For a project in her Geometry class, Chloe uses a mirror on the ground to measure the height of her school’s flagpole. She walks a distance of 8.85 meters from the flagpole, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.1 meters to the other side of the mirror, until she can see the top of the flagpole clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the flagpole? Round your answer to the nearest hundredth of a meter.

Step-by-step explanation:

yes, they are, because both triangles have the same 3 angles :

the right angle = 90°

65°

25°

now, the side lengths can be different, but because of the same angles, the ratio between the corresponding side lengths will be the same for all sides (e.g. if one pair of sides has the scaling factor of 3 from the smaller to the larger triangle, then the other pairs will also have the same scaling factor 3).

that is the difference between equivalent and similar : for "equivalent" also the side lengths must be the same.

for "similar" only the angles need to be the same.

One centimeters is equal to 0.01 meters. Centimeter (cm) and meter (m) are both units of length in the International System of Units (SI).

One centimeter is equal to 0.01 meters.

This can be derived by using the conversion factor that 1 meter is equal to 100 centimeters:

1 meter = 100 centimeters

Dividing both sides by 100, we get:

1 centimeter = 1/100 meters

Simplifying this, we get:

1 centimeter = 0.01 meters

Therefore, one centimeter is equal to 0.01 meters.

A centimetre is a metric length unit that equals one tenth of a metre. It is typically used to measure short distances, such as an object's length or width, or a person's height.

A metre, on the other hand, is the SI system's base unit of length and is defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second. Larger distances, such as the length of a room, a building, or a road, are measured with it.

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The following formula is used for conversion of amu to kg:

1 amu = 1.66054 x [tex]10^{-27}[/tex]kg

The atomic mass unit (amu) is a unit of mass used in chemistry and physics to express the masses of atoms and molecules, whereas the kilogramme (kg) is the International System of Units' basic unit of mass (SI). We may use the following relationship to convert from amu to kg:

1.66054 x  [tex]10^{-27}[/tex]kg = 1 amu

To convert a mass from amu to kg, multiply the mass in amu by 1.66054 x [tex]10^{-27}[/tex]. For instance, if we have a mass of 10 amu, we may convert it to kg using the formula:

10 amu x 1.66054 [tex]10^{-27}[/tex] kg/amu = 1.66054 [tex]10^{-26}[/tex] kg.

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We can estimate that about 98 million more megawatt hours were generated from wind in 2020 than in 2016.

What is Division?

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse operation of multiplication and is represented using the division symbol ÷ or the forward slash /.

Solution:

To estimate how many more megawatt hours were generated from wind in 2020 than in 2016, we need to make some assumptions and approximations since the problem only provides data for 2009 and 2017.

Assuming that the wind energy generation continued to increase at the same constant rate between 2017 and 2020, we can estimate the amount of wind energy generated in 2020 as follows:

1. From 2009 to 2017, the wind energy generation increased by 254 million - 74 million = 180 million megawatt hours.

2. The time period between 2009 and 2017 is 8 years, so the average annual increase in wind energy generation is 180 million / 8 years = 22.5 million megawatt hours per year.

3. Therefore, we can estimate the wind energy generation in 2020 as 254 million + 3 years x 22.5 million = 322.5 million megawatt hours.

4. Similarly, we can estimate the wind energy generation in 2016 as 74 million + 7 years x 22.5 million = 224.5 million megawatt hours.

5. The difference in wind energy generation between 2020 and 2016 is then:

322.5 million - 224.5 million = 98 million megawatt hours.

Therefore, we can estimate that about 98 million more megawatt hours were generated from wind in 2020 than in 2016.

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Trigonometric functions derivative is a method for calculating how quickly trigonometric functions change in relation to a variable angle.

Differentiation of trigonometric functions refers to the process of determining a trigonometric function's derivatives. In other words, finding the rate of change of the function with respect to the variable is what is meant by the differentiation of trigonometric functions. There are differentiation formulas for the six trigonometric functions that can be applied to a variety of derivative application issues.

The sine (sin x), cosine (cos x), tangent (tan x), cotangent (cot x), secant (sec x), and cosecant are the six fundamental trigonometric functions (cosec x).

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The equivalent expression is 0.7 - 1.8h.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2.1 + (-3.7h) + 1.9h - 1.4

Combine the like terms.

