In the figure below, I ll m. Find x,

Answer:

d    ↔   - π

e    ↔    - √8

f     ↔    - 3/2

Step-by-step explanation:

Point d is to the left of -3

All points to the left of - 3 will be smaller than -3

Smaller than -3 means the absolute value will be greater than 3 but prefixed with a negative sign

Thus - 3.5 < - 3

-4 < -3

-99 < -3

etc

π = 3.14 approx

- π = - 3.14

- 3.14 < -3 and so it is to the left of -3. The only point to the left of -3 is point d

Similarly points to the right of -3 will have absolute values > 3 but prefixed by a negative sign

So -2.5, -2, -1, -0.5 etc are all greater than -3

√8 = √(4 · 2) = √4 · √2 = 2√2

√2 ≈ 1.414

so 2√2 ≈ 2.818

-√8 = - 2.818

so it is to the right of -3 but very close to -3

That would be point e

That leaves -3/2

-3/2 = - 1 1/2 and therefore lies halfway between -2 and - 1

That would be point f

Answer:

24 inches

Step-by-step explanation:

First, we need to convert the height of the wall to inches since the diameter of the window is given in inches:

18 feet = 18 x 12 inches = 216 inches

Next, we can find the distance from the floor to the top of the window by subtracting the height of the door from the height of the wall and then dividing by 2 (since the window will be centered above the door):

Distance from floor to top of window = (216 inches - 80 inches) / 2 = 68 inches

Finally, we can use the Pythagorean theorem to find the distance from the ceiling to the top of the window. We can consider the triangle formed by the height of the wall, the distance from the floor to the top of the door, and the distance from the floor to the top of the window. We can let x be the distance from the floor to the top of the window, then we have:

x^2 + 80^2 = 216^2

Simplifying this equation, we get:

x² = 216² - 80²

x² = 43,296 - 6,400

x² = 36,896

x = [tex]\sqrt{36,896}[/tex] = 192 inches

Therefore, the distance from the ceiling to the top of the window is:

Distance from ceiling to top of window = 216 inches - 192 inches = 24 inches

So the distance from the ceiling to the top of the window is 24 inches.

The statement as a function of Jessica earnings is f(x) = 10x + 15

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

Represent the number of hours worked with x

So, we have

f(x) = babysitting * x + bonus

This gives

f(x) = 10x + 15

Hence, the function is f(x) = 10x + 15

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Answer:

{-1, 1, 2, 3}

Step-by-step explanation:

To find A, we need to determine the set of all possible values of the first component of the ordered pairs in AxB.

Looking at the ordered pairs in AxB, we see that the possible values of the first component are -1, 1, 2, and 3. These correspond to the first components of the pairs (-1, 0), (1, 0), (2, 4), and (3, 5), respectively.

Therefore, A = {-1, 1, 2, 3}.

Answer:

Standard Deviation = 7.4

Standard deviation (denoted by symbol: σ ) is a measure of how dispersed or spread out the data is in relation to the mean. i.e, by how much the data deviates from the mean. A low standard deviation represents a sample that has its data clustered around the mean, and a high standard deviation represents indicates the data is more dispersed.

There are two primary ways of calculating the standard deviation. One is with the calculator, which will depend on what model/brand you use. The other method involves the formula for standard deviation:

[tex]\boxed{\sigma = \sqrt{\frac{\Sigma (x-\mu)^2}{N}}}[/tex]

[tex]\begin{tabular}{c | c | c }x & \math{(x - \mu)} & \math{(x-\mu)^2} \\\cline{1-3}1 & -9.8 & 96.04\\7 & -3.8 & 14.44\\9 & -1.8 & 3.24\\14 & 3.2 & 10.24\\23 & 12.2 & 148.84\\\end{tabular}\\\\\mu = 10.8\\\Sigma(x-\mu)^2 = 272.8 \\ N=5[/tex]

Now we have all the information we require, we can input values into the formula:

[tex]\sigma = \sqrt{\frac{272.8}{5}} = 7.38647... \approx 7.4[/tex]

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An equation for the transformed logarithm shown below, that passes through points (0, 0) and (-5, 2) is f(x) = 2log₆(x + 1).

By critically observing the logarithmic graph (see attachment) that models the logarithm function, we can logically deduce that it was reflected across the y-axis.

In Mathematics, the general form of a logarithm function is represented by the following mathematical equation:

f(x) = alog(±x + c)

Where:

Note: The vertical asymptote is at x = 1.

Next, we would determine the value of c and a by using the points (0, 0) and and (-5, 2):

0 = alog(0 + c)    .....equation 1.

2 = alog(5 + c)    .....equation 2.

By solving equations 1 and 2 simultaneously, we have:

1 = 0 + c

c = 1.

For the value of a, we have:

2 = alog(5 + c)

2 = alog(5 + 1)

2 = alog(6)

a = 2/log(6)

Therefore, the required logarithm function in compact form is given by:

f(x) = alog(±x + c)

f(x) = 2/log(6) × log(-x + 1)

f(x) = 2log₆(-x + 1)

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Answer:

it's 48

Step-by-step explanation:

you must do 480×10÷100

The measure of the angle is 35 degrees.

Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.... For example, a 50-degree angle and a 40-degree angle are complementary; a 60-degree angle and a 120-degree angle are supplementary.

Let's assume that x is the measure of the angle in question.

The complement of x is the angle that, when added to x, forms a right angle (90 degrees). Therefore, the complement of x can be represented as 90 - x.

