A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.

Which graph represents this situation?

The piecewise function will be written as y= -x { x < 0 } and y = x { x > 0 }.

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

Given that the function is f(x)= x. The piecewise function of the given function will vary from x being less than zero and x being greater than zero. The function can be written as  y= -x { x < 0 } and y = x { x > 0 }.

The graph of the piecewise function of the given function is attached with the answer below.

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The evaluation of the expression 12.75 ÷ 1.5 is 51  / 6.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Therefore, let's evaluate the expression as follows:

Hence,

12.75 ÷ 1.5

Let's convert each decimal to fractions for easy evaluation

Therefore,

12.75  = 1275 / 100

1.5 = 15 / 10

Therefore,

1275 / 100 ÷ 15 / 10

Let's change the division sign to multiplication sign.

1275 / 100 × 10 / 15

1275 / 150

Therefore,

255 / 30 = 51 / 6

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Complex fractions are called complex because they contain one or more fractions within the numerator and/or denominator of the fraction. These fractions within the fraction make the fraction more complex or difficult to simplify than a regular fraction, which only has a single numerator and denominator.

The term "complex" in mathematics often refers to something that is composed of multiple parts or layers, and that requires more steps or understanding to work with or solve.

In this case, the presence of one or more fractions within the fraction makes it more complex than a regular fraction, hence the name "complex fraction."

Another reason for the term complex is that the fractions in the numerator and denominator may have different or even the same variables, making it difficult to cancel them or simplify the expression.

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The inverse of 7 is 1/7.

A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1.

The reciprocal of a and 1/a.

For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1.

Multiplicative inverse:

The multiplicative inverse of a number can either be expressed as a fraction or as a number raised to the power of a negative one. A number multiplied by its multiplicative inverse is one.

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No, it is not possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(6cm + 8cm) =15cm

14cm = 15cm

LHS<RHS

A triangle is not possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Answer:

n_(n-1)+6

Step-by-step explanation:

n_(n-1)+6

im pretty sure?

When the numerator of the fraction is greater than the denominator, the the fraction is an improper fraction.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part is denominator.

consider a fraction 1/6.

Here, numerator is 1, denominator is 6

When certain thing is divided into 6 equal parts then each part of is represented by fraction1/6

As we the types of fractions are: Proper fraction, Unit Fraction ,Improper fraction, Mixed fraction, Like fractions, Unlike fractions and Equivalent fractions

An improper fraction is a fracton in which the numerator of the fraction is greater than the denominator.

For example, 8/7 is an improper fraction.

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Answer:

54 Hours

Step-by-step explanation:

first of all 540-54 he started with is 486 and 486/9 is 54 since you get 9 per hour

Answer: 54 Hours of babysitting

Step-by-step explanation: 540-54=486 Then you take 486 and you divide it by 9 to see how many hours you have to work and that would be 54 hours.

Answer: Positive

Hope this helps :)

Step-by-step explanation:

When multiplying or dividing with two negative numbers, the product/quotient will always be positive.

-8/-4 = 2

Answer: Positive

Step-by-step explanation:

Example for multiplication:

Imagine 4 friends that owe you $8 each.

Each friend that pays you back represents their payback as -$8.

-$8 * 4 friends = -$32 that they owe you.

The moment they give it back, you now have +$32. The Debt was taken away.

Example for Division:

Imagine splitting 8 dollars in debt with 4 friends, each friend then has $2 in debt. Each payback means you have +$2.

Another visual way to think of this is with Number Lines.

On a number line, when you multiply by a larger absolute value the numbers get bigger and go farther away from 0. So, taking a negative and multiplying it by a positive makes it MORE negative, as opposed to multiplying it by negative and then it reflects the number line,

From the box-and-whisker plot of the data, the Interquartile range is 6.

What is the Interquartile range?

An interquartile range is finding the median of the first half of the data set, and the second half, then subtracting the first median from the second one.

Steps to create a box-and-whisker plot and find the interquartile range.

Step 1: Sort the data in ascending order: 7, 7, 9, 10, 11, 12, 12, 12, 12, 13, 15, 15, 17, 18, 18

Step 2: Find the median (middle value) of the data: 12

Step 3: Divide the data into two halves:

Lower half: 7, 7, 9, 10, 11, 12, 12

Upper half: 12, 12, 13, 15, 15, 17, 18, 18

Step 4: Find the median of the lower half (Q1) and the median of the upper half (Q3).

Q1: 9

Q3: 15

Step 5: Draw a box-and-whisker plot:

Draw a number line and mark the minimum, Q1, median, Q3, and maximum values.

Draw a box between Q1 and Q3 and a vertical line inside the box to represent the median.

Draw lines (whiskers) from the box to the minimum and maximum values.

Step 6: Find the interquartile range (IQR) by subtracting Q1 from Q3: 15 - 9 = 6.

