You look at a local newspaper to post your advertisement. You find it is going to cost you $50 for the first 200 words. Anything over200 words will be an additional $0. 05 per word. You used 84 words. Write this as a piecewise function

The domain of the function f(x) = x² is all real numbers, including negative numbers, zero, and positive numbers.

The domain of a function is the set of all values for which the function is defined. For the function f(x) = x², the domain is all real numbers. This includes negative numbers, zero, and positive numbers. This means that the function is defined for any real number, no matter how large or small. In other words, the domain of f(x) = x² is the set of all real numbers, {x ∈ R}. This is because the square of any real number is still a real number, and so the function is defined for all real numbers. Thus, the domain of f(x) = x² is all real numbers.

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The given system of equations y = -2x + 4 and 7y = -14x + 28 have Infinite solutions.

We have two equations are y = -2x + 4 and 7y = -14x + 28

We have to find the number of solutions for this set of equations

Let us first solve the given equations

y = -2x + 4   eqn 1

7y = -14x + 28   eqn 2

Substitute eqn 1 into eqn 2

7(-2x + 4) = -14x + 28

-14x + 28 = -14x + 28

0 = 0

This means that given equations y = -2x + 4 and 7y = -14x + 28 have infinitely many solutions.

Therefore, The two lines may have an infinite number of intersecting points (infinite solutions).

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Answer:

30 m/s

i believe

Answer:30 m/s

Step-by-step explanation:It travels 150 m in 5 seconds. What is its average speed ? Thus, the average speed of the car is 30 m/s.

Logarithmic functions are important largely because of their relationship to exponential functions.

What is logarithm ?

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.

The first section explains the meaning of the logarithmic function f (x) = c·loga(x - h) + k. It describes how to evaluate logarithms and how to graph logarithmic functions. This section also addresses the domain and range of a logarithmic function, which are inverses of those of its corresponding exponential function.

The next section presents two special logarithmic functions--the common logarithmic function and the natural logarithmic function. The common logarithm is log10x, and it corresponds to the "log" button on most calculators. The natural logarithm is logex, and it corresponds to the "ln" button on most calculators. The natural log has a particular use in economics--it is used to perform calculations involving compound interest.

Logarithmic functions are important largely because of their relationship to exponential functions.

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The required values of slope and y-intercept are 10 and 15.

The formula for these lines is y = mx + b, where m denotes the slope and b the y-intercept. Our line has a slope of 3 and a y-intercept of -5, which we know from the question. By entering these numbers, we obtain the equation of our line as y = 3x - 5.

We have,

y = 10x + 15

On comparing with general equation of line.

Y = mx + c

m is slope of line, c is y-intercept.

Then,

m = 10

And

y-intercept = 15

Thus,the required values of slope and y-intercept are 10 and 15.

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Answer:

Step-by-step plotttt

Answer:

23.54

Step-by-step explanation:

The 25th percentile for the given dataset is 5, and the 80th percentile is 16.

What is the percentile?

A percentile is a measure used in statistics that indicates the value below which a given percentage of observations in a group of observations fall. Percentiles divide a set of observations into 100 equal parts, where each part represents 1% of the observations.

To find the 25th percentile (also known as the first quartile) and 80th percentile (also known as the fourth quartile) for a set of data, you can use the following steps:

Arrange the data in increasing order:

1, 3, 5, 9, 10, 11, 14, 15, 16, 18, 20, 22, 24, 25, 27, 29, 31, 37

To find the 25th percentile, use the following formula:

25th percentile = (N+1) x 25%

where N is the number of observations. In this case, N = 18.

Plugging in the values, we get:

25th percentile = (18+1) x 25% = 19 x 25% = 4.75

So, the 25th percentile is the 4.75th value in the ordered list. Rounding up to the nearest whole number, we get 5 as the 25th percentile.

To find the 80th percentile, use the following formula:

80th percentile = (N+1) x 80%

where N is the number of observations. In this case, N = 18.

Plugging in the values, we get:

80th percentile = (18+1) x 80% = 19 x 80% = 15.2

So, the 80th percentile is the 15.2th value in the ordered list. Rounding up to the nearest whole number, we get 16 as the 80th percentile.

Hence, the 25th percentile for the given dataset is 5, and the 80th percentile is 16.

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The set of polynomials is not closed under division.

A polynomial is a mathematical statement made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division operations. Polynomial means "many terms" since it combines the words poly-, which means "many," and -nomial, which in this context means "term." A polynomial may have exponents (like the 2 in y2), constants (like x and y), variables (like the x and y exponents), and other terms, but only those that can be mixed using addition, subtraction, multiplication, and division are permitted. Constants, variables, and exponents are all permitted in polynomials, but variable division is never permitted.

In addition, they are now only limited to a finite number of terms, which can be one or more.

The dividend appears at the top of the division at first, similar to how long multiplication is written.

