describe the transformation of f(x) = sin x to g(x) = sin (x - pi/3)

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

c = 3

Step-by-step explanation:

\( 32^{2c} = 8^{c + 7} \)

\( (2^5)^{2c} = (2^3)^{c + 7} \)

\( 2^{10c} = 2^{3c + 21} \)

\( 10c = 3c + 21 \)

\( 7c = 21 \)

\( c = 3 \)

Answer:10−45

Step-by-step explanation: if you actually saw it then you will get that answer

Answer: 26.4

Step-by-step explanation: 1.2x22=

Answer:

hello some information is missing below is the missing information

8 classes for n = 75 measurements; minimum value = 20; maximum value = 175

answer : width = 20

               class boundary : 20,40,60,80,100,120,140,160,180

Step-by-step explanation:

Using the information given the convenient class width

= (maximum value - minimum value) / number of class

= ( 175 - 20 ) / 8

= 155 / 8 = 19.375 to the nearest multiple of 5 =  20

Using the minimum value as the smallest class boundary

the class boundary will be :

20,40,60,80,100,120,140,160,180

since the maximum value 175

Answer:No. A strong correlation does not imply causation.

Step-by-step explanation:

Cause and effect relationship is not explained by correlations. A cause and effect relationship can only be established by carrying out carefully controlled experiments.

Hence, a strong correlation between the the intake of soda and accidents does not necessarily imply that soda intake causes accident.

A lurking variable in this study may be the speed of the drivers. A lurking variable is not controlled but significantly impacts results obtained from the study.

Since the speed of the drivers is not strictly controlled, it may just be a lurking variable.

The statement is always true. When reflected, each point of original figure is mapped to corresponding point on reflection, such that the line connecting each point and its corresponding point is perpendicular to line of reflection.

The adage is always accurate. Each point on the original figure is mapped to a corresponding position on the reflection when a figure is reflected, with the result that the line connecting each point to its corresponding point is perpendicular to the line of reflection. This essential characteristic of reflections can be demonstrated using simple geometry.

Consider a line of reflection and a point P on the original figure to understand why this is the case. Let P' represent P's reflected image. We know that PP' is perpendicular to the line of reflection because the line of reflection is the perpendicular bisector of the line segment connecting P and P'. The resulting segments are all perpendicular to the line of reflection because this is true for every point on the original figure and its corresponding point on the reflection.

This reflection characteristic has numerous practical uses, not just in mathematics. When designing optical components like mirrors and lenses, for instance, where the direction of reflected or refracted light is important, this technique is applied. Furthermore, reflections are frequently utilised in geometric proofs and constructions, where they can make complex issues easier to understand by reducing them to more straightforward, symmetric situations.

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Step-by-step explanation:

-63x-56y=10

-56y=10+63x

y= 10+63x/-56

The area of the pool given by the expression, ∆ × 102 + ∆ × 101 + 6, gives;

A) The whole number x = 33

B) The perfect square number closest to 33 is 36

The side length of a square pool with an area of 36 square units is 6 units

C) The side length of a square pool with the area chosen in part A is 33•√33

An expression is a mathematical statement which consists of 2 or more numbers and, or variables joined together by mathematical operators.

A) The given equations for the pool is presented as follows;

Area of the pool = ∆ × 102 + ∆ × 101 + 6

Area of the pool = x³

x = A whole number

Expressing the word problem mathematically gives;

∆ × 102 + ∆ × 101 + 6 = x³

203•∆ + 6 = x³

Which gives;

\( \displaystyle{ \triangle = \frac{ {x}^{3} - 6}{203} }\)

Using a graphing calculator, when x = 33, we get;

\( \displaystyle{ \triangle = \frac{ {33}^{3} - 6}{203} = 177 }\)

The value of the number is x = 33 and ∆ = 177

B) The perfect square that is closest to x = 33 is 36

The side length of a square pool with an area of 36 is √(36) = 6

C).The area of the pool chosen is 33³ = 35937

The side length of a square pool with an area of 35937 is √(35937) = 33•√(33)

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SOLUTION

Given the data in the table below, we are to write the best equation that fits the data in the table in the form,

We will be resolving it using the graphical method,

Therefore, the graph is shown below:

From the graph above,

Therefore, the equation is

Final answers

The notation is

The function notation is

Answer:

D) A search warrant

Step-by-step explanation:

A search warrant is required before the search and collection of evidence to ensure legal authorization and protection of individuals' rights against unreasonable searches and seizures.

Option B, "A crime", is incorrect because the presence of a crime is not a prerequisite for conducting a search and collection of evidence. There are various situations where searches and evidence collection may occur without a crime being involved, such as regulatory inspections, consented searches, or investigations into potential threats or risks.

By your logic when you say law enforcement can conduct a search without a search warrant if there is consent by the owner, that would mean option A would be right, but of course, it's not.

Answer: invinitely many solutions to answer the question you have asked... ( I think this is correct).

Step-by-step explanation: 2x you want to be alone. X-15/2=7. 15/2 you want to divide this and then add to 7 makes 14.5. X=14.5

Or you can not divide and leave it as x= -7+15/2

Answer:

Hi

Please mark brainliest ❣️

Answer:

9.7

Step-by-step explanation:

97/10= 9.7

formula for rectangle= length x width

area divided by width= 97/10

97/10=9.7

length=9.7

9.7x10=97

Answer: n>5

Step-by-step explanation:

Answer:

ok so each 1/3 centimeter is 9 meters

1/3 goes into 4 2/3 =14

so we multiply 14*9=126

so 126 meters or j

Hope This Helps!!!

Answer:

J. 126

Step-by-step explanation:

To answer this it is basically like direct proportion so

\(\frac{1}{3} cm= 9m\)

You make the mixed numeral into an improper fraction (multiply the denominator with the big number and then add the numerator):

\(4\frac{2}{3} =\frac{14}{3}\)

To find the hallway of finished building in metres you divide the blueprint's measurement with the representative measurement (sorry if it is not clear)

\(\frac{14}{3}\)÷\(\frac{1}{3}\)\(= 14\)

Then you times 14 with 9m, which gives:

9 × 14 = 126m

So the answer is J

Hope it is right, feel free to ask anything you are unsure about :]

Answer:

7

Step-by-step explanation:

The format for a coordinate pair is (x-coordinate, y-coordinate). This means the y-coordinate comes second, and since the 7 comes second here we can say that 7 is the y-coordinate.

That is the answer

- Kan Academy Advance

Answer:

(C) Multiply first equation by -2 and second equation by 3, solution (1, 1)

Step-by-step explanation:

Simultaneous equations are set of equations which possess a common solution. The equations can be solved by eliminating one of the unknowns by multiplying each of the equations in a way that a common coefficient is obtained in the unknown to be eliminated.

Given the simultaneous equations:

3x - 5y = -2

2x + y = 3

First step:

Multiply first equation by -2 and multiply second equation by 3,

-6x + 10y = 4

6x + 3y = 9

Second step:

Add the two equations together,

13y = 13

Divide both sides by 13

y = 1

Third step:

Put y = 1 in the first equation

3x - 5(1) = -2

3x - 5 = -2

3x = 5 - 2

3x = 3

Divide both sides by 3:

x = 1

solution (x,y) = (1,1)

Option C

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We know that the sum of the angles of a triangle must be 180°. Let's call the first, second, and third angles A, B, and C respectively. Therefore, we have as follows:

Therefore, we can now replace the equation that stated the sum and find the value of A as follows:

Now that we have the measure of angle A, we can find the other two, as follows:

Therefore, the first angle measures 44°, the second one 48°, and the third one 88°. We can verify if it is correct by making sure that the sum is 180.

The required algebraic expression that represents the perimeter of the dining room table is 8w - 4.

Perimeter is the measure of the figure on its circumference.

Here,
The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Substituting the given expressions for the length and width of the dining room table, we get:

P = 2(3w - 2) + 2w

Simplifying the expression, we get:

P = 6w - 4 + 2w

Combining like terms, we get:

P = 8w - 4

Therefore, the algebraic expression that represents the perimeter of the dining room table is 8w - 4.

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Answer:

150

Step-by-step explanation:

Because I looked it up

Answer:

4.9 in

Step-by-step explanation:

6/11 = x/9

6/11 times 9 = x

x = 4.9

Answer:

w = 18

Step-by-step explanation:

Step 0: Set up the equation

=> -3w - 4 + 5w = 32

Step 1: Move the same variable together

=> -3w + 5w = 32 + 4

Step 2: Add up and simplify

=> 2w = 36

Step 3: Divide both by 2

=> w = 18

Answer:

W=18

Step-by-step explanation:

-3w-4+5w=32

-3w+5w-4=32

2w-4=32

2w=32+4

2w=36

W=18

The probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (u) is 47 words per minute and the standard deviation (o) is 4 words per minute is; 68%

The empirical rule in statistics states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

x' = 51

μ = 47

σ = 4

Thus;

z = (51 - 47)/4

z = 1

From empirical formula at 1 standard deviation above the means, the probability is 68%.

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Answer:

7

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³