Hence, the Interquartile range is 6.

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The values of x for which the product:

√(5x)*√(x + 3)

Is defined are:

x ≥ 0

Here we want to see for which values of x is the following product not defined.

√(5x)*√(x + 3)

Ok, remember that the argument of the square root must be zero or larger, then we have two inequalities here:

5*x ≥ 0

x + 3≥ 0

We can simplify both of these inequalities to get:

x ≥0

x≥ -3

We take the first one, which is more restrictive, the values of x for which the product is defined are:

x ≥0

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The correct expression to solve te sum of polynomials is [(-3x)+(-8x)]+4x+[9+5] (D).

To solve any polynomials problems, it is important for us to take a close look on the orders of each number. For the sum and substraction operation, we need to categorize each number based on its orders.

From the case, we have a problem as:

(9 - 3x²) + (-8x² + 4x  + 5)

We can categorize each order:

Order 2 = (-3x²) and (-8x²)

Order 1 = 4x

Order 0 = 9 and 5

Hence, we can solve the problem as:

(9 - 3x²) + (-8x² + 4x + 5)

= [(-3x²) + (-8x²)] + 4x + (9 + 5)

= -11x² + 4x + 14

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Answer:

Step-by-step explanation:

nhbjbjhbnjbjnjnjny6778899

The orange bookmarks that Mateo can make than aqua bookmarks is 1.

Based on the information given, let x = number of aqua bookmarks

(1/6) × x = 3/4

x = (3/4) × (6/1)

x = 18/4

x = 4.5

Rounding down shows that we can make 4 aqua bookmarks.

y = number of orange bookmarks

(1/6)y = 9/10

y = (9/10)*(6/1)

y = 54/10

y = 5.4

This rounds down to 5 orange bookmarks.

Therefore, Mateo can make 5-4 = 1 extra orange bookmark compared to aqua.

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Mateo is making bookmarks with different colored ribbon. The

amount of each color he has is shown in the table. Each bookmark

will be yard long. How many more orange bookmarks can he make

than aqua bookmarks?

Table:

Color: Length (yd):

———————————-

Aqua. 3/4

Orange. 9/10

Yellow. 15/16

The inverse operations can be graphed by determining the inverse of the function by swapping the x and y variables,

Not all functions have inverses, and in order for a function to have an inverse, it must be a one-to-one function that is, there must not be repeated output for many inputs which indicates that not all functions have inverses. The various steps to graph inverse functions can be noted as -

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The mathematical symbol ∑∑ is used to represent a double summation. It is a way of expressing the sum of two series of numbers.

Double summation is a way of expressing the sum of two series of numbers, written as ∑∑. The upper sigma symbol represents the outer summation, while the lower sigma symbol represents the inner summation. The two series of numbers that form the double summation can be related or unrelated.

The double summation is written in the following form: ∑∑ aij, where aij is an element from the two series of numbers, i and j are the upper and lower limits of the double summation, respectively.

This type of expression is used to find the sum of a set of numbers that are related to each other in some way, such as the sum of the elements in a matrix or a table, or the sum of two series of numbers that are not related. The double summation is a useful tool for expressing the sum of two series of numbers and is widely used in mathematics and science.

Complete answer:

What does ∑∑ mean?

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An obtuse angle has 120 degrees in them.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Any angle more than 90 degrees is called obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.

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Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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In the word problem the number of the adult ticket is 225.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here total number of tickets = 516.

Which is contains adult and students tickets. Then let us take x is number of adult ticket and y is number of student tickets then,

=> x + y = 516 ------> 1

Now  there were 66 more student tickets sold than adult tickets then

=> y = x+66 -----> 2

Now put 2 into 1 then

=> x+66+x = 516

=> 2x = 516-66 = 450

=> x = 225.

Now put x = 225 into then

=> y = 225+66 = 291.

Hence the number of adult tickets is 291.

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The given equation y = -3x + 5 has infinitely many solutions.

We have linear equation y = -3x + 5

We need to encounter how many solutions can satisfy the given equation. 

We know that,

y = -3x + 5 is a linear equation in two variables in the form ax + by + c = 0

For x = 0, y = 0 + 5 = 5. Therefore, (0, 5) is one solution.

For x = 1, y = -3 × 1 + 5 = 2. Therefore, (1, 2) is another solution.

For y = 0, -3x + 5 = 0, x = 5/3. Therefore, (5/3, 0) is another solution.

Clearly, for different values of x, we get different values for y. Thus, any value substituted in the place of x in the given equation will form another solution for the given equation. So, there is no limitation to the number of different solutions obtained by substituting real values for x in the given linear equation. Thus, a linear equation in two variables can have infinitely many solutions.

Thus, y = -3x + 5 has infinitely many solutions.