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Answer: The answer is 4 units(AD=4)

Step-by-step explanation:

basically we are given two similar shapes. We know that OM = 2  and OK = 1, so we already know the scale factor: 2. Therefore, we multiply BC by two to get 4 which is AD.

Answer:

your answer is 4

Step-by-step explanation:

yeah whatever it said above.

Answer: 644.99999

Step-by-step explanation:

6 4/5 = 34/5 = 6.8

6.8 as a percent is 680%

Hope this helps!

the scale factor will be √5.

What is dilation?

resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.

The given figure ABCD dilated to A'B'C'D'

take DC =√ (9-13)² + (4-7)²

DC = √16+9= 5

D'C' = √(4-6)²+(3-4)²

= √5

Hence the scale factor will be √5.

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Answer:

factor out the GCF

Step-by-step explanation:

The equation y = 3x - 1 and x² + y² = 73 then x = -1, y = -2.

Simultaneous linear equations are a pair of linear equations in two or three variables that are solved simultaneously to arrive at a single answer.

Simultaneous equations are two or more algebraic equations that share the same unknown variables and have the same solution for each of them. The simultaneous equations must therefore have a single solution, according to this.

Add together the equations if the signs vary. Subtract the indications from one another if they match. Different Add, Same Subtract, or DASS, is a simple way to remember this.

Substitute y = 3x + 1 in [tex]$x^2+y^2=5$[/tex]

[tex]$$x^2+(3 x+1)^2=5 \quad \Rightarrow \quad 10 x^2+6 x-4=0$$[/tex]

Hence

[tex]$$\begin{aligned}& 5 x^2+3 x-2=0 \Rightarrow 5 x^2+5 x-2 x-2=0 \quad \\\& 5 x(x+1)-2(x+1)=0 \quad \Rightarrow \quad(5 x-2)(x+1)=0\end{aligned}$$[/tex]

Hence, either [tex]$x=\frac{2}{5}, y=3 \times \frac{2}{5}+1=\frac{11}{5}$[/tex]

or [tex]$x=-1, y=3 \times(-1)+1=-2$[/tex].

The complete question is:

How do you solve the simultaneous equations [tex]$x^2+y^2=5$[/tex] and y=3x+1?

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A possible second point with a y-coordinate of 8 is equal to 5.

In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following slope and data points on the line:

Points on x-axis = (1, 2).

Points on y-axis = (_, 8).

Slope, m = 3/2

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

Slope, m = (y₂ - y₁)/(x₂ - x₁)

3/2 = (8 - 2)/(x₂ - 1)

3/2 = 6/(x₂ - 1)

Cross-multiplying, we have:

3(x₂ - 1) = 12

x₂ - 1 = 12/3

x₂ - 1 = 4

x₂ = 4 + 1

x₂ = 5

In conclusion, we can logically deduce that the second point (x₂) is 5.

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Solving a formula for a variable means rewriting the formula so that the variable is Isolated to one side.

Solving a formula for a particular variable entails placing that variable alone with a coefficient of 1 on one side of the equals sign. The other side of the equals sign represents all other variables and constants.

A formula is a mathematical representation of how two variables relate to one another. In the sciences, including physics, biology, and chemistry, formulas are also employed. They are employed in medicine to do computations for calculating body mass index or distributing medication. Calculations are done using formulas in spreadsheet systems.

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The simplification of the given expression would be = -60

The simplification of an expression is defined as the representation of a large number or sophisticated equation into a simpler one.

The given expression = -50 + 5/13P

where P.= -26

Therefore, -50 + 5/13(-26)

Solve for; 5/13(-26) = 5/13 × -26 = -130/13 = -10

= -50 -10 = -60.

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The amount that the store donate will be $50

It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, for every camera sold in February the store donated $2 to a charity. If 25 cameras are sold, the amount that the store donate will be:

= 25 × $2

= $50

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Complete question

For every camera sold in February the store donated $2 to a charity. If 25 cameras are sold, how much did the store donate ?

How to Name a Graph: Tips for Writing Great Chart Captions

Now, According to the question:

The title should concisely tell the reader what is in the graph. Avoid the obvious use of “vs.” or “versus” or the word “plotted” in the title. Graphs that will appear as a figure in a publication or in a formal laboratory report will not have a title (the information is given in the figure caption).

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Answer:

A) angle

Step-by-step explanation:

This is a definition.

Answer:

0

Step-by-step explanation:

1. Review the definition for a real number: Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers

2. Review the definition for a non real number: The numbers which are not real and are Imaginary (such as i or a square root)

3. Your question may be missing an answer choice

4. Since all 4 of these numbers are positive, negative, whole, fraction, or decimal numbers, they are all real. Unless you are missing a number in the answer choices, there are no non real numbers.

But, wait! I may have missed something here. '0' is technically both an imaginary and real number, so it may be the answer to your problem!

