What does y varies inversely as x mean *?

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3860\\ r=rate\to 3.08\%\to \frac{3.08}{100}\dotfill &0.0308\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-monthly, thus 24} \end{array}\dotfill &24\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 3860\left(1+\frac{0.0308}{24}\right)^{24\cdot 2} \implies A = 4105.09[/tex]

The 9th term of the geometric sequence is equal to 8.0090 rounded up to the nearest thousandth.

A geometric sequence or progression is a sequence where every term bears a constant ratio to its preceding term. The nth term of a geometric sequence is calculated as ar^(n - 1) where a is the first term and r is the common ratio.

the first term a = 80

we get the common ratio by dividing the preceding term by the previous term;

r = 60/80 = 3/4

the 9th term is evaluated as follows:

80 × (3/4)^(9-1)

80 × (3/4)^8

80 × 6561/65536

524880/65536

8.0090

Therefore, the 9th term of the geometric sequence is 8.0090 approximately to the nearest thousandth.

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Answer:

Step-by-step explanation:

To determine whether two triangles are comparable, compare the ratios of their corresponding sides. The triangles are identical if the ratios of the respective sides are the same. The "side-side-side" (SSS) similarity criteria is used for this.

To demonstrate that the three triangles are similar, examine the ratios of the corresponding angles. The triangles are identical if the ratios of the respective angles are equal. The "angle-angle-angle" (AAA) similarity criteria is used for this.

To determine whether three triangles are comparable, measure and compare the ratios of at least three matching angles.

The star is 20 parsecs away which is approximately equal to 63.66 light-years away.

What is parallax angle ?

The parallax angle, also known as the parallax shift or the annual parallax, is the angle between the observer's line of sight to a celestial object at two different points in the Earth's orbit. It is a method used to measure the distance to stars and other celestial objects.

The parallax angle is defined as the angle between the observer's line of sight to the star at two different points in Earth's orbit. The distance to a star can be calculated using the formula ,

Distance = 1 / parallax angle (in arcseconds)

In this case, the parallax angle is 1/20 arcseconds, so the distance to the star is,

Distance = 1 / (1/20) = 20 parsecs

Note that one parsec is equivalent to 3.26 light-years.

So the star is 20 parsecs away which is approximately equal to 63.66 light-years away.

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We use the format (x, y) to write the coordinates in format XY. Coordinates XY is a coordinate that use in Cartesian coordinate.

What is Cartesian coordinate?

Cartesian coordinate is system to draw a specific location of an unique point in the numerical condition that oriented in the two constant line where the vertical line called ordinate or Y and the horizontal line called abscess or X. The Cartesian coordinate commonly use in architecture or  a design of a certain object that has a certain dilate with its original plan. This design later is use to control the construction process of the original object.

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Answer:

You should -5x on both side of the equation instead of adding 5x on the left side.

The domain of the graph is 2 ≤ x ≤ 5.

Domain refers to the specific space of a website, including a domain name, associated IP address and a set of web pages that are hosted by a web server. Domain names are used to identify websites, and they are often used as a way to easily access a website. Domain names are assigned to each web server, allowing users to access the website by typing in the domain name instead of the IP address.

This means that all x-values must be greater than or equal to 2 and less than or equal to 5 in order for them to be part of the domain. This can also be written in interval notation as [2,5].

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The values of x that make the rational expression undefined are x = -2 and x = 5.The rational expression is undefined when the denominator is equal to zero.

To determine which values of x make the rational expression undefined, we can set the denominator equal to zero and solve for x.

Let's look at our rational expression:

(x + 2)(x - 5) = 0

We can simplify this expression to solve for x:

x + 2 = 0

x - 5 = 0

From these equations, we can solve for x:

x = -2

x = 5

Therefore, all the values of x that make the rational expression undefined are x = -2 and x = 5.

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To graph a natural log function, plot points on the coordinate plane and connect them with a smooth curve. The graph will be shaped like an "S" and will have asymptotes at x = 0 and y = 0.

A natural logarithm (ln) function is a function of the form y = ln(x). To graph this type of function, you will need to plot points on the coordinate plane and connect them with a smooth curve. The graph of a natural logarithm will be shaped like an "S". The graph will have two asymptotes: one at x = 0 and one at y = 0. This means that the function will approach but never reach either of these values. To plot points on the graph, you can use a chart of values or you can use a graphing calculator. To find the exact coordinates of points, you can use the natural logarithm function on your calculator. Once you have plotted several points, you can connect them with a smooth curve to get the graph of the natural logarithm.

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Vertical lines that are dotted at: as a result, and the numerator is zero. The graphed function is as follows: 1 / (x+3)(x-7)

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). X is the input. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

X values for which the function is not defined, or points beyond a function's domain, are referred to as vertical asymptotes;

These vertical asymptotes are shown in a graph by vertical lines that are dashed.

A value of x when the function's denominator equals zero serves as an illustration.

In this diagram:

Vertical lines that are dotted at: as a result, and the numerator is zero.

The graphed function is as follows: 1 / (x+3)(x-7)

And option C provides the right response.

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Answer:

need more in fo

Step-by-step explanation:

The prime factors of 625 and 1000 are listed below

1000: 2 * 2 * 2 * 5 * 5 * 5

625: 5 * 5 * 5 * 5

reducing 625/1000 gives 5/8

The prime numbers that divide a positive integer exactly are said to be its prime factors. Integer factorization, often known as prime factorization, is the process of locating these integers.

The prime factorization of 625 and 1000 are

1000: 2 * 2 * 2 * 5 * 5 * 5

625: 5 * 5 * 5 * 5

Reducing 625 / 1000

= (5 * 5 * 5 * 5) / ( 2 * 2 * 2 * 5 * 5 * 5 )

= 5 / (2 * 2 * 2)

= 5 / 8

the term 625 / 1000 is reduced to 5/8

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A seven-sided polygon is called a heptagon. A polygon with seven sides, seven angles, and seven edges is referred to as a heptagon. A heptagon's total number of angles comes to 900°.

It is also occasionally referred to as a septagon, though this usage is not advised because it combines the Latin prefix sept- (derived from septua-, meaning "seven") with the Greek suffix -gon (from gonia, meaning "angle").

A heptagon can be drawn using fourteen diagonals. Heptagon is also referred to as septagon on occasion. The Greek terms "heptá," which means "seven," and "gna," which means "angle," are combined to form the English word "heptagon. There are seven vertices, seven angles, and seven sides to it. A heptagon's internal angles add up to 900°.

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The Area of equilateral triangle that have the side length as 6cm is  [tex]9\sqrt{3} \; cm^{2}[/tex] .

An Equilateral Triangle is defined as a type of triangle in which all the side lengths are equal and measure of all the angles is also equal .

The Ares of Equilateral is calculated by formula  : [tex]\frac{\sqrt{3} }{4} \times a^{2}[/tex] ;

where "a" = side length ;

the side length of triangle is given as : 6 cm .

substituting the value of "a" as 6  in the formula ,

we get ;

Area = [tex]\frac{\sqrt{3} }{4} \times 6^{2}[/tex]

= [tex]\frac{\sqrt{3} }{4} \times 36[/tex]      ....because [tex]6^{2} =36[/tex] ;

Simplifying further ,

we get ;

= [tex]9\times \sqrt{3}[/tex] .

Therefore , the area of given equilateral triangle is [tex]9\sqrt{3} \; cm^{2}[/tex] .

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Answer:

A 140 degree counterclockwise rotation is the same as a 40 degree clockwise rotation. To determine the equivalent angle of a rotation in the opposite direction, you can subtract the angle of rotation from 360 degrees. In this case, 140 degrees counterclockwise is equivalent to 360 - 140 = 220 degrees, which is the same as a 40 degree clockwise rotation.

Step-by-step explanation:

The requied inequality is 0 ≤ p 2720 shows the possible power, p, that the waste-to-energy facilities in the United States are capable of producing.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We can write the inequality as follows:

0 ≤ p 2720

This inequality states that the power p that the waste-to-energy facilities in the United States are capable of producing is greater than or equal to 0 megawatts, and less than or equal to 2720 megawatts.

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Answer:

7. y-8 = [tex]\frac{3}{4}[/tex](x-4)

8. y+3 = 4(x-1)

9. y+5 = [tex]\frac{-1}{7}[/tex](x-7)

10. y-3 = [tex]\frac{5}{3}[/tex](x-3)

11. y+4 = -2(x+1)

The total amount of money that Johnny will have to pay is f(10) = 30.

What are expressions?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Given is that it costs Johnny $15 a month plus $1.50 per song to download music. This situation is represented by the expression →

1.5(x) + 15.

The expression is given by -

f(x) = 1.5(x) + 15

where [x] is the number of songs downloaded.

For [x] = 10 songs, the total amount of money that Johnny will have to

pay is -

f(10) = 1.5 x 10 + 15

f(10) = 15 + 15

f(10) = 30

Therefore, the total amount of money that Johnny will have to pay is f(10) = 30.

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The cost that Johnny has to pay to download 10 songs is 30$

as per given in the question,

johnny's  regular cost is 15$ a month

$1.50 is to be added for every song download

The cost to be find for 10 songs download

the equation which can be formed is

let x be the number of songs

1.5 times the number of songs + the cost of every month

therefore

1.5(x) + 15

the total number of songs to be downloaded is  10

so,

1.5(10) + 15

=> 15 +15

=> 30 $

Now the cost that has to pay by johnny after the downloading of 10 songs is 30 $

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Answer:

32−4x=12,

25 over x end fraction plus 4 equals 9 ((25)/(x)+ 4 equals 9), and

x over 5 end fraction plus 5 equals 6 ((x)/(5) plus 5 equals 6)

Answer: C. 3,500 grams

Step-by-step explanation:

Rodney got D as the answer by because he thought there are three zeros and adding 3 and 5 to the 1,000  35,000.

Because we know the unit rate: 1(kilogram) = 1,000(grams)

Rodney chose the incorrect answer.

Therefore, 3.5 x 1000 = 3,500 is correct

Answer:

The correct answer is C. 3500g

Step-by-step explanation:

3.5kg×1000=3500g

Rodney got answe D. by moving the decimal place of 3.5kg over by 4 places instead of 3.

His equation could have been 3.5kg×10000= 35000

Rodney did NOT choose the correct answer

312 different 5-digit even numbers can be found using the given digits which are 0, 1 , 2, 3, 4 , 5.

Even numbers can be made by placing either 0 or 2 or 4 at the rightmost digit, meaning that even numbers end at either 0 or 2 or 4.

Now consider these three cases individually:

Case 1 where the rightmost digit is 0:

Available digits = 0, 1 , 2, 3, 4 , 5.

Now you can write either 1 or 2 or 3 or 4 or 5 in the leftmost digit's place.

So, the number of ways of filling the leftmost digit = 5

When the leftmost digit has been written, then you are left with 4 digits to be placed between the leftmost digit and the rightmost digit via 4 different ways.

Proceeding this way, the next 3 and then 2 digits can be filled in 3 and 2 different ways respectively.

Thus, the number of possible numbers = 5 . 4. 3. 2 = 120

Case 2 where the rightmost digit is 2:

Available digits = 0, 1, 3 , 4 ,5

Now you can write either 1 or 3 or 4 or 5 in the leftmost digit's place. But not 0, because it makes the resulting number a four-digit number.

So, the number of ways of filling the leftmost digit = 4

When the leftmost digit has been written, then you are left with 4 digits to be placed between the leftmost digit and the rightmost digit via 4 different ways.

Proceeding this way, the next 3 and then 2 digits can be filled in 3 and 2 different ways respectively.

Thus, the number of possible numbers = 4 . 4. 3. 2 =  96

Case 3 where the rightmost digit is 4:

Available digits = 0 , 1, 2, 3, 5

Now you can write either 1,  2 or 3 or 5 in the leftmost digit's place. But not 0, because it makes the resulting number a four-digit number.

So, the number of ways of filling the leftmost digit = 4

When the leftmost digit has been written, then you are left with 4 digits to be placed between the leftmost digit and the rightmost digit via 4 different ways.

Proceeding this way, the next 3 and then 2 digits can be filled in 3 and 2 different ways respectively.

Thus, the number of possible numbers = 4 . 4. 3. 2 = 96

So, the total number of arrangements can be calculated as follows:

= 120 + 96 + 96

= 312

312 different 5-digit even numbers can be made using the given digits which are 0, 1 , 2, 3, 4 , 5.

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The required value of a function of function (g°f)(-6) is given as 52.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
f(x) = -x - 2

g(x) = x²

g(f(x)) = [-x - 2]²
g(f(x)) = [x + 2]²   [since [-a]² = a²]
g(f(x)) = x² + 2x + 4

Now, put x = 6,
g(f(6)) = 6² + 2[6] + 4

g(f(6)) = 36 + 12 + 4
g(f(6)) = 52

Thus, the required value of a function of function (g°f)(-6) is given as 52.

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[tex]x=106^{\circ}[/tex] (linear pair)

[tex]y=106^{\circ}[/tex] (corresponding angles with [tex]x[/tex])

[tex]z=106^{\circ}[/tex] (vertical angles with [tex]y[/tex])

Answer: x=13 units

Step-by-step explanation:

Answer:

22

From the numbers already shown it looks like each time they are adding 5 to the number before it.

The parent function is 2 units to the left in the graph, which is shifted vertically.

What exactly is a math graph?

In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

A vertical shift in a graph is a transformation that moves the graph up or down along the y-axis, without changing the shape of the graph. The amount of the shift is determined by the value of a constant in the function's equation. For example, in the equation y = f(x) + k, where k is a constant, a positive value of k will result in a shift upward and a negative value of k will result in a shift downward.

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The concept given here is Trigonometric expression, are non-routine appearing problems.  The answer is 0, π/2, 3π/2.

These expressions represent the connections between digression and the sine/ cosine functions. These expressions are complementary trigonometric individualities by description. While we solve trigonometric expressions, it is best to change everything into sine or cosine.

Given:

n= integer

sin²(θ) = 2sin²(θ/2)

[2sin(θ/2)cos(θ/2)]² =  2sin²(θ/2)

4sin²(θ/2)cos²(θ/2) = 2sin²(θ/2)

4sin²(θ/2)cos²(θ/2) -  2sin²(θ/2) = 0

2sin²(θ/2) [2cos²(θ/2) - 1] = 0

sin(θ/2) = 0

θ/2 = nπ

θ = 2nπ

θ = 0, π, 2π

Since,

θ = 0

2cos²(θ/2)-1 = 0

cosθ = 0

x= π/2 + πn

so,

θ = π/2 , 3π/2.

So, we can conclude that the solutions will be 0, π/2, 3π/2.

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The value of x in the equation "2 (x - 3) + 9 = 3 (x + 1 )+ x" is 0.

Solving this equation and finding the value of x,

2 (x - 3) + 9 = 3 (x + 1 )+ x

2x - 6 + 9 = 3x + 3 + x  

Bringing values with x to one side of the equation and constant to another side of the equation so that the value of x can be found.

2x  - 3x - x = 3  + 6 - 9

2x - 4x  = + 3 - 3

-2x = 0

  x   =  0 / -2

  x = 0

After solving the equation '2 (x - 3) + 9 = 3 (x + 1 )+ x' for x, the value of x to be found is 0.

Therefore, the equation '2 (x - 3) + 9 = 3 (x + 1 )+ x' gives the value of x equal to 0.

"

Complete question :

What is the value of x in the equation 2 (x - 3) + 9 = 3 (x + 1 )+ x'?

"

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The solutions of the given trigonometric equation are 60°, 180°, and 300°.

What is a trigonometric equation?

A trigonometric equation is an equation that contains one or multiple trigonometric ratios of unknown angles.

The given trigonometric equation is:

cos ([tex]\frac{x}{2}[/tex]) - sin (x) = 0

⇒ cos ([tex]\frac{x}{2}[/tex]) - 2sin ([tex]\frac{x}{2}[/tex]) cos ([tex]\frac{x}{2}[/tex]) = 0

⇒ cos ([tex]\frac{x}{2}[/tex]) [1 - 2sin ([tex]\frac{x}{2}[/tex])] = 0

Therefore,  cos ([tex]\frac{x}{2}[/tex]) = 0 = cos (90°)  ([tex]\frac{x}{2}[/tex] can't be 270°)

⇒ x = 180°

Again,  [1 - 2sin ([tex]\frac{x}{2}[/tex])] = 0

⇒ 2sin ([tex]\frac{x}{2}[/tex]) = 1

⇒ sin ([tex]\frac{x}{2}[/tex]) = 1/2

⇒ ([tex]\frac{x}{2}[/tex]) = 30°, 150°

⇒ x = 60°, 300°

So, The solutions of the given trigonometric equation are 60°, 180°, and 300°.

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