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The experimental probability that the next customer to come into Chandler's boutique wears a size small is; 1/19

Theoretical probability is defined as the term used to describe what we expect to happen based on math theory, while experimental probability refers to what actually happens when the actual situation is tried out as an experiment.

In this question, we are given;

Number of small wears = 3

Number of medium wears = 32

Number of large wears = 22

Thus;

Total number of wears = 3 + 32 + 22

= 57

Probability that next customer wears small size = 3/57 = 1/19

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Research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.

A research plan is the main part of a grant application and describes a principal investigator's proposed research.

A research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.

We write a research plan by given steps.

Define the project purpose.

Identify individual objectives.

Select a research method.

Recruit participants and allocate tasks.

Prepare a project summary.

Create a realistic timeline.

Determine how to present your results.

The bibliographic information has Author name, Title of publication., Article title (if using a journal), Date of publication, Place of publication., Publisher, Volume number of a journal, magazine or encyclopedia and

Page number(s)

Hence, research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.

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The solution sets are called algebraic sets.

An algebraic set is the locus of zeros of a collection of polynomials, and it is the set of solutions.

A solution set is a set of values that satisfy a given set of equations or inequalities.

The set containing all the solutions of an equation is called the solution set for that equation. If an equation has no solutions, we write ∅ for the solution set. ∅ means the null set.

A linear system with a unique solution has a solution set with one element. Solution sets are a challenge to describe only when they contain many elements.

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Answer: view below

Step-by-step explanation:

a. [tex]-\frac{2}{3}x \geq 7[/tex]

[tex]x\leq -\frac{21}{2}[/tex]

b. 32>23-x

x>-9

c. 2(x+6)<10

x+6<5

x<-1

d. 15-4x[tex]\leq 3x-6[/tex]

21[tex]\leq[/tex]7x

3[tex]\leq[/tex]x

x[tex]\geq[/tex]3

The solution to the system of equations is y equals 1. 5 x 4 and y equals negative x is-= (1.6,-1.6)

In this case option A is correct

The coordinates of the ordered pair (s) that satisfy all of the equations in the system are the solution set to a system of equations. To put it another way, those x and y values will make the equations true. As a result, when a system of equations is graphed, the intersection points of the graphs are the system's solution.

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What is the solution to the system of equations y equals 1. 5 x 4 and y equals negative x?.

So, in 4 years, there will be 1176 people attending.

To find out how many people will be attending in 4 years, you need to determine the total decrease in attendance over that time period. The attendance is decreasing at a rate of 0.5% per year, so over 4 years, the decrease in attendance will be 4 years x 0.5% = 2%

To find out how many people will be attending in 4 years, you can then subtract the 2% decrease from the current attendance of 1200 people:

1200 x (1 - 0.02) = 1176 people

So, in 4 years, there will be 1176 people attending.

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You must ascertain the overall drop in attendance over that time span in order to calculate the number of attendees in 4 years. If enrollment drops by 0.5% annually, it will drop by 2% over the course of four years (4 years x 0.5%).

Then, from the present attendance of 1200 people, subtract the 2% decline to determine how many attendees there will be in 4 years:

1200 times (1-0.02) ≈ 1176 individuals

Therefore, there will be 1176 attendees in 4 years.

The graph that depicts a function is graph when the vertical line test is used (b).

By visually counting the number of times the curve crosses vertical lines, the vertical line test is a graphical approach for verifying whether a curve in the plane accurately depicts the graph of a function. the graph of a function can only be intersected by any vertical line in the plane once as a result.

A graph must satisfy the vertical line test in order to be considered a function representation. The vertical line test requires that the line from the x-axis only once crosses an associated y-value.

Graphs (a), (c), and (e) fail the vertical line test, indicating that they do not reflect a function.

So, graph is the name of the graph that represents a function (b)

The complete question is:

Use the vertical- line Test to determine which graph represents a function? I'm thinking it's the first one...

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The equation y = 2x + 5 is already in standard form.

Standard form of a linear equation is Ax + By = C, where A, B, and C are constants and A and B cannot be both zero. In this case, A=2, B=1 and C=5, which meets the standard form equation, y = 2x + 5 is already in standard form.

Answer: y = 2x + 5 in standard form is 2x - y = -5

Step-by-step explanation: I hope this helps!

Answer:

72.5 / 2.5 = 29

29 - 8 = 21

21 / 3 = 7

7

Step-by-step explanation:

The height of the building is given as follows:

36 ft.

In this problem, we have two similar triangles, meaning that their side lengths are proportional.

As the triangles are similar, the equation involving proportions for the equivalent side lengths is given as follows:

x/6 = 45/7.5.

Applying the division on the right side of the equality, we have that:

45/7.5 = 6.

Hence:

x/6 = 6.

Applying cross multiplication, the height is given as follows:

x = 6(6) = 36 ft.

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