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Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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Yes, the selling price of an item is a function of the cost of making the item.

A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.

Cost is often the expenditure incurred for producing a product or service that a firm sells. The selling price is the amount paid by the buyer to purchase a product or products.

The selling price of an item is a function of the cost of creating the item since the manufacturer must sell at a price higher than the cost of making the item in order to recoup his investment and make a profit.

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The equation that represent the proportional relationship is t = 2 / 5 H.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x if:  

y = kx

for some constant k , called the constant of proportionality .

The equation that represent the proportional relationship can be represented as follows:

t = KH

using

t = 2

H = 5

Hence,

2 = 5k

k = 2 / 5

Therefore,

t = 2 / 5 H

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Option D. The statement that is true from the equations that we have here is D. The equation x3 - x2 - x + 1 = 0 is equivalent to the equation x2(x - 1)-(x-1)=0.

I will have to start for the equation D, because at close glance we can easily see that the powers would be equal

The equation x3 - x2 - x + 1 = 0 is equivalent to the equation x2(x - 1)-(x-1)=0.

We are to simplify x²(x - 1)-(x-1)

we would have to open the brackets from the above

 x² * x +  x² * (-1) - x - (-1) = 0

It would be important to pay attention at the signs

such that we would have

x³ -  x² - x + 1 = 0

Therefore the equation  x^3 - x^2 - x + 1 = 0 is equivalent or equal to  x³ -  x² - x + 1 = 0 because they have the same solution

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The number of bags of popcorn = 6

The number of pretzels  = 4

Let the number of bags of popcorn = x

the number of pretzels = y

From the question, we have

she bought $60 worth of bags of popcorn and pretzels.

Each bag of popcorn costs $7.50 and each pretzel costs $3.75.

7.50x+3.75y = 60................(i)

She bought 2 more bags of popcorn than pretzels.

x-y = 2................(ii)

Solving equation (i) and (ii), we get

x = 6

y = 4

The number of bags of popcorn = 6

The the number of pretzels  = 4

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

The expression of 602.16 dam in decimeters can be written as 60216 decimeter.

The concept that will be used in the calculation is conversion. to perform this conversion, it is important to note that 1 Decimeter (dm) is equal to 0.01 dekameter (dam).

Then, if 1dm = 0.01 dam

               Xdm     = 602.16 dam

Where x is the value in decimeter.

Then we can cross multiply as :

X= (602.16 dam * 1dm)/ 0.01 dam

= 60216 decimeter.

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Loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

When energy moves through a medium (such as air, water, or any other liquid or solid matter), it creates a pattern of disturbance known as a sound wave that propagates away from the sound source.

When an object vibrates, sound waves are produced that are similar to pressure waves, like when a phone rings.

Pitch, intensity, and timbre are three key components of the field of sound psychology or psychoacoustics. People can distinguish the harmonics of a complex periodic sound wave under certain conditions thanks to the way that humans perceive sound and music.

Thus, loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

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sin(x+5pi/4) sin(x+5pi/4) in terms of sin(x) and cos(x) can be rewritten as cos (x) . sin [tex](\frac{x + 5\pi }{4} )[/tex] .sin (x)

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles

Let find the common multiplier of sin

[tex](\frac{x + 5\pi }{4} )[/tex]sin (x), cos(x); cos (x) sin[tex](\frac{x + 5\pi }{4} )\\[/tex] sin (x)

Find the least common Multiplier of sin [tex](\frac{x + 5\pi }{4} )[/tex] sin (x) , cos (x)

Lowest common multiplier (LCM)

The LCM of a, b is the smallest multiplier that is divisible by both a and b

Factor sin [tex](\frac{x + 5\pi }{4 } )[/tex]sin ( x)

sin[tex]( \frac{x + 5\pi }{4} )[/tex]. sin(x)

Multiplier each factor with the highest power;

cos (x) .sin [tex](\frac{x + 5\pi }{4} )[/tex].sin (x)

Therefore, the trigonometry sin(x+5pi/4) in terms of sin(x) and cos(x) can be rewritten as cos (x) . sin [tex](\frac{x + 5\pi }{4} )[/tex] .sin (x)

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Answer:

The distance between these two points with coordinates (-1, -4) and (-9, -8) is 8.94 unites

Answer:

HNO3. AND H3O

Step-by-step explanation:

BECAUSE THE TWO OF THEN GIVE AN (H) to the base

Answer:

12

Step-by-step explanation:

36 / (x - 3) = 4

multiply both sides by (x - 3):

(x - 3)(36 / (x - 3)) = 4(x - 3)

36 = 4(x - 3)

expand right side:

36 = 4x - 12

add 12 to both sides:

36 + 12 = 4x - 12 + 12

48 = 4x

divide both sides by 4:

48/4 = 4x/4

x = 12

Answer:

the answer is 12

explanation 12x12= 144

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The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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The simplification form of the expression √5 + √5 is 2√5 after adding like terms.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

The number expression is:

√5 + √5

After adding like terms:

2√5

The question is:

Solve the expression:

√5 + √5

Thus, the simplification form of the expression √5 + √5 is 2√5 after adding like terms.

