A turtle lives in a garden and a hedgehog lives in the woods. They leave their homes at the same time, walk toward each other, and meet in 5 hours. The turtle walks 10 meters per hour slower than the hedgehog. It the turtle had left home 4.5 hours earlier than the hedgehog, the two have me 150/ from the hedgehog's house. Find the distance between the garden and the woods.

Answer:

Step-by-step explanation:

Typically you see f(x)=something like you do up in the original equation.

that is your function/graph.

a) f(0)  means plug in 0 for x

   f(0) =  (-0)³-0²-0+13

   f(0) = 13

b)  f(2) =(-2)³-2²-2+13          >simplify the exponenents first

                                               (-2)³ = (-2)(-2)(-2)= -8

    f(2) = -8-4-2+13               >simplify work from left to right

    f(2) = -12-2+13

    f(2) = -14+13

    f(2) = -1

c)  f(-2) = [-(-2)]³-(-2)²-(-2)+13              >multiply - and -  for  (-(-2))³

    f(-2) = (2)³-(-2)²-(-2)+13                  >simplify exponents

    f(-2) = 8-4-(-2)+13          

    f(-2) = 4-(-2)+13

    f(-2) = 6+13

    f(-2) = 18

d)  means add f(1) and f(-1)

f(1) +f(-1) = (-1)³-1²-1+13 +[-(-1)]³-(-1)²-(-1)+13  

f(1) +f(-1) = -1-1-1+13 +[1]³-1-(-1)+13

f(1) +f(-1) = -1-1-1+13 +1-1+1+13            

f(1) +f(-1) = -2-1+13 +1-1+1+13

f(1) +f(-1) = -3 +13 +1-1+1+13

f(1) +f(-1) = 10+1-1+1+13

f(1) +f(-1) = 11 -1+1+13

f(1) +f(-1) = 10 +1 +13

f(1) +f(-1) = 24

The coordinates of the resulting point, R', are (1,-4).

A translation is a type of transformation in geometry that moves a point or an object from one place to another without changing its size, shape, or orientation.

To translate a point, you need to specify the direction and distance of the movement.

Given that:

The point R(1,-2) is being translated 2 units down, which means that it will move vertically downwards by a distance of 2 units.

The x-coordinate will remain the same, as the movement is only in the y-direction.

So, to find the coordinates of the resulting point, R', we subtract 2 from the y-coordinate of the original point R:

R' = (1, -2 - 2)

R' = (1, -4)

Therefore, resulting coordinates of R' are (1,-4).

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Answer: 9

Step-by-step explanation:

Range = maximum number - minimum number (in a data set)

50-41 = 9 minutes

Therefore, the slope of line s is equal to (d + b) / (a - c).

In mathematics, the slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between those same two points. In other words, the slope is the change in the y-coordinate divided by the change in the x-coordinate. If the slope is positive, the line is increasing from left to right and has an upward direction. If the slope is negative, the line is decreasing from left to right and has a downward direction. If the slope is zero, the line is horizontal. If the slope is undefined, the line is vertical. The concept of slope is important in various fields of mathematics, science, and engineering, as it helps to describe the relationship between two variables and make predictions based on that relationship. It is also used in calculus to find the rate of change of a function, and in geometry to find the equation of a line or the angle between two lines.

Here,

Since line s is parallel to line t, it has the same slope as line t. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, the points on line t are (a, -b) and (-c, d), so the slope of line t is:

slope of t = (d - (-b)) / (-c - a)

slope of t = (d + b) / (a - c)

Since line s is parallel to line t, it has the same slope as line t:

slope of s = (d + b) / (a - c)

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Answer:

To write the Hindu-Arabic numeral 872 as a Babylonian numeral using the symbols I and <, we need to break it down into its place values:

The digit 8 is in the hundreds place.

The digit 7 is in the tens place.

The digit 2 is in the ones place.

To represent 800 in the hundreds place, we use 8 symbols <. To represent 70 in the tens place, we use 7 symbols < followed by 1 symbol I. To represent 2 in the ones place, we use 2 symbols I.

Putting these symbols together, we get the Babylonian numeral:

<<<<< <<<< <<<< <<<< IIII

So, the Babylonian numeral equivalent of the Hindu-Arabic numeral 872 is <<<<< <<<< <<<< <<<< IIII.

Answer:

$30.25

Step-by-step explanation:

55% of 55$ is $30.25. she wants 45 % off of 55$. which is $24.75. 55-24.75 is 30.25

$30.25

since it's 45% off, you need to subtract 45% from 100%

100%-45%=55%

then turn the % into a decimal

55%/100=0.55

now multiply the original price by 0.55

0.55*55=30.25

In the quadratic formula, the number for "a" is filled in with the coefficient of x².