Answer:

Solution

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = \frac{rise}{run}

run

rise

= \frac{y_{2}-y_{1} }{x_{2}-x_{1} }

x

2

−x

1

y

2

−y

1

with (x₁, y₁ ) = (- 1, - 5) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \frac{1-(-5)}{2-(-1)}

2−(−1)

1−(−5)

= \frac{1+5}{2+1}

2+1

1+5

= \frac{6}{3}

3

6

= 2

We can write the measurements as -

Given is a right angled triangle.

We can write -

{ 1 } -

sin (A) = a/c

a = c sin(A)

a = 12 sin(40°)

a = 12 x 0.65

a = 7.8

{ 2 } -

cos (A) = b/c

b = c cos(A)

b = c cos(40°)

b = 12 x 0.77

b = 9.24

{ 3 } -

tan (B) = b/a

tan (B) = 9.24/7.8

tan (B) = 1.19

(B) = 50°

Therefore, we can write the measurements as -

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If the scale for the drawing is 1 inch : 4 feet , then the length of the rug in the drawing  is 2 inches  .

the actual length of the rug in the hallway is = 8 feet ;

the scale factor for the drawing is given as 1 inch : 4 feet  ;

that means 4 feet of actual length is represented by 1 inch in the drawing ,

So , 1 feet in the actual length will be = [tex]\frac{1}{4}[/tex] inch in the drawing ;

that means , 8 feet of the actual length will be = [tex]\frac{8}{4} =2[/tex] inch in drawing .

Therefore , the length of the rug in the drawing is 2 inches .

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The side length of BC in ∠ABC is 11.

Solution:

∠A = 32°

∠C = 39°

∠B = 180°-39°-42°

∠B = 99°

side length of AC = 16

a / sin A = b / sin B = c / sin C

a / sin42° = 16 / sin99°

a = 16 sin42°/ sin99°

a = 10.84

a = 11

The side length of BC = 11

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Answer:

-4

Step-by-step explanation:

a1 is 2

a2 = a1^2-5 = 4-5 = -1

a3 is a2^2-5 = 1-5 = -4

the general term will be a,ar,ar², .... i.e 3, 12, 48..

What is geometric sequence?

The sequence where another varies each word by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.

Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.

Given,

a = 3

ar+ar² = 60

r+r² = 20

r(r+1)=20

r = 4

So the general term will be a,ar,ar², .... i.e 3, 12, 48..

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Y-axis divides the line segment joining the given points (-2, -3) and (3, 7) in the ratio is equal to 2 : 3.

As given in the question,

Given points of the line segments are :

( x₁ , y₁ ) = ( -2 , -3 )

( x₂ , y₂) = ( 3, 7 )

When y-axis divides the line segment its coordinate are ( 0, y)

Let the ratio which divides the line segment be m : n

( 0 , y ) = [ ( mx₂ + nx₁) / ( m + n) ,  ( my₂ + ny₁) / ( m + n)]

⇒( 0 , y ) = [ ( 3m -2n) / ( m + n) ,  ( 7m -3n) / ( m + n)]

⇒( 3m -2n) / ( m + n) = 0

⇒ 3m -2n = 0

⇒3m = 2n

⇒ m : n = 2 : 3

Therefore, the y-axis divides the given line segment in the ratio equals to 2 : 3.

The above question is incomplete , the complete question is:

In what ratio is a line segment joining the points (-2, -3) and (3, 7) divided by y-axis?

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The number of weed killer cans needed is 2.4 cans and it will cost $ 47.4

A trapezium is a quadrilateral with at least one pair of parallel lines. The two parallel lines are named a and b. The area of a trapezium is given as:

A = ½( a+b) h

where a and b are the parallel sides and h is the height of the trapezium.

since the lawn takes the shape of a trapezium,

The height of the lawn is calculated as:

h² = 17²- 8²

h² = 289-64

h² = 225

h = √225 = 15m

therefore A = ½(12+20)15

A = ½×32× 15

A = 16×15

A = 240m²

If one can will go for 100m², then the number of can that will be needed for the lawn = 240/100 = 2.4 can of weed killers.

If one weed killer cost $19.75, then

2.4 weed killers will cost 19.75 × 2.4 = $47.4

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ln 3x = ln (3x). The derivative of ln (3x) is 1/3x. in this case, f(x) = ln (x) and g(x) = 3x. The derivative of ln (x) is 1/x and the derivative of 3x is 3. Therefore, the derivative of ln (3x) is 1/3x which is equal to 1/(3x).

in this case, f(x) = ln (x) and g(x) = 3x. The derivative of ln (x) is 1/x and the derivative of 3x is 3. Therefore, the derivative of ln (3x) is 1/3x which is equal to 1/(3x). Using the chain rule, the derivative of ln (3x) can be found. The chain rule states that the derivative of a function f(g(x)) is f'(g(x)) * g'(x). In this case, f(x) = ln (x) and g(x) = 3x.ln 3x = ln (3x). The derivative of ln (3x) is 1/3x.

ln 3x = ln (3x). The derivative of ln (3x) is 1/3x.

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Answer:

B) USA

Step-by-step explanation:

USA is in North America