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The number of men and women that work at the company are;

Number of men = 36

Number of women = 18

Let the total number of employees in the company be x.

Now, we are told that 75% of the employees were men. Thus;

Number of men = 75% * x = 0.75x

Number of women = 0.25x

Now, we are told that after 6 women joined, the ratio of men to women became 2: 1.

Thus;

New total employees = x + 6

New total number of women = 0.25x + 6

Thus;

0.75x/(0.25x + 6) = 2/1

Cross multiply to get;

0.75x = 2(0.25x + 6)

0.75x = 0.5x + 12

0.75x - 0.5x = 12

0.25x = 12

x = 12/0.25

x = 48

Number of women = 0.25(48) + 6 = 18

Number of men = (48 + 6) - 18 = 36

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The rooms which the three artists Richard, Allan and Shelby will work together are room 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 making a total of 10 rooms.

Find the multiples of 3 and 5

The common multiples of 3 and 5 are; 15, 30, 45, 60, 75, 90, 105, 120, 135, 150

Each common multiple represent a room

= 10 rooms

Therefore, the rooms which the three artist will work together is 10 rooms

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Answer:

(2,-1)

Step-by-step explanation:

Given system of equations:

We are going to use the substitution method.

Step 1: Solve for x = y + 3 for x:
(Substitute y + 3 for x in 3x + 2y = 4)

3x+2y=4

3(y+3)+2y=4

5y + 9 = 4 ----> Simplify both sides of the equation

5y+9+−9=4+−9  -------> Add -9 to both sides

5y=−5

5y5 = -5/5  ------> Divide both sides by 5

y = −1

Step 1: Substitute -1 for y in x = y + 3:

x = y + 3

x = -1 + 3

x = 2 --------> (Simplify both sides of the equation)

Answer:

(2,-1)

Answer:

8p^6q^4

6qp-7

Step-by-step explanation:

The slope of the normal line is proved to be -1/m using tangent

Slope is similar to tangent and sometimes used interchangeably

assuming two lines of slope m and m', the angle between the two lines is x

tan x =  (m - m') / (1 + mm')

for a normal line x = 90

tan 90 =  (m - m') / (1 + mm')

tan 90 is ∞ = 1 / 0

1 / 0 =  (m - m') / (1 + mm')

cross multiplying

1 * (1 + mm') =  0 *  (m - m')

1 + mm' = 0

mm' = -1

m = -1/m'

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Answer:

the son age is 13band Evans age is 52 years old at present day

Dan is 12 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the Age of Dan is x years

Mr. Evans Age = 4x

If Mr. Evans was 46 years old 2 years ago

The, Present age of Mr. Evans = 48 years

So, Dan's Age = 48/4

                        = 12 years.

Hence, Dan is 12 years old.

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[tex]f'(x)=\frac{1}{\sqrt{1-(-4x^{2} + 3)^{4})^2} } 4.(-4x^2+3)^{3}[/tex] is differentiation of   [tex]f(x)=sin^{-1}(-4x^{2} + 3)^{4}[/tex]

A differential equation is an equation that contains one or more functions with its derivatives.

The given function is [tex]f(x)=sin^{-1}(-4x^{2} + 3)^{4}[/tex]

By using chain rule we differentiated the function.

d/dx sin⁻¹x=1/√1-x²

[tex]f'(x)=\frac{1}{\sqrt{1-(-4x^{2} + 3)^{4})^2} } 4.(-4x^2+3)^{3}[/tex]

Hence,[tex]f'(x)=\frac{1}{\sqrt{1-(-4x^{2} + 3)^{4})^2} } 4.(-4x^2+3)^{3}[/tex] is differentiation of  [tex]f(x)=sin^{-1}(-4x^{2} + 3)^{4}[/tex]

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a) 7y and (2y²-9) are the length and width expressions where one dimension is the GCF.

b) When y= 2, the area of the rectangle is -14

The area amount expresses the size of a region on a planar or curved surface.

