What is the length of the apothem of the regular pentagon shown be low? Round to one decimal place.

The homogeneous equation and a particular solution of the given nonhomogeneous equation is [tex]& y=c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}[/tex].

The given nonhomogeneous equation is y" - 4y = 2

We are given [tex]$y_1=e^{-2 x}$[/tex]

Let [tex]$y_2=u y_1$[/tex]

Non-homogeneous differential equations are simply differential equations that do not satisfy the conditions for homogeneous equations. In the past, we’ve learned that homogeneous equations are equations that have zero on the right-hand side of the equation.

The two most common methods when finding the particular solution of a non-homogeneous differential equation are:

[tex]$$\begin{aligned}& y_2=u e^{-2 x} \\& y_2^{\prime}=u^{\prime} e^{-2 x}-2 u e^{-2 x} \\& y_2^{\prime \prime}=u^{\prime \prime} e^{-2 x}-2 u^{\prime} e^{-2 x}-2 u^{\prime} e^{-2 x}+4 u e^{-2 x} \\& y_2^{\prime \prime}=u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}+4 u e^{-2 x}\end{aligned}$$[/tex]

Substitute in [tex]$y^{\prime \prime}-4 y=0$[/tex], we get

[tex]$$\begin{aligned}& u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}+4 u e^{-2 x}-4 u e^{-2 x}=0 \\& u^{\prime \prime} e^{-2 x}-4 u^{\prime} e^{-2 x}=0 \\& e^{-2 x}\left(u^{\prime \prime}-4 u^{\prime}\right)=0 \\& u^{\prime \prime}-4 u^{\prime}=0 \\& u^{\prime \prime}=4 u^{\prime}\end{aligned}$$[/tex]

Substitute [tex]$$u^{\prime}=v$ and $u^{\prime \prime}=v^{\prime}$[/tex], we get

[tex]$$\begin{aligned}& v^{\prime}=4 v \\& \frac{d v}{d x}=4 v \\& \frac{1}{v} d v=4 d x\end{aligned}$$[/tex]

Integrate both sides, we get

[tex]$u=\frac{1}{4} C_1 e^{4 x}+C_2$$[/tex]

put in [tex]$y_2=u y_1$[/tex]

[tex]$$y_2=\left(\frac{1}{4} C_1 e^{4 x}+C_2\right) e^{-2 x}$$[/tex]

Choose [tex]$$C_1=4$ and $C_2=0$[/tex], we get

[tex]$$y_2=e^{2 x}$$[/tex]

[tex]$$\begin{aligned}& y_c=c_1 y_1+c_2 y_2 \\& y_c=c_1 e^{-2 x}+c_2 e^{2 x}\end{aligned}$$[/tex]

Particular Solution

[tex]$$\begin{aligned}& y_y=A \\& y_y{ }^{\prime}=0 \\& y_y{ }^{\prime \prime}=0\end{aligned}$$[/tex]

Substitute in [tex]$y^{\prime \prime}-4 y=2$[/tex], we get

[tex]$$\begin{aligned}& 0-4 A=2 \\& -4 A=2 \\& A=-\frac{1}{2} \\& \therefore y_y=-\frac{1}{2}\end{aligned}$$[/tex]

General Solution

[tex]$$\begin{aligned}& y=y_6+y_y \\& y=c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}\end{aligned}$$[/tex]

Therefore, the second equation is [tex]& y_{2} =c_1 e^{-2 x}+c_2 e^{2 x}-\frac{1}{2}[/tex].

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The quotient of the given expression is calculated by dividing one fraction by another fraction. The result is 0.75.

When two numbers are divided, a new number called a quotient is produced. The formula to calculate this quotient is Quotient = Dividend÷Divisor. Consider the expression 40÷4. Here, 40 is the dividend, 4 is the divisor, 10 is the quotient, and 0 is the remainder.