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Mathematically, the quadratic formula is represented by this mathematical equation:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

For instance, given the quadratic equation 2x² - 3x - 1 = 0, we have:

a = 2

b = -3

c = -1

[tex]x = \frac{-(-3)\; \pm \;\sqrt{(-3)^2 - 4(2)(-1)}}{2(2)}\\\\x = \frac{3\; \pm \;\sqrt{9 + 8}}{4}\\\\x = \frac{3\; \pm \;\sqrt{17}}{4}[/tex]

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In a case whereby Michelle has 3 kg of strawberries that she divided equally into small bags with 1/5 kg in each bag  the number of bags of strawberries she make is 15bags of strawberries.

We should note that 1kg = 1000g

3kg = 1000g

Since each of the bag is  1/5 kg = 1000/5 g = 200g

The needed bag will now be =3000/200= 15

Therefore, we can see that she made 15bags of strawberries the conversion were made so that it can be calculated easily since ythe kg are very small.

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The answers of the matrix of A after  adding  -5 times row 1 to row 3 of matrix is

1  -1  5  |  -1

1  -1 -4  |   5

0   9 -25 |   4

A matrix is described as  a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.

We perform the row operation and have:
1  -1  5  |  -1

1  -1 -4  |   5

0   9 -25 |   4

The result after  adding  -5 times row 1 to row 3 of matrix is shown below:

1  -1  5  |  -1

1  -1 -4  |   5

0   9 -25 |   4

In conclusion,  in  a matrix function, the input and the output values are matrices.

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To solve the problem, we need to find Julian's average speed, given that he started biking from a position behind the simulated biker at a speed of 20 km/h, and after 15 minutes, his position was reported as -214 km.

We can use the formula for average speed:

Average speed = total distance / total time

To find the total distance, we need to calculate the displacement of Julian from the initial position of -d (where d is the distance between Julian and the simulated biker when he started biking) to the position of -214 km after 15 minutes.

Displacement = final position - initial position

Displacement = (-214 km) - (-d) = d - 214 km

The total distance covered by Julian is equal to the absolute value of the displacement, since the direction of the motion does not matter when computing distance.

Total distance = |d - 214 km|

To find the total time, we need to convert 15 minutes to hours:

Total time = 15 minutes / 60 minutes/hour = 0.25 hours

Now we can substitute the values into the formula for average speed:

Average speed = total distance / total time

Average speed = |d - 214 km| / 0.25 hours

Since Julian was traveling at a constant speed of 20 km/h, we can also express the distance in terms of time:

Average speed = (20 km/h) x t / 0.25 hours

where t is the time Julian biked in hours.

Setting the two expressions for average speed equal to each other, we can solve for t:

|d - 214 km| / 0.25 hours = (20 km/h) x t / 0.25 hours

|d - 214 km| = 20 km/h x t

Solving for t:

t = |d - 214 km| / 20 km/h

Now we can substitute this expression for t into either expression for average speed:

Average speed = (20 km/h) x t / 0.25 hours

Average speed = |d - 214 km| / 0.25 hours

Substituting the expression for t:

Average speed = |d - 214 km| x 4 / |d - 214 km|

Simplifying:

Average speed = 80 km/h

Therefore, Julian's average speed so far has been 80 km/h.

The inverse of matrix C is C⁻¹ = [1/9 4/27] [1/27 -5/27].

To find the inverse of matrix C, use the following formula:

C⁻¹ = 1/det(C) × adj(C)

where det(C) = determinant of matrix C and adj(C) = adjugate of matrix C.

To find the determinant of C, use the following formula for a 2x2 matrix:

|a b|

|c d| = ad - bc

So:

det(C) = |5 1|

|12 -3| = (5)(-3) - (1)(12) = -27

Find the adjugate of C, which is the transpose of the matrix of cofactors of C, which is:

|-3|

| 1| = -(-3) = 3

So the upper left cofactor is 3, which is:

|12|

|-3| = -(12) = -12

So the upper right cofactor is -12, which is:

| 1|

|-3| = -(1) = -1

So the lower left cofactor is -1, which is:

|5|

|1| = 5

So the lower right cofactor is 5. Putting the cofactors into a matrix and transposing it gives the adjugate of C:

adj(C) = [ 3 -12]

[-1 5]

Now find the inverse of C:

C⁻¹ = 1/det(C) × adj(C)

= -1/27 × [ 3 -12]

[-1 5]

= [1/9 4/27]

[1/27 -5/27]

So the inverse of matrix C is:

C⁻¹ = [1/9 4/27]

[1/27 -5/27]

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The equation of the quadratic function in standard form is f(x) = 5x² - 3x - 7

To write an equation for a quadratic function in standard form, we need to use the general form of the equation, which is: f(x) = ax² + bx + c where a, b, and c are constants that determine the shape and position of the graph of the function.