A two-dimensional figure's area is the amount of space it occupies. It is the number of unit squares that cover the surface of a closed figure in other words. Square units, which are frequently expressed as square inches, square feet, and so on, are the standard unit of area.

A rectangle is a two-dimensional figure, and if one of the dimensions is the GCF, as indicated in the job, then:

7y and (2y²-9) are the length and width expressions where one dimension is the GCF.

Furthermore, when y= 2, the area of the rectangle is;

14(2³) - 63(2) = 112-126

= -14

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Answer:

x = 1/2

y = 4

Step-by-step explanation:

2x + 3y = 13 ----------------------(1)

4x - y = -2  ------------------------(2)

Multiply Eq. (1) by 2

2(2x + 3y) = 13 × 2

4x + 6y = 26 -------------------(3)

Subtract Eq. (3) from Eq. (2)

4x - y - 4x - 6y = -2 - 26

-y - 6y = -28

-7y = -28

7y = 28

Divide 7 to both sides

Put y = 4 in Eq. (2)

4x - 4 = -2

Add 4 to both sides

4x = -2 + 4

4x = 2

Divide 4 to both sides

x = 2/4

[tex]\rule[225]{225}{2}[/tex]

We will see that the functions are inverses by proving that the composition is equal to the identity.

Two functions are inverses if their composition is equal to the identity, this means that if h(t) and k(t) are inverses, then we can write:

h(k(t)) = t

and

k(h(t)) = t

Proving one of these will be enough.

Here the functions are:

h(t) = (3t + 5)/t

k(t) = 5/(t - 3)

Let's find h(k(t))

We will get:

h(k(t)) = (3*k(t) + 5)/k(t)

Now we can replace the function k(t) there.

h(k(t)) = (3*5/(t - 3) + 5)/(5/(t - 3))

Now we can simplify this using algebra.

h(k(t)) = ( 15/(t - 3) + 5)*(t - 3)/5

h(k(t)) = (15/(t - 3))*(t - 3)/5 + 5*(t - 3)/5

h(k(t)) = 3 + (t - 3) = t

h(k(t)) = t

So yes, the two functions are inverses.

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The solution for the given expression is 14∛x. The correct option is (C).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

5∛x + 9∛x

The given expression can be simplified as follows,

5∛x + 9∛x

Here, both the terms have equivalent variables. So, both are like terms.

As per the rules like terms can be added or subtracted keeping the variable as the same.

Thus, 5∛x + 9∛x = 14∛x

Hence, the given expression can be evaluated as 5∛x + 9∛x = 14∛x.

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Answer: [tex]7.39466666[/tex]

Step-by-step explanation:

Setting [tex]x=2.2[/tex] and [tex]n=3[/tex],

[tex]e^{2.2} \approx \sum^{3}_{k=0} \frac{2.2^{k}}{k!}=\frac{2.2^0}{0!}+\frac{2.2^1}{1!}+\frac{2.2^2}{2!}+\frac{2.2^3}{3!} \approx 7.39466666[/tex]

Answer:

7.39466667 (8 d.p.)

Step-by-step explanation:

We can approximate the value of eˣ for any x using the following sum formula:

[tex]\boxed{e^{x} \approx \displaystyle \sum^n_{k=0}\dfrac{x^k}{k!}}[/tex]

To approximate [tex]e^{2.2}[/tex] with n = 3, substitute x = 2.2 and n = 3 into the given sum formula:

[tex]e^{2.2} \approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}[/tex]

To calculate the sum, substitute k with each value from 0 to 3 and add the results together:

[tex]\begin{aligned}e^{2.2} &\approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\\\\&= \dfrac{2.2^0}{0!}+\dfrac{2.2^1}{1!}+\dfrac{2.2^2}{2!}+\dfrac{2.2^3}{3!}\\\\&= \dfrac{1}{1}+\dfrac{2.2}{1}+\dfrac{4.84}{2}+\dfrac{10.648}{6}\\\\&= 1+2.2+2.42+1.774666666...\\\\&=7.39466667\; \sf (8\;d.p.)\end{aligned}[/tex]

Therefore, the approximate value of [tex]e^{2.2}[/tex] is:

[tex]\large \textsf{$e^{2.2}$}=\boxed{7.39466667}\; \sf (8\;d.p.)}[/tex]

Note: To obtain a more accurate approximate value, increase the value of n.

Answer:

page 1=45 points

page 2

1=30

2=10

3=56

page 3

$1000

Step-by-step explanation: