The figure shows two regular pentagons. What is the perimeter of the larger pentagon?

A. 5n

B. 10n

C. 15n

D. 60n

Answer:

P<-18

multiply both sides by 3 3p/3<3(-6)

Simplify p<-18

Step-by-step explanation:

Answer:

486 ft²

Step-by-step explanation:

For this, you want to replace every w with 16.

This gives (16+2)(2×16-5) or 2×16²-16-10.

I'm going to show this with the first example because the numbers are a bit easier.

You want to begin by working out the brackets. 16+2=18, and 2×16=32, giving us 18(32-5).

32-5=27, giving 18×27 as the equation.

This equals to 486, so the area is 486 ft².

**This content involves polynomials and area, which you might want to revise. I'm always happy to help!

Answer:

y

=

3

x

−

13

Explanation:

the equation of a line in

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where x is the slope and b the y-intercept

here

m

=

3

⇒

y

=

3

x

+

b

←

is the partial equation

to find b substitute

(

2

,

−

7

)

into the partial equation

−

7

=

6

+

b

⇒

b

=

−

7

−

6

=

−

13

⇒

y

=

3

x

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is the equation of line

Hope this helped :)

Answer:

\(Selling\ Price = 12b(1.55)\)

Step-by-step explanation:

Given

\(Cost\ Price = \$12\)

\(Selling\ Price = 55\%\ more\)

Required

Write an expression for the selling price for b birdbaths

This selling price for 1 birdbath is calculated as:

\(Selling\ Price = Cost\ Price + 55\% * Cost\ Price\)

Substitute 12 for Cost Price

\(Selling\ Price = 12 + 55\% * 12\)

Factorize:

\(Selling\ Price = 12(1 + 55\%)\)

Express percentage as decimal

\(Selling\ Price = 12(1 + 0.55)\)

\(Selling\ Price = 12(1.55)\)

For b birdbaths, the selling price is:

\(Selling\ Price = 12(1.55) * b\)

\(Selling\ Price = 12b(1.55)\)

The options are not clear; However \(12b(1.55)\) answers the question.

Answer:

Slope: -3/5

Step-by-step explanation:

To find the general solutions of the given differential equations using D-operator methods, we will use the fact that D-operator (D) represents differentiation with respect to x.

3.1 For the differential equation (D² - 5D + 6)y = e^(-x) + sin(2x), we can factorize the characteristic equation as (D - 2)(D - 3)y = e^(-x) + sin(2x). Solving each factor separately, we have: (D - 2)y = e^(-x) => y₁ = Ae^(2x) + e^(-x) (where A is a constant). (D - 3)y = sin(2x) => y₂ = Bsin(2x) + Ccos(2x) (where B and C are constants). The general solution is y(x) = y₁ + y₂ = Ae^(2x) + e^(-x) + Bsin(2x) + Ccos(2x).

3.2 For the differential equation (D² + 2D + 4)y = e^(2x)sin(2x), the characteristic equation is (D + 2i)(D - 2i)y = e^(2x)sin(2x). Solving each factor separately, we have: (D + 2i)y = e^(2x)sin(2x) => y₁ = Ae^(-2ix)e^(2x)sin(2x) = Ae^(2x)sin(2x)

(D - 2i)y = e^(2x)sin(2x) => y₂ = Be^(2ix)e^(2x)sin(2x) = Be^(2x)sin(2x)

The general solution for the first differential equation is y(x) = Ae^(2x) + e^(-x) + Bsin(2x) + Ccos(2x), and the general solution for the second differential equation is y(x) = Ae^(2x)sin(2x) + Be^(2x)sin(2x), where A, B, and C are constants.

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Answer:

b

Step-by-step explanation:

The given expression √200 is equivalent to 10√2.

An algebraic expression is a combination of terms both variables and constants. We can write the examples of algebraic expression as -

2x + 3y + 5

5x + 4y + 1

Given is to find the equivalent expression for the -

√200

We have the following expression as -

√200

We can write it as -

√(2 x 2 x 2 x 5 x 5)

√2² x 2 x 5²

(2 x 5) √2

10√2

Therefore, the given expression √200 is equivalent to 10√2.

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The sentence that explains why two of the fractions shown on the number lines below are equivalent is "The fractions \(\frac{1}{2}\) , \(\frac{2}{4}\) are equivalent because both fractions have the same denominator."

The two fractions \(\frac{1}{2}\) and \(\frac{2}{4}\)  have the same denominator, which is 4. If we multiply the numerator and denominator of \(\frac{1}{2}\) by 2, we get \(\frac{2}{4}\) which means they are equivalent.

When two fractions have the same denominator, they can be easily compared and converted to their equivalent forms.

A number line is a graphical representation of numbers on a straight line, which can be used to compare numbers and determine their value and relationships. Although the number line helps in understanding the fractions, it does not have any direct relation with the equivalence of the given fractions.

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Using exponential function it will take approximately 2.6 years for the population to reach 26676

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.

The formula given in this question is

P(t) = 988(3.5)ˣ

The time it will take to reach a population of 26676 is

26676 = 988(3.5)ˣ

x = 2.6 years

It will take approximately 2.6 years

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The result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

To calculate log4 57 to the nearest thousandth, we can use a scientific calculator or a logarithmic table.

Using a calculator, we can find the logarithm of 57 to the base 4 directly:

log4 57 ≈ 3.682

Therefore, the correct answer is option C: 3.682.

If you prefer to verify the result using logarithmic properties, you can do so as follows:

Let's assume log4 57 = x. This means \(4^x\) = 57.

Taking the logarithm of both sides with base 10:

log (\(4^x\)) = log 57

Using the logarithmic property log (\(a^b\)) = b \(\times\) log a:

x \(\times\) log 4 = log 57

Dividing both sides by log 4:

x = log 57 / log 4

Using a calculator to evaluate the logarithms:

x ≈ 3.682

Thus, the result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

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Answer:

0 - 20

1 -22

5 - 30

10 - 40

15 - 50

20 - 60

Step-by-step explanation:

The initial amount this equation is 20 so that is why at 0 shirts its still 20 dollars for the set up fee and 2 dollars per shirt. Now that we have this information we can actually make a linear equation

y = 2x + 20

y = the total cost

x = the number of shirts

All you have to do next is plug in the number of shirts to get the total cost

Example:   2(1) + 20 = y

2 + 20 = y

22 = y

Meaning for 1 shirt it would be 22 dollars in total

The required value of the function is 2

In the case of a function from one set to the other, each element of X receives exactly one element of Y.

The given function is of the form :

g(x) = - x² - 7

Now let us find the required values.

g (-3) = - (-3)² - 7 = 2

g (-2) = - (-2)² - 7 = -3

g (1 ) = - ( -1 )² - 7 = -6

Hence the required value of the function is 2 at x = -3 .

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

A) 4 Hours (of running)

B) 5 Hours (of biking)

Step-by-step explanation:

So Suzette ran and biked for a total of 80 miles,

and she did all of that in 9 hours.

Let x equal the total hours of Suzette ran and let y equal the total hours of Suzette biked.

Therefore:

\(x+y=9\)

This represents the total hours. We know that the hours she had ran and biked totals 9. Thus, x plus y must equal 9.

And also:

\(5x+12y=80\)

The 5x represents the miles she had ran in x hours, while the 12x represents the miles she had biked in y hours. All together, they must equal 80 miles total.

Therefore, our system is:

\(x+y=9\\5x+12y=9\)

We can solve this using substitution. First, subtract x from the top equation:

\(x+y=9\\y=9-x\)

Now, substitute the y into the second equation:

\(5x+12y=80\\5x+12(9-x)=80\)

Distribute:

\(5x+108-12x=80\)

Combine like terms:

\(-7x+108=80\)

Subtract 108 from both sides:

\((-7x+108)-108=(80)-108\\-7x=-28\)

Divide both sides by -4:

\(x=4\)

Therefore, Suzette ran for a total of 4 hours.

Since she biked and ran for a total of 9 hours, she must have biked for 9-4 or 5 hours.

Checking:

4 hours of running plus 5 hours of biking does indeed equal 9 hours total:

\(4(5)+5(12)=20+60=80\)

So by running 5mph for 4 hours and by biking 12mph for 5 hours, she did indeed reach a total of 80 miles.

Answer:

48 ft^2.

Step-by-step explanation:

In this case, our formula is known as 3s^2 which can be written out as 3 x s x s or 3(s x s). S is the variable to represent our length and width because the formula for finding the area is l x w which can be written out as length x width. If the total area of each garden bed has a length of 4 feet, our equation would be 3(4 x 4) or 3 x 4 x 4 or 3(4)^2. 4 x 4 or 4^2 is 16. If we multiply 16 by 3, the answer would be 48. That is why the total area of each garden bed would be 48 ft^2.

There are a total of 48 soccer games in the season.

Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:

Number of day games = Total number of games - Number of night games

= 12 games/month x 4 months - 8 night games/month x 4 months

= 48 games - 32 games

= 16 games

Therefore, the total number of games in the season is:

Total number of games = Number of day games + Number of night games

= 16 games + 32 games

= 48 games

So, there are 48 soccer games in the season.


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Answer:

.68 Centiseconds

Step-by-step explanation:

A microsecond is exactly 1 x 10-6 seconds. 1 µs = 0.000,001 s. One millionth of a second.

and a centisecond is exactly 0.01 seconds. One hundredth of a second.

Im not really sure how to explain it. But I hope that I helped.

There are 0.68 Centiseconds in 6800 microseconds.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometres, or feet, or any other measure of length.

Given that, Convert 6800 microseconds to centiseconds

We know that 1 centisecond = 10000 microseconds

Thereforre, 6800 microseconds = 6800/10000 centiseconds

= 0.68 Centiseconds

Hence, There are 0.68 Centiseconds in 6800 microseconds.

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Answer:

  both size boxes are $18 each

Step-by-step explanation:

Let x and y represent the costs of the small and large boxes, respectively. Then the two sales are ...

  3x +14y = 306

  7x +7y = 252

Doubling the second equation and subtracting the first, we have ...

  2(7x +7y) -(3x +14y) = 2(252) -(306)

  11x = 198

  x = 18

  y = 252/7 -x = 36 -18 = 18

A small box costs $18, as does a large box.

Answer:

both size boxes are $18 each

Step-by-step explanation:

Let x and y represent the costs of the small and large boxes, respectively. Then the two sales are ...

3x +14y = 306

7x +7y = 252

Doubling the second equation and subtracting the first, we have ...

2(7x +7y) -(3x +14y) = 2(252) -(306)

11x = 198

x = 18

y = 252/7 -x = 36 -18 = 18

A small box costs $18, as does a large box.

Answer:

Step-by-step explanation:

f(g(x))

g(x) = 7x -4

f(7x - 4) = 2(7x - 4) + 15 = 14x - 8 + 15 = 14x + 7

Answer:

x = 4, -4, 7i, -7i

Step-by-step explanation:

(x^2 – 16)(x^2 + 49) = 0

x^2 – 16 = 0 or x^2 + 49 = 0

x^2 = 16 or x^2 = -49  

x = ± 4 or x^2 = ±7√-1  =±7i

Answer:

27÷ x=?

Step-by-step explanation:

if yuu want to share 27 cookies equally you have to kno the number of members in that case that number is "x" nd yuu have to divide

The correct statements regarding the transformations to the volumes are given as follows:

1. A cone's radius increases x 3: -> The cone's volume will increase x 9.

2. A cone's height increases x 3: -> The cone's volume will increase x 3

3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.

4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.

The equations that give the volumes of each solid are given as follows:

Then the increases are given as follows:

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An estimate of DEF Company's cost of equity is 7.14%.

To estimate the cost of equity, we can use the dividend growth model. The formula for the cost of equity (Ke) is: Ke = (Dividend per share / Current share price) + Growth rate

Given data:

The cost of equity iss:

Ke = ($0.55 / $16) + 0.037

Ke ≈ 0.034375 + 0.037

Ke ≈ 0.071375.

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Both the cost of equity and the cost of preferred stock play important roles in determining a company's overall cost of capital and the required return on investment for different types of investors.

To estimate DEF Company's cost of equity, we need to calculate the dividend growth rate and use the dividend discount model (DDM). The cost of preferred stock can be found by dividing the fixed dividend by the current price of the preferred stock.