2.1 - 1.4 - 3.7h + 1.9h

0.7 - 1.8h

Thus,

0.7 - 1.8h is the equivalent expression.

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Answer:

36

Step-by-step explanation:

We know that a statistical technique that allows a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is known as the Factor analysis.

Factor analysis is most likely a statistical procedure that identifies clusters of related items also known as factors which are on a test; used to identify different dimensions of performance that underlie one's total score.

We can say that factor analysis is more like a technique which is used in mathematics for reducing a larger number into a smaller number.

In other words, its a method for reducing a large variable into a smaller variable factor also this technique takes out the maximum ordinary variance from all of the variables and then puts them in the common score.

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The 3rd term of the geometric sequence is 6.

In mathematics, an equation is a statement that two expressions are equal. It usually contains one or more variables, which are unknown quantities that can take on different values. Equations are used to represent relationships between quantities, and they can be used to solve problems by finding the values of the variables that make the equation true.

An equation typically consists of two sides, separated by an equal sign. Each side can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. For example, the equation:

2x + 3 = 7

contains the variable x, as well as constants 2, 3, and 7, and mathematical operations of addition and multiplication.

Equations can be solved by applying algebraic techniques to isolate the variable on one side of the equation. For example, to solve the above equation for x, we can first subtract 3 from both sides to get:

2x = 4

Then, we can divide both sides by 2 to get

x = 2

This is the solution to the equation, which means that x must be equal to 2 in order to make the equation true.

Equations are used in many areas of mathematics, including algebra, calculus, geometry, and trigonometry. They are also used in physics, engineering, and other sciences to model physical phenomena and solve problems related to them.

Let's call the first term of the geometric sequence "a" and the common ratio "r".

The formula for the nth term of a geometric sequence is:

an = a *[tex]r^(n-1)[/tex]

We are given that the 2nd term is 2, so we know that:

a * r = 2 --(1)

We are also given that the 5th term is 432, so we know that:

a * [tex]r^4[/tex] = 432 --(2)

Now we need to solve for "a" and "r" in order to find the 3rd term.

First, let's solve equation (1) for "a":

a = 2 / r

Now we can substitute this expression for "a" into equation (2):

(2/r) *[tex]r^4[/tex]= 432

Simplifying, we get:

[tex]r^3[/tex]= 54

Taking the cube root of both sides, we get:

r = 3

Now we can substitute this value for "r" back into equation (1) to solve for "a":

a * 3 = 2

a = 2/3

So the first term of the sequence is 2/3 and the common ratio is 3.

Now we can use the formula for the 3rd term of a geometric sequence:

a3 = a * [tex]r^(3-1)[/tex]

a3 = (2/3) *[tex]3^2[/tex]

a3 = (2/3) * 9

a3 = 6

Therefore, the 3rd term of the geometric sequence is 6.

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300 kilogrammes is equal to about 661.39 pounds.

Weight = mass x gravity is the formula for relating mass and weight.

Such equation is known as Newton's Second Law of Motion.

The Latin word "libra," which means balance and weight, is where the name "pound sterling" comes from.

In Newtons, N, force (or weight) is measured.

the mass is measured in kilograms, kg.

You can use the conversion factor 1 kg = 2.20462 pounds to change kilogrammes to pounds.

Thus, 300 kg divided by 2.20462 pounds per kilogramme results in:

300 kg times 2.20462 pounds/kg equals 661.386 pounds (rounded to three decimal places).

300 kilogrammes is equal to about 661.39 pounds.

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2.75 can be written as a fraction in lowest terms as 11/4.

To convert a decimal like 2.75 to a fraction, we can follow these steps:

Step 1: Write the decimal as a fraction with the decimal as the numerator and 1 as the denominator.

In this case, we can write 2.75 as a fraction with a denominator of 1:

= 2.75/1

Step 2: Multiply the numerator and denominator of the fraction by 10 until the decimal is gone.

We can remove the decimal by multiplying both the numerator and denominator by 100 (since there are two decimal places):

2.75/1 x 100/100 = 275/100

Step 3: Simplify the fraction.

We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 25 in this case:

275/100 ÷ 25/25 = 11/4

Therefore, the fraction is 11/4

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Answer:

The rate of change between two points is the difference in the y-coordinates divided by the difference in the x-coordinates.

Let's call the first point (-4, 1/2) Point 1, and the second point (1, -1) Point 2.