Let's choose the points (-2, -16), (-1, -15), and (0, -12) from the table. Substituting these values into the equation above, we get:

-16 = 4a - 2b + c -15 = a - b + c -12 = c

We can use the third equation to solve for c, which is -12 in this case. Substituting this value into the first two equations, we get:

-16 = 4a - 2b - 12 => 4a - 2b = 4 -15 = a - b - 12 => a - b = 3

Now we have two equations in two unknowns, which we can solve by substitution or elimination. Let's use substitution to solve for b first:

a - b = 3 => b = a - 3

Substituting this into the first equation, we get:

4a - 2(a - 3) = 4 => 2a = 10 => a = 5

Now we can substitute the values of a and b into one of the original equations to find c:

-15 = 5 - b + c => -15 = 5 - (5 - 3) + c => c = -7

Therefore, the equation of the quadratic function in standard form is:

f(x) = 5x² - 3x - 7

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The equation, for the simple harmonic motion of a particle moving uniformly is s ( t ) = A x cos (ωt).

An object undergoing simple harmonic motion follows a periodic oscillation in a straight line, resembling a sinusoidal curve. Likewise, when an object continuously traverses upon a circle with uniform motion, its projection along the diameter travels back and forth in a simple harmonic motion pattern.

Assuming that the particle commences at the highest point of the simple harmonic motion at time t = 0, either the sine or cosine function is utilized to derive the equation for the simple harmonic motion formula. Thus, let us employ the cosine function in this instance:

s ( t ) = A x cos (ωt)

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Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.

If two angles share a side and a vertex, they are said to be neighbouring in geometry. In other words, neighbouring angles do not overlap and are placed next to one another immediately.

Given data:

From the figure:

m∠RST  = m∠QST + m∠QSR

Put the values

70 = 2x + 3x - 10

5x = 80

x = 16

Thus,

m∠QSR = 3x - 10  = 3(16) - 10

m∠QSR = 38

Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.

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Complete question:

If m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10, what is the m∠QSR?.

The figure is attached:

16

48

32

38

The following are stated goals for this class:

1. Help students develop their ability to apply math concepts to real-world problems.

2. Increase your knowledge of consumer applications and personal financial management.

3. Explain the basics of home mortgages.

These goals are aimed at providing students with practical skills and knowledge that can be applied to their everyday lives, such as managing personal finances, understanding the mortgage process, and planning for retirement.

By learning math concepts in the context of real-world situations, students are better equipped to make informed decisions and solve problems that they may encounter in their personal and professional lives.

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The mean age of the U.S. presidents at inauguration is 54.7 years and the population standard deviation is approximately 5.7 years.

To find the mean and population standard deviation of the ages of the U.S. presidents at inauguration, we first need to calculate the sum of the ages and the number of presidents in the data set.

The sum of the ages is:

57 + 61 + 57 + 57 + 58 + 57 + 61 + 54 + 68 + 51 + 49 + 64 + 50 + 48 + 65 + 52 + 56 + 46 + 54 + 49 + 50 + 47 + 55 + 55 + 54 + 42 + 51 + 56 + 55 + 51 + 54 + 51 + 60 + 62 + 43 + 55 + 56 + 61 + 52 + 69 + 64 + 46 + 54 + 47 = 2,405

There are 44 presidents in the data set.

Therefore, the mean age is:

mean = sum of ages / number of presidents = 2,405 / 44 = 54.7

To find the population standard deviation, we first need to calculate the sum of the squared deviations from the mean:

(57 - 54.7)² + (61 - 54.7)² + ... + (47 - 54.7)² = 3,391.5

Then, we divide the sum of squared deviations by the number of presidents and take the square root:

population standard deviation = √(3,391.5 / 44) ≈ 5.7

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Answer:

392 conbinations

Step-by-step explanation:

multiply all 3 numbers to find conbinations.

      8x7x7

=56x7(or 49x8)

=392

its prob wrong cuz i guessed so yeah

The matrix operation add -4(row 1) to row 3 is[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

From the question, we have the following parameters that can be used in our computation:

[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right][/tex]

From the question, we understand that

We are to add -4(row 1) to row 3

This means that

row 3 = row 3 - 4 * row 1

When these values are evaluated, we have

4: 4 - 4 * 1 = 0

-1: -1 - 4 * 2 = -9

6: 6 - 4 * 1 = 2

-8: -8 - 4 * -5 = 12

This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12

Using the above as a guide, we have the following:

[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

Hence, the result of the matrix expression is [tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

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If Alonso pays the monthly payment each month for the full term. Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.

To calculate the total amount that Alonzo will repay over the 6-year term of the loan, we need to use the formula for the monthly payment on an amortized loan:

M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)

where:

M is the monthly payment

P is the principal amount

r is the monthly interest rate (which is the annual interest rate divided by 12)

n is the total number of payments (which is the number of years multiplied by 12).

Using the values given in the problem, we have:

P = $49,000

r = 6.55% / 12 = 0.005458333 (monthly interest rate)

n = 6 years * 12 months/year = 72

Substituting these values into the formula, we get:

M = $49,000 * 0.005458333 * (1 + 0.005458333)^72 / ((1 + 0.005458333)^72 - 1)

= $824.85 (rounded to the nearest cent)

To find the total amount he will repay, we can simply multiply the monthly payment by the number of payments:

Total amount =$824.85 * 72

Total amount = $59,389.2

Therefore, Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.

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2nd and 4th is correct. Hope you got it!

A)  The continuous rate of growth of this bacterium population = 0.35

B) The initial population of the culture = 920

C) The number of bacteria at time t=5 are 5294

Here, the function [tex]n(t)=920\times e^{(0.35\times t)}[/tex] represents the number of bacteria in a culture at time t

A) We know that in exponential function f(x) = [tex]ae^{kx}[/tex], k is the rate of growth

Here, in this function n(t) = [tex]920\times e^{(0.35\times t)}[/tex],  the continuous rate of growth is 0.35

B) To find the initial population of the culture

Substitute t = 0, in n(t)

n(0) = [tex]920\times e^{(0.35 \times 0 )}[/tex]

n(0) = 920 × e⁰

n(0) = 920

This is the initial population.

C) Now we find the number of bacteria at time t=5

[tex]n(t)=920\times e^{(0.35\times t)}[/tex]

Substitute t = 5 in above equation.

n(5) =[tex]920 \times e^{(0.35 \times 5)}[/tex]

n(5) = 5294.23

n(5) ≈ 5294

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The number of bacteria in a culture is given by the function

n(t) =920e^0.35t Where t is measured in hours

A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent

B) what is the initial population of the culture (at t=0) your answer is __

C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria

Therefore , the solution of the given problem of expressions comes out to be there are roughly 7,000 grains of sand in 7 grammes of sand.

Instead of using random estimates, it is preferable to use shifting numbers that may also prove increasing, reducing, variable or blocking. They could only help one another by trading tools, information, or solutions to issues. The justifications, components, or quantitative comments for tactics like further disagreement, production, and blending may be included in the assertion of truth equation.

Here,

A kilogramme (1000 grammes) of sand is thought to contain around 1 million grains of sand. This indicates that 1 gramme of sand contains roughly 1000 grains of sand.

Using this calculation, we can determine how many sand grains there are in 7 grammes roughly as follows:

=> Number of sand grains in 7 grammes = (# of sand grains in 1 gramme) x (7 grams)

=> 1000 x 7 = the number of sand grains in 7 grammes.

=> 7,000 sand grains are included in 7 grammes.

In accordance with this calculation, there are roughly 7,000 grains of sand in 7 grammes of sand.

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To solve this problem, we can use the formula for inverse variation, which is:

time = k/ rate

where k is a constant of proportionality.

We can start by finding the value of k using the given information. We know that when the pumping rate is 400 gallons per hour, it takes 12 hours to drain the pool. Therefore:

12 = k/400

Multiplying both sides by 400 gives us:

k = 4800

Now we can use this value of k to answer the second part of the question. We want to know how many hours faster the pool can be drained if the pumping rate is increased to 500 gallons per hour. Let's call this new time t:

t = 4800/500

t = 9.6 hours

So the pool can be drained 12 - 9.6 = 2.4 hours faster if the pumping rate is increased to 500 gallons per hour.

If population of rabbits is increasing at a rate of 1.5% per month, after 10 months, there will be approximately 71 rabbits in the population.

To solve this problem, we need to use the formula for exponential growth:

A = P(1 + r)ᵗ

where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time period. In this case, we have P = 60, r = 0.015 (1.5% expressed as a decimal), and t = 10.

Plugging these values into the formula, we get:

A = 60(1 + 0.015)¹⁰

A ≈ 71

t's important to round to the nearest whole, so we can't be exact, but we know the answer will be somewhere between 70 and 72 rabbits.

Exponential growth is a model that assumes continuous growth over time, which may not be entirely accurate in real-world scenarios.

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Answer:

15.04 (3.s.f)

Step-by-step explanation:

Cos a = adjacent/ hypotenuse

Cos 43 = 11/ x

so,

x= 11 / cos 43

= 15.04

Answer:

Step-by-step explanation:  find the circumference and then consider the shape (circle) after that get rid of options that don't make sense like 7.3 and 7.1, 8 for the radius might be too big leaving you with    7     (use a calculator if needed)

The other value of x where g(x) = 15 is 16 in the absolute value function

Since the vertex of the absolute value function is at (10,0), the equation for the function can be written as:

g(x) = a|x - 10|

To find the value of a, we can use the fact that the function passes through the point (4,15):

15 = a|4 - 10|

15 = 6a

a = 2.5

So the equation for the absolute value function is:

g(x) = 2.5|x - 10|

To find another value of x where g(x) = 15, we can set the equation equal to 15 and solve for x:

2.5|x - 10| = 15

|x - 10| = 6

x - 10 = 6 or x - 10 = -6

x = 16 or x = 4

Therefore, there are two possible values of x where g(x) = 15: x = 16 and x = 4.

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Answer: Since 1 and 2 have the same measure, angle CED is also equal to 1 and 2. Therefore, triangle CED and triangle CAB are similar by the Angle-Angle (AA) criterion.

Using the properties of similar triangles, we can set up the following proportion:

$\frac{CE}{CA}=\frac{CD}{CB}$

Substituting the given values:

$\frac{CE}{x+4}=\frac{x}{14}$

Cross-multiplying:

$14CE = x(x+4)$

$14CE=x^2+4x$

We also know that triangle ADE and triangle ABC are similar by the AA criterion. Therefore, we can set up the following proportion:

$\frac{DE}{AB}=\frac{AE}{AC}$

Substituting the given values:

$\frac{DE}{18}=\frac{AE}{x+4}$

Cross-multiplying:

$AE = 18\frac{DE}{x+4}$

Now, we can substitute the value of $AE$ in terms of $DE$ into the first equation:

$14CE=x^2+4x$

$14\frac{DE}{x+4}=x^2+4x$

$14DE=x^2+4x(x+4)$

$14DE=x^2+4x^2+16x$

$18x^2+16x-14DE=0$

We can now use the quadratic formula to solve for $x$:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-16\pm\sqrt{(16)^2-4(18)(-14DE)}}{2(18)}$

$x=\frac{-16\pm\sqrt{256+1008DE}}{36}$

Since $DC=x$, we can now use this equation to find the value of $DC$ for a given value of $DE$. For example, if $DE=5$, we have:

$DC=\frac{-16\pm\sqrt{256+1008(5)}}{36}$

$DC\approx 2.3$ or $DC\approx -3.1$

Since distance cannot be negative, we choose the positive solution:

$DC\approx 2.3$ units.

To find $DE$, we can substitute the value of $DC$ back into one of the earlier equations:

$\frac{CE}{x+4}=\frac{x}{14}$

$\frac{CE}{2.3+4}=\frac{2.3}{14}$

$CE\approx 1.34$ units

Now we can use the second similarity proportion to find $DE$:

$\frac{DE}{18}=\frac{AE}{x+4}$

$\frac{DE}{18}=\frac{18-1.34}{2.3+4}$

$DE\approx 3.64$ units

Therefore, $DC\approx 2.3$ units and $DE\approx 3.64$ units.

Step-by-step explanation:

The equation that represents the circle is (x + 1)² + (y - 1)² = 16

The equation of a circle with center (h,k) and radius r is:

(x - h)² + (y - k)² = r²

To find the equation of the circle with center (-1,1) and radius 4, we need to shift the center of the circle to (-1,1).

We can do this by replacing x with (x - (-1)) = (x + 1) and y with (y - 1) in the equation of the original circle. This gives:

(x + 1)² + (y - 1)² = 16

This equation represents a circle with center (-1,1) and radius 4.

Therefore, the correct option is (O) (x + 1)² + (y - 1)² = 16.

The other options do not have the correct center or radius to describe the circle.

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