The calculations will provide the cost of equity and cost of preferred stock as percentages.

To estimate DEF Company's cost of equity, we use the dividend growth model. First, we calculate the expected dividend for the next year, which is given as $0.55 per share.

Then, we calculate the dividend growth rate by taking the expected growth rate of 3.7% and converting it to a decimal (0.037). Using these values, we can apply the dividend discount model:

Cost of Equity = (Dividend / Current Share Price) + Growth Rate

Plugging in the values, we get:

Cost of Equity = ($0.55 / $16) + 0.037

Calculating this expression will give us the estimated cost of equity for DEF Company as a percentage.

To calculate the cost of preferred stock, we divide the fixed dividend per share ($1.8) by the current price per share ($27.6). Then, we multiply the result by 100 to convert it to a percentage.

Cost of Preferred Stock = (Fixed Dividend / Current Price) * 100

By performing this calculation, we can determine DEF Company's cost of preferred stock as a percentage.

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True. When performing econometric analysis on time-series data, it is a best practice to sort the data in chronological order. Econometric analysis involves using statistical methods to study and understand economic relationships, trends, and patterns.

Time-series data refers to a set of observations collected at regular intervals over time, such as stock prices, GDP growth, or unemployment rates.

Sorting the data in chronological order is essential because it allows for a proper understanding of the temporal relationship between different data points. This ordering helps researchers identify patterns, trends, and potential causal relationships within the data. Additionally, many econometric models, such as autoregressive or moving average models, rely on the assumption that the data points are arranged sequentially in time.

In summary, when conducting econometric analysis on time-series data, it is crucial to sort the data in chronological order to accurately analyze patterns, trends, and relationships. This practice enables researchers to develop robust models that can be used for forecasting and understanding the underlying economic processes.

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Answer:

Each girl (m) had $18.

Step-by-step explanation:

The Equation to determine the amount of money, m, each girl received is 4m = 72 or m = 12(4) + 24

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Each girl spent $12.

Afterward, the girls had $24 altogether.

let each Girl received amount of $x.

So, the four spend = 12 x 4 = $48

Then, the total they have = 48 + 24 = $72

So, each of Girl have = 72/ 4 = $18.

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Answer:36

Step-by-step explanation:

90/10= 9 9x4=36

The equation representing the vertical asymptote of the graph you described can be determined by examining the behavior of the curve near x = 12.

For a vertical asymptote, the curve approaches infinity or negative infinity as it gets closer to the asymptotic value of x. In this case, the curve is asymptotic to y = 0 from both negative x values (left side) and positive x values (right side) near x = 12.

Let's consider the left side of the curve first. As x approaches 12 from the negative side, the curve approaches y = 0. To find the equation of the asymptote, we need to determine the behavior of the curve as x gets infinitely close to 12 from the negative side. If the curve approaches y = 0, it means that the value of y becomes very large (positive or negative) as x approaches 12 from the negative side.

Therefore, the equation of the asymptote for the left side can be represented as x = 12.

Similarly, for the right side of the curve, as x approaches 12 from the positive side, the curve also approaches y = 0. Thus, the equation of the asymptote for the right side can also be represented as x = 12.

In summary, the equation representing the vertical asymptote of the graph you described is x = 12. This equation indicates that the curve approaches y = 0 as x gets closer to 12, both from the negative and positive sides.

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On solving we got that. he shorter pieces will therefore be 3 feet long and the longer pieces will therefore be 8 feet long.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

The lengths of the shorter and longer pieces of a board should be determined.

the case

Let's say that the shorter parts are x in length.

as stated

Jared has an 11-foot wooden board with him.

In order for the longer piece to be 4 feet less than 4 times as long as the shorter piece, he wants to cut it into two pieces.

The length of the longer pieces is then equal to 4x - 4.

The equation then becomes

\(x + 4x - 4 = 11\\ 5x = 11 + 4\\ 5x = 15\\ x = 3 ft\)

The shorter pieces will therefore be 3 feet long.

The longer pieces' length -

\(4x - 4\\ = 4 X 3 - 4\\ = 12 - 4\\ = 8 ft\)

The longer pieces will therefore be 8 feet long.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)