The difference in the y-coordinates is:

-1 - 1/2 = -3/2

The difference in the x-coordinates is:

1 - (-4) = 1 + 4 = 5

So, the rate of change between the two points is:

(-3/2) / 5 = -3/10

Therefore, the rate of change between Point 1 and Point 2 is -3/10.

Step-by-step explanation:

espero te ayude

The average rate of change of the cost from the 6th month to the 8th month is 1.

Rate of change is a major of house quickly one quantity change in relation to another it is parisu of the changing 122 the changing another quantity over specified time period.


The average rate of change from the 6th month to the 8th month can be calculated by taking the difference between the 6th and 8th month's cost and dividing it by the number of months between the two. In this case, the difference is 8.5 - 6.5 = 2, and the number of months is 2, so the average rate of change is 2/2 = 1. Therefore, the average rate of change of the cost from the 6th month to the 8th month is 1.

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Step-by-step explanation:

This is the correct answer

Answer:

Step-by-step explanation:

Applying the distance formula, we get that the distance is sqrt(14^2+(-3)^2)=sqrt(205), which is approximately 14.3178211. Rounding to the nearest tenth, we get that the distance is 14.3 units long.

Inverse trigonometric integrals involve inverse trigonometric functions and are used to evaluate integrals containing trigonometric functions and their derivatives

Inverse trigonometric integrals are a group of integrals that include inverse trigonometric functions like arcsine, arccosine, and arctangent. These functions are utilized to assess integrals that include expressions containing trigonometric functions and their derivatives.

Inverse trigonometric functions are the Inverse of their respective trigonometric functions and can be utilized to find the point that compares to a given ratio of sides in a right triangle. Inverse trigonometric integrals are generally experienced in analytics and are helpful in different fields like physics, engineering, and statistics. They are ordinarily assessed utilizing algebraic manipulation, substitution, and integration by parts

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The length of the diagonal is 5 in. The solution has been obtained by using the pythagoras theorem.

What is Pythagoras theorem?

The Pythagorean Theorem states that the square of the hypotenuse side of a right-angled triangle is equal to the sum of the squares of its other two sides.

We are given that the figure is a 12 in by 12 in square.

So, the lengths of the triangle come out to be 3 and 4.

Now, using the pythagoras theorem,

⇒Hypotenuse² = 3² + 4²

⇒Hypotenuse² = 9 + 16

⇒Hypotenuse² = 25

⇒Hypotenuse = 5

Hence, the length of the diagonal is 5 in.

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When x = 6 and y = -4, the value of of the expression 50-3(x²-y²)+x is -4.

An algebraic expression is when we use numbers and words in solving a particular mathematical question.  The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Substitute x=6 and y=-4 into the expression 50-3(x²-y²)+x:

50 - 3(6² - (-4)²) + 6

= 50 - 3(36 - 16) + 6

= 50 - 3(20) + 6

= 50 - 60 + 6

= -4

Hence, when x = 6 and y = -4, the value of 50-3(x²-y²)+x is -4.

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The area of the shaded sector is given as follows:

24π cm².

The length of the arc is given as follows:

2π.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The radius is the distance of the center of the circle to a point on the circumference of the circle, hence:

r = 12.

The entire area has an angle measure of 360º, hence the area of the sector with a central angle of 60º is given as follows:

A = 60/360 x π x 12²

A = 24π cm².

The circumference of a circle is given as follows:

C = 2πr.

Hence the length of the arc is given as follows:

C = 2 x 60/360 x π x 6

C = 2π.

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Answer:

7:a

Step-by-step explanation:

-15:-2a+9-a-3

-15:-3a+9-3

-15:-3a+6

-15-6:-3a

-21:-3a

Minus sign with be cancelled by each other

21:3a

21/3:a

7:a

Answer:

f(n)= f( n-1 ) + 6

The Inverse tangent is defined as the mathematical function that returns the angle whose tangent is a given number and the step to calculate the inverse tangent has been explained

Inverse tangent (also known as arctangent) is a mathematical function that returns the angle whose tangent is a given number. The inverse tangent function is denoted by "tan^-1" or "arctan".

To calculate the inverse tangent of a number, you can follow these steps:

Determine the input value (the number whose inverse tangent you want to find).

Use the inverse tangent function on your calculator.

