Rearrange the equation so nnn is the independent variable. m + 1=-2(n + 6).

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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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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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:

Step-by-step explanation:

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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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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Answer:

  See attached

Step-by-step explanation:

You want to know which of the graphed relations shows a function.

The graph of a function will not intersect any vertical line in more than one place. A graph that has multiple values for any given x-value is not a graph of a function.

The attachment shows the one graph here that represents a function.

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[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 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 multiplied form of the expression 5abc⁵⋅3a²b³ is 15 a³b⁴c⁵.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given expression is,

5abc⁵⋅3a²b³.

To multiply the given expression,

Use multiplication mathematical operation,

15abc⁵.a²b³

15 a³b⁴c⁵

The required expression is 15 a³b⁴c⁵.

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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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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 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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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 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:

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

On solving the provided question, we can say that - the slope we have from the graph is [tex]m = \frac{y2 - y1}{x2 - x1}[/tex] +. m= 2

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

By the graph;

[tex](x1,x2) = (0,0)\\(y1,y2)=(2,1)[/tex]

[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

m= 2

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Answer:

need more in fo

Step-by-step explanation:

The height of the tree is 1.9 meters

From the question, we have the following parameters that can be used in our computation:

The height of the tree can then be calculated using the following ratio expression

Tree's height : Caden's height = Caden's distance from the tree : Caden's distance from Nova

Substitute the known values in the above equation, so, we have the following representation

Tree's height : 1.2 = 6.5 : 4.2

Express as fraction

Tree's height/1.2 = 6.5/4.2

So, we have

Tree's height = 1.2 * 6.5/4.2

Evaluate

Tree's height = 1.9

Hence, the tree's height is 1.9 meters

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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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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

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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[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])

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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Answer:

22

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

d. positive or negative square root of 2 comma ±

The zeros of the function f(x) = x4 − 4x2 − 5 are the values of x that make the equation equal to 0. To find these, we must solve the equation f(x) = 0. We can do this by factoring the equation to give (x2 + 5)(x2 − 2) = 0. This gives us the solutions x2 = −5 and x2 = 2. From this, we can find the zeros of the function, which are ±√2 and ±i. Therefore, the zeros of the function f(x) = x4 − 4x2 − 5 are positive or negative square root of 2 comma ±i.

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The corresponding angles and sides of the two triangles need to be given in order to prove congruence by side-angle-side.

In order to prove congruence by side-angle-side, the corresponding angles and sides of the two triangles must be given. The sides must be proportional, which means that two sides of one triangle must be equal to two sides of the other triangle, and the angles between these two sides must also be equal. In other words, if two sides of one triangle are equal to two sides of the other triangle, and the angle between those two sides is also equal, then the two triangles are congruent. This can be expressed as “If two sides and the included angle of one triangle are equal to the corresponding sides and angle of a second triangle, then the two triangles are congruent.” In order to prove congruence by side-angle-side, all of the corresponding sides and angles must be given in order to show that they are equal.

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The additional information that is needed to prove the triangles are congruent by Side-Angle -Side us that the corresponding angles and sides of the two triangles need to be given .

What is Side-Angle-Side Congruence ?

The Two Triangles can be called as  Congruent by Side-Angle-Side rule  if any 2 sides and angle included between sides of one triangle is equivalent to corresponding 2 sides and angle between sides of second triangle .

In order to prove the Congruence by Side-Angle-Side, the corresponding angles and the sides of the 2 triangles must be given.

The sides must also be in proportional, that means that the two sides of one triangle must be equal to two sides of other triangle, and

the angles between these two sides of the triangle must  be equal.

So , In order to prove a triangle congruent by Side-Angle-Side, all of the corresponding sides and angles must be given in order to prove  that they are equal.

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According to the Inequalities  the prices for a single chair and a single table:

B. Chair: $22, Table: $60

The correct option is B.

Inequalities specify the relationship between two different values. Not equal is the definition of inequality. In most cases, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are employed to compare the values, whether is less than or more than.

8c + 3t> $350

2c + 5t < $350

Putting the value in the equation:

8c + 3t> $350

8×22 + 3×60> $350

176 + 180 > 350

356 > 350

2c + 5t < $350 equation 2

2 × 22 + 5 × 60 < $350

44 + 300 < 350

344 < 350

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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)

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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