-by-step explanation:

-25, -19, -15, -4, 5, 7, 22 is the order from least to greatest

The bigger the negative number, the smaller it is; that is why the order is

-25, -19, -15, -4, 5, 7, 22

The measure of the length MP is equal to 6.

Two triangles are similar triangles if they have the same corresponding angle measures and proportional side lengths.

Given is a triangle ΔOMN.

Now, ΔOMN and ΔOPQ are similar. This means that the side lengths are proportional to each other. We can write -

OP/OM = PQ/MN

12/OM = PQ/MN

12/(OP + PM) = PQ/MN

It is given that -

PQ = MP + 2

12/(OP + PM) = (MP + 2)/MN

12MN = (MP + 2)(OP + PM)

12 x 12 = (MP + 2)(MP + 12)

(MP)² + 12MP + 2MP + 24 = 144

(MP)² + 14(MP) - 120 = 0

Let MP = x, then we can write -

x² + 14x - 120 = 0

(x + 20)(x - 6) = 0

(x + 20) = 0   and    (x - 6) = 0

x = - 20   and   x = 6

x = 6      {Lengths cannot be negative}

Therefore, the measure of the length MP is equal to 6.

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Answer:

[tex]x=\dfrac{\log 6}{\log 23}[/tex]

Step-by-step explanation:

Given exponential equation:

[tex]23^x=6[/tex]

[tex]\textsf{Apply the log law}: \quad a^c=b \iff \log_ab=c[/tex]

[tex]\implies\log_{23}6=x[/tex]

[tex]\textsf{Given change of base formula}: \quad \log_by=\dfrac{\log y}{\log b}}[/tex]

Apply the given change of base formula:

[tex]\implies x=\dfrac{\log 6}{\log 23}[/tex]

The exponential function y = a · 2ⁿ ⁻ ¹, where a is any real number, is generates the geometric series.

Geometric series are sets of elements generated by exponential functions of the form:

y = a · bⁿ ⁻ ¹, where a and b are real numbers and n is a natural number.

Where:

According to the statement, we derive the following expression between the two sums:

9 · a · (1 + b + b²) = a · (1 + b + b² + b³ + b⁴ + b⁵)

Now we proceed to simplify and find the value of b:

8 · a · (1 + b + b²) = a · (b³ + b⁴ + b⁵)

8 · (1 + b + b²) = b³ + b⁴ + b⁵

b⁵ + b⁴ + b³ - 8 · b² - 8 · b - 8 = 0

Then, the value of b by numerical methods is equal to 2.

The geometric series is generated by the exponential function y = a · 2ⁿ ⁻ ¹, where a is any real number.

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The total number of pizzas consumed by the 10 members of the club is 2.5 and 3.5 pizzas remain, as Mr. Cam bought 6 pizzas and each of the 10 members ate 1/4 of a pizza.

Mr. Cam bought 6 pizzas for the club and each of the 10 members ate 1/4 of the pizza. To find out how many pizzas were eaten, we can use the formula:

Number of members x Pizza per member = Total Pizzas Consumed

In this case, we can substitute the given values in the formula:

10 members x 1/4 pizza/member = 10/4 = 2.5 pizzas

This means 2.5 pizzas were consumed by the members. Since Mr. Cam bought 6 pizzas and 2.5 pizzas were eaten, the total number of pizzas remaining is 6 - 2.5 = 3.5 pizzas.

This equation works because it uses the concept of the unitary method, where we find the total number of pizzas consumed by multiplying the number of members by the number of pizzas each member ate. This way we can find the total amount of pizza consumed.

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The volume of the can based on mentioned radius and height of can is 471 inches³.

Volume of cylinder is defined the capacity or amount of fluid that can be held in the object. The mentioned object is can which is cylindrical in shape.

Use the below mentioned formula to calculate the volume -

V = πr²h, where V is volume, r is radius and h is height.

Keep the values in formula to find the value of volume of cylinder

V = 3.14×5²×6

Next step is to perform multiplication on Right Hand Side of the equation

V = 471 inches³

The obtained volume is already rounded off. Thus, the volume of the can is 471 inches³.

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The expression for f(x) using exponent properties is 8x+11.

Let's first simplify the following statement in order to determine f(x):

[tex]\[\left(\frac{1}{49}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11}\][/tex]

Rewrite now with [tex]\(\left(\frac{1}{49}\right)^x\)[/tex] and [tex]\(\left(\frac{1}{7}\right)^{6x + 11}\)[/tex] as a single term's powers:

[tex]\[\left(\frac{1}{7^2}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11} \][/tex]

Now, using the rule for exponents [tex](a^{(m*n)} = (a^m)^n)[/tex],

Combine the following words using the same base (1/7 in this case):

[tex]\[ \left(\frac{1}{7}\right)^{2x} \cdot \left(\frac{1}{7}\right)^{6x + 11} \][/tex]

Add their exponents to multiply phrases with the same base:

[tex]\[ \left(\frac{1}{7}\right)^{2x + (6x + 11)} \][/tex]

[tex]\[ \left(\frac{1}{7}\right)^{(8x + 11)} \][/tex]

Now, the given expression becomes:

[tex]\[ \left(\frac{1}{7}\right)^{(8x + 11)} \][/tex]

Now, compare  [tex]\(\left(\frac{1}{7}\right)^{f(x)}\)[/tex],and [tex]\(f(x) = 8x + 11\)[/tex] gives f(x) = 8x+ 11.

So, the expression for f(x) is: [tex]\[ f(x) = 8x + 11 \][/tex].

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The question attached here is in appropriate form the appropriate form is

Find the expression for f(x) when rewriting the following expression in the form [tex]\(\left(\dfrac{1}{7}\right)^{f(x)}(7^1) ^{\dfrac{1}{49}^x \cdot \dfrac{1}{7}^{6x+11}}\):[/tex]

[tex]\(\left(\frac{1}{49}\right)^x \cdot \left(\frac{1}{7}\right)^{6x + 11}\)[/tex]

Answer:

[tex] \sf \: \frac{75}{12} \: (or) \: 6.25[/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]

[tex] \sf \rightarrow \: \frac{(15 \times 5)}{12} [/tex]

[tex] \sf \rightarrow \: \frac{75}{12} = 6.25[/tex]

Hence, the product is 6.25.

Yes, it is a perfect square trinomial.

Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."

The equation X² + 10X + 25 can be factored into (X + 5)²,

which is a perfect square trinomial. In general, a perfect square trinomial is any polynomial of the form A² + 2AB + B² where A and B are constants or variables.

This is because such a polynomial can be factored into (A + B)².

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Option C is correct. The coordinates of ADE'F' after dilation by a scale factor of 4 are A'(8,0), D'(8,0), E'(12,12), and F'(16,4).

Using one or more numbers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such Euclidean space. The order of the coordinates is important, and they can sometimes be distinguished by their place in an ordered tuple or by a letter, such as "the x-coordinate." In simple mathematics, the coordinates are assumed to be real numbers, while they could also be complex numbers or components of a more abstract structure, such a commutative ring. Analytic geometry is based on the usage of coordinate systems, which make it possible to convert geometry-related problems into numerical problems and vice versa.

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