The output of the inverse tangent function will be in radians. If you want the result in degrees, you can convert it using the formula: degrees = radians * (180/π), where π (pi) is approximately 3.14159

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Answer: $725

Step-by-step explanation:

100%-28%=72%

$522/72=7.25

7.25*100%=$725

To check the answer $725-28% (discount)=$203

$725 (yesterday price) - $203 (discount) = $522 (price today)

the total area available for the design on the soapbox car should be 636 inches² (square inches).

The correct calculations for the area of each side are:

Area of the first side = 6 inches x 54 inches

= 324 square inches

Area of the second side = 54 inches x 14 inches

= 756 square inches

Area of the third side = 14 inches x 24 inches

= 336 square inches

Area of the fourth side = 24 inches x 6 inches

= 144 square inches

To get the total area available for the design, we need to subtract the area of the top and bottom of the soapbox car, which are not included in the original measurements. If we assume the top and bottom are each rectangular and have the same dimensions as the first and third sides, we can calculate their total area as:

Area of the top = 6 inches x 54 inches

= 324 square inches

Area of the bottom = 6 inches x 54 inches

= 324 square inches

Total area of the top and bottom = 324 + 324

= 648 square inches

Finally, we can subtract the area of the top and bottom from the total area of the four sides to get the area available for the design:

Total area available for the design = (324 + 756 + 336 + 144) - 648

= 636 square inches.

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The converted value representing in grams and ounce is given by 30 grams is equal to 1.05822 ounce.

Conversion factor representing the relation between ounce and grams is given by :

28 grams equal to one ounce

Substitute the required grams value to be converted into ounce we have,

⇒ 28 grams = 1 ounce

⇒ 1gram = ( 1 / 28 ) ounce

⇒ 30 gram = ( 30 ) × ( 1 / 28 ) ounce

⇒ 30 gram =  ( 1.05822 ) ounce

Therefore, the value after conversion grams into ounce is given by            30 gram =  ( 1.05822 ) ounce .

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The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

What is an angle of depression?

If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle formed between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.

There is an angle of elevation from point R to S. Thus point R is lie above S.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

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The y-coordinate for the solution to the system of equations is 6.

Equation is a physical and mathematical statement the describing physical phenomenon the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable maybe pointed search is the energy.

The y-coordinate for the solution to the system of equations is 6. This is calculated by substituting the given y-value (2/3) into the equation -x+3y=9 and solving for x. Specifically, -x+3(2/3) = 9, which reduces to -x = 3. Therefore, x = -3 and substituting this value into the first equation yields 3y = 9, which simplifies to y = 3. Therefore, the y-coordinate for the solution to the system of equations is 6.

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Answer:

The rate of change between (-2/3, -4) and (-3, 4) is:

(change in y) / (change in x) = (4 - (-4)) / (-3 - (-2/3))

= 8 / (-2/3)

= -12

Therefore, the rate of change is -12.

Step-by-step explanation:

=]

The correct that represents the total amount of popcorn, in quarts, produced by x scoops of unpopped kernels

If 3 scoops of unpopped kernels produce 6 quarts of popcorn, we can find the rate of popcorn produced per scoop by dividing the total popcorn by the number of scoops:

6 quarts popcorn / 3 scoops = 2 quarts popcorn per scoop

We can use this rate to fill out the table for any number of scoops:

Number of scoops      Total amount of popcorn (in quarts)

1                                                             2

2                                                            4

3                                                            6

4                                                            8

5                                                            10

...                                                            ...

x                                                            2x

Therefore, the correct table that represents the total amount of popcorn, in quarts, produced by x scoops of unpopped kernels is:

Number of scoops    Total amount of popcorn (in quarts)

1                                                     2

2                                                    4

3                                                    6

4                                                    8

5                                                     10

...                                                     ...

x                                                      2x

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The wax cost to cover the floor is $1,569.75.

The correct option is B.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

Given:

A maintenance worker needs to wax a restaurant floor shaped like the image shown.

A six-sided figure.

There is a horizontal base of 35 feet then another horizontal base below it of 20 feet.

The longest side is to the right and is 40 feet.

The top is 30 feet.

There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet.

The total area of the composite figure is,

= (15 x10) + (20 x 40) + (1/2 x 25 x 15)

= 1137.5 square feet.

If the wax cost $1.38 a square foot,

the cost is,
= 1137.5 x 1.38

= $1569.75

Therefore, the total cost is $1569.75.

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