The given expression is (-2/3)/(-8/9). This can be solved using the formula   [tex]\frac{A}{B}\div\frac{C}{D}=\frac{A}{B}\times\frac{D}{C}[/tex]. Here, A is -2, B is 3, C is -8, and D is 9. Substituting these values, we get,

[tex]\begin{aligned}\frac{A}{B}\div\frac{C}{D}&=\frac{A}{B}\times\frac{D}{C}\\\frac{-2}{3}\div\frac{-8}{9}&=\frac{-2}{3}\times\frac{9}{-8}\\&=\frac{3}{4}\\&=0.75\end{aligned}[/tex]

The required answer is 0.75.

The complete question is -

What is the quotient (-2/3)/(-8/9)?

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Answer:

"A) 12n + 14m + 4" would be the standard form.

Step-by-step explanation:

the expression written correctly in standard form would be "A) 12n + 14m + 4"

10m + 3(n + 8) + 4(m - 5) + 9n you need to first clear the parenthesis by applying distributive property:

10m + 3(n + 8) + 4(m - 5) + 9n = 10m + 3n + 24 + 4m - 20 + 9n

After that you combine like terms

= 10m + 4m + 3n + 9n + 24 - 20 = 14m + 12n + 4

"A) 12n + 14m + 4" would be the standard form.

The correct statement regarding the scatter plot is given as follows:

C. There were three athletes who had the same time in both races.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

The input and output variables for this problem are given as follows:

The points are given as follows:

(15, 15), (16, 15), (17, 15), (19, 15), (16, 16), (17, 16), (18, 16), (19, 16), (18, 18), (17, 19)

For example, the point (16, 15) means that the person took 16 seconds for the first race and 15 seconds for the second race.

Hence statement C is correct, as the points (15,15), (16, 16) and (18,18) means that there were three athletes who had the same time in both races.

The scatter plot is given by the image presented at the end of the answer.

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Options A and B are the correct answers.

The exponent or power to which a base must be raised to yield a given number is called a logarithm.

x is the logarithm of n to the base b if bx = n, in which case one writes

x = logb n.

“The logarithm of a positive real number a with respect to base b, and a positive real number not equal to 1^[nb 1], is the exponent by which b must be raised to yield a”.

b^y=a ⇔logba=y

To calculate the value of log₁₂81 we use the formula of

log ab=logb/loga=ln b/ln a

log₁₂81=log₁₀81/log₁₀12

           =log81/log12

Also, log e81=loge81/loge12

                    =ln81/ln12

So, choose log81/log12 and ln81/ln12

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Answer:

see photo, they change out answer order to look close.  :-)

Step-by-step explanation:

Plato/Edmentum

Answer:

There are 100 centimeters in 1 meter, so Maria'e height in meters would be:

1 meter and 36 centimeters, tall.

Step-by-step explanation:

Hope it helps! =D

The four parts of a polygon are: sides, vertices, diagonals, and interior angles.

Polygon is a closed figure in a plane made of of straight line or curved line that insert in pairs a polygon has at least three side of angle the height can be of any length and the angle can be of any measure polygon or classified according to the number of side they have such as triangle.

A polygon is a closed, two-dimensional shape with three or more straight sides. The four parts of a polygon are: sides, vertices, diagonals, and interior angles. The sides are the straight line segments that make up the shape. The vertices are the points where the sides meet. The diagonals are line segments joining any two non-adjacent vertices. The interior angles are the angles inside the polygon, which are determined by the number of sides the polygon has.

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The number of sodas sold was three times the number of hot dogs sold, so if we set up an equation, it would be 3x + x = 220, where x is the number of hot dogs sold. To solve this equation, we can subtract x from both sides, leaving us with 2x = 220. Then, we can divide both sides by 2, leaving us with x = 110. This means that 110 hot dogs were sold and 3x = 330 sodas were sold.

Answer:

1.5 or greater than 1.5

Step-by-step explanation:

First, we need to determine the total score of your opponent's dive:

40.8 points / 2.4 (degree of difficulty) = 17 (total score)

Now, we know that your total score needs to be greater than 17, and the scores awarded by the three judges are added together.

To calculate the scores from the third judge, we can use the following equation:

(Total score) - (score from judge 1) - (score from judge 2) = (score from judge 3)

Let's assume that you received scores of 8 and 7.5 from the first two judges.

We can plug in the values into the equation:

(Total score) - (8) - (7.5) = (score from judge 3)

We know that your total score needs to be greater than 17, so we have to find the score from the third judge, that when added to the scores 8 and 7.5, gives a total score greater than 17

17 - 8 - 7.5 = 1.5

The score from the third judge should be 1.5 or greater than 1.5 in order to give you more points than your opponent.

Answer: 3 : 8

Step-by-step explanation:

red to blue is 3 : 5

blue to yellow is 3 : 8

red to yellow is 3 : 8

A homogeneous mixture with two or more substances is called a solution. Household remedies frequently take the form of substances that have been dissolved in water, like juice concentrate.

Solutions are any mixtures of substances that have been dissolved.

A solution can be diluted by adding more solvent or by removing solutes. You can concentrate it by removing solvent or adding more solutes.

The following are some illustrations of simple fixes:.

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The fourth graph (the right graph in the bottom row) is discovered to represent the function f using translation notions (x).

A sort of transformation called a translation involves moving each point in a figure the same distance in the same direction.

In terms of operations like multiplication or sum/subtraction in its definition, a translation is represented as a change in the function graph.

has a vertex at the origin and [tex]$f(x)=\sqrt{x}$[/tex] is the parent function.

In this issue, the translated function is [tex]$f(x)=2 \sqrt{x+1}$[/tex] It was left 1 unit relocated and vertically stretched by a factor of 2 units, resulting in a new vertex position of (0,-1).

As a result, the fourth graph, on the right side of the bottom row, represents the function f. (x).

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Answer:

  176 cm

Step-by-step explanation:

You want the circumference of a wheel with a radius of 28 cm.

The circumference of a circle is given by ...

  C = 2πr

For r = 28 cm, this is ...

  C = 2π(28 cm) = 56π cm ≈ 176 cm

The circumference of the wheel is 56π cm, about 176 cm.

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Gametes carry half the genetic information of an individual, one ploidy of each type, and are created through meiosis, in which a germ cell undergoes two fissions, resulting in the production of four gametes.

Mendel's Law I has another name, namely the Law of Segregation. In the Law of Segregation it states that "In the formation of gametes (sex cells) in the two genes which are partners, will be separated in two daughter cells". Mendel's Law I or the Law of Segregation applies to monohybrid crosses, aka crosses with one different trait.

Mendel's First Law also states that two alleles (gene variants) that regulate certain traits will separate in two different gametes (sex cells). Mendel's Law I includes several things, namely:

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The series of transformations that would map figure D onto figure E is a

reflection over Y = -X.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The coordinates of Figure D are:

(4, 1), (1, 9), (5, 9), (7, 4), (6, 4).

The coordinates of Figure E are:

(-1, -4), (-9, -1), (-9, -5), (-4, -7), (-4, -6)

We see that,

The coordinates transformation:

(4, 1) → (-1, -4)

(1, 9) → (-9, -1)

(5, 9) → (-9, -5)

(7, 4) → (-4, -7)

(6, 4) → (-4, -6)

This is a reflection over Y = -X.

The reflection over Y = -X is (x, y) → (-y, -x).

Thus,

The transformations that would map figure D onto figure E are a

reflection over Y = -X.

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[tex](7j+8)-(4j+6)[/tex]

Distribute negative sign:

[tex]7j+8+-1(4j)+(-1)(6)[/tex]

[tex]7j+8-4j-6[/tex]

Combine Like terms:

[tex](7j-4j)+(8-6)[/tex]

[tex]\fbox{3j + 2}[/tex]

Answer:

The Answer would be 0.6666 repeated

Step-by-step explanation:

I don't think that I have to explain the process. it would be too long to read!

The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction number is given below.

⇒ 35 / 80

⇒ 7 / 16

⇒ 21 / 48

The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

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Therefore, the appropriate response for function problem  is Option B) This cat weighs 4 kilos at 7 months of age.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single variable, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x).

Here,

When the cat is m months old, w provides the cat's weight in kg.

the meaning of w(7) = 4 must be determined.

We already know that w represents weight in kilos.

When we enter the age in years, it returns the weight, which is what we consider to be the input.

W(7) stands for the weight of the cat at 7 months old.

where w(7) = 4 denotes the cat's weight at 7 months old, which is 4 kilograms.

Therefore, the appropriate response is Option B) This cat weighs 4 kilos at 7 months of age.

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The measure of the other two angles are 88 degrees and 22 degrees.

Let's call the two unknown angles x and y. Since the sum of all angles in a triangle is 180 degrees, we have:

x + y + 70 = 180

We also know that the ratio of the two angles is 4:7. We can set up a proportion to express this relationship:

x/y = 4/7

We can cross-multiply to get:

7x = 4y

We can substitute this equation into the first equation to eliminate one of the variables.

7x + y + 70 = 180

Now we have:

7x + y = 110

We can use the second equation to eliminate x:

7(4y/7) + y = 110

4y + y = 110

5y = 110

y = 22

Now that we know one of the angles is 22 we can substitute it back in the first equation

x+22+70 = 180

x = 88

Therefore, the measures of the other two angles are 88 and 22 degrees

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Answer:

$6.36

Step-by-step explanation:

6 x 1.06 = 6.36

Answer:

1.  7[tex]\frac{1}{2}[/tex] = [tex]\sqrt{7}[/tex]

2. 4[tex]\frac{7}{2}[/tex] = [tex]\sqrt{4} x^{7}[/tex]

3. 7[tex]\frac{1}{4}[/tex] = [tex]\sqrt[4]{7}[/tex]

4. 4[tex]\frac{1}{7}[/tex] = [tex]\sqrt[7]{4}[/tex]

Step-by-step explanation:

The fraction of the marble in the bag are blue is 4/15

The term fraction can be found by dividing part of a whole by the whole. Here the example if 2 students out of a total of 4 are picked, then the part is 2 and the whole is 4 while the fraction is 2 by 4.

Here we have given that a bag has 16 blue, 20 red, and 24 green marbles.

And we need to find the fraction of the marbles in the bag are blue

While looking into the given question, we have identified that the number of blue marbles is 16.

And the total number of marbles is calculated by adding the number of each marbles, then we get,

=> 16 + 20 + 24 = 60.

Here we know the the resulting fraction is obtained by the number of blue marbles out of the total marbles is,

Then it can be written as

=> 16/60

When we simplify this one then we get,

=> 4/15

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Food lion sells one can at $0.8 and Aldi sells one can at $1.

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:

Food Lion sells 5- 15 ounce cans of beans for $4.00.

Aldi sells 4- 15 ounce cans for $4.00.

So, Food lion sell one can

= 4/5

= $0.8

and, Aldi sells one can at

= 4/4

= $1

Hence, Food lion sell at $0.8 and Aldi sells for $1.

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The rate of change of the area of the right triangle at that instant is -1.5 sq km/h.

Make ABC a right triangle with a right angle to B.

BC = x on the side decreasing be

with AB = y being the rising side.

After that, AC = z = (x² + y2) (using Pythagoras theorem)

Given that dx/dt is equal to -5 km/h and dy/dt is equal to 14 km/h

When x = 3 and y = 9, respectively.

currently, the triangle's area equals xy/1/2.

A = 1/2 xy

dA/dt = 1/2 (y) (y).

dy/dt = dx/dt + x/2.

by inserting the values at x = 3 and y = 9,

(dA/dt) = 1/2 (9)(-5) + 3/2 (14) (14)

= -1.5

As a result, the right triangle's area is changing at a rate of -1.5 sq km/h at the moment when x=3 and y=9.

Your question is incomplete but most probably your full question was

One leg of a right triengle is decreasing at a tate of 5 kilometers per hour and the other leg of the triangle is increasing at a rete of 14 kilometers per hour. Ara certain anstant the decreasing leg is 3 kilometers and the increasing leg is 9 kilometers. What is the rate of change of the area of the right triangle at that instant (in square kilometers per hour)? 11 e 111 01.5 -1.5 Stuck?

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Answer:

------------------------

Given system:

Rewrite equations to bring to slope-intercept form:

Plot each line and find the intersection, this is the solution.

The solution is (2, 4) as per attached graph.