According to the problem, the measure of the angle is 130 less than three times its own complement. We can write this information as an equation:

x = 3(90 - x) - 130

Simplifying and solving for x, we get:

x = 270 - 3x - 130

4x = 140

x = 35

Therefore, the measure of the angle is 35 degrees.

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Angela will earn interest of $50 at the end of 5 years and total earnings will be $550 at stated period.

The amount of simple interest will be calculated by the formula -

S.I. = P × R × T/100

Keep the values in formula to find the earned interest

S.I. = 500 × 2 × 5/100

Cancelling zeroes and performing multiplication

S.I. = 50

The simple interest is $50

Total amount will be calculated by adding the interest and principal value.

Total amount = 500 + 50

Total amount = $550

Hence, interest is $50 and total earnings are $550.

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The sums are 48, 52, 39, and 50

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here: The addition of three numbers

When adding, always line up the addends, the two numbers being combined, one on top of each other according to their place values. Add the numbers in the ones column first, then the tens column, and finally the hundreds column, to get the sum, or the total.

1) [tex]24+14+10=\bold{48}[/tex]

2) [tex]17+25+10=\bold{52}[/tex]

3) [tex]16+13+10=\bold{39}[/tex]

4) [tex]26+14+10=\bold{50}[/tex]

Thus the sums of the respective equations gives 48, 52, 39, and 50 respectively

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Answer:

Step-by-step explanation:

If you added all angles of triangle, add up to 180

to find 3rd angle subtract other 2 from 180.

ex.

1. 180-49-82 =49

2.  all angles are same so divide 180/3 =60

3. 45

4.  90

5. 79

6.   29

7.  70

8.   76

9.   30

10.  55

Answer:

Answer: (B) $2,450.

Step-by-step explanation:

To find the profit if the store sold 100 books, we can simply substitute n = 100 into the profit function:

p = 27n - 250

p = 27(100) - 250

p = 2,450

Therefore, the profit if the store sold 100 books is $2,450. Answer: (B) $2,450.

In that figure, we are informed that value of diameter is 20 feet. Radius would be (Diameter /2)=20/2 = 10 feet.

Circumference of circle = 2πr = 2*π*10=20πfeet =20*3.14 ft = 62.8ft

Answer:

If y varies directly with the square of x, we can express this relationship using the equation:

y = kx^2

where k is the constant of proportionality. To find the value of k, we can use the given information that y is 16 when x is 8:

16 = k * 8^2

Simplifying the equation, we get:

16 = 64k

Dividing both sides by 64, we get:

k = 16/64 = 1/4

So the equation that relates y and x is:

y = (1/4)x^2

We can use this equation to find the value of y for any given value of x. For example, if x is 10, we have:

y = (1/4) * 10^2 = 25

Therefore, when x is 10, y is 25.

Hence, the area of the patio is approximately 226.98 square feet, rounded to the nearest tenth.

In geometry, the circumference is the perimeter of a  ellipse or circle . That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

Area is the measure of a region size on a surface. The area of a plane area  or plane region  refers to the area of a planar lamina or shape , while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

To  determine the area of a  circular patio, we need to know its radius , by using  the formula:

Circumference = 2 *[tex]\pi[/tex]* radius

where [tex]\pi[/tex]  is  approximately 3.14.

radius = [tex]\frac{Circumference}{2 * \pi}[/tex]

according to  question,

radius = [tex]\frac{53.38}{2 * 3.14}[/tex] ≈ 8.5 feet

Now  , we know  that the area of a circle:

Area = [tex]\pi * radius^{2}[/tex]

Substituting the value of the radius

Area = 3.14 *[tex](8.5 feet)^{2}[/tex] ≈ 226.98 square feet

Therefore, the area of the patio is approximately 226.98 square feet, rounded to the nearest tenth.

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Answer: 3200, less

Step-by-step explanation:

The rate at which the space explorers fly in miles per hour is the slope.

Space explorer B flies at a rate of 6400 miles per hour. This is because

y=mx+b, where m is the slope.

Space explorer A flies at a rate of (32000-16000)/(10-5) = 3200 miles per hour.   Slope is (y2 - y1) / (x2 - x1) where the coordinates are (x1,y1) and (x2,y2).

Space explorer B - Space Explorer A = 6400 - 3200 = 3200.

Therefore space explorer A travels 3200 miles per hour less than explorer B.

Answer:

Step-by-step explanation:

From the graph A find slope = (32000-16000)/(10/5)=3200

So for the equation y=3200x  plug 1 in you get 3200

For B if you plug in 1 you get 6400 miles per hour

6400-3200=3200

A travels 3200 miles per hour slower than B

The probability that both M&Ms are green is 29% and the probability that John eats a red M&M then a green M&M is 25%

Here, we have

Red = 27

Green = 32

This means that

Total = 27 + 32

Total = 59

So, we have

P(Both green) = 32/59 * 31/58

Evaluate

P(Both green) = 29%

Here, we have

Red = 27

Green = 32

This means that

Total = 27 + 32

Total = 59

So, we have

P(Red and green) = 27/59 * 32/58

Evaluate

P(Red and green) = 25%

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The missing side of the triangle given the angle as 71° and hypotenuse as 17 to the nearest tenth is 16.1.

The correct answer choice is option C

Hypotenuse= 17

Opposite = x

Angle = 71°

Sin 71° = opposite / hypotenuse

sin 71° = x / 17

0.95105 = x / 17

cross product

0.95105 × 17 = x

x = 16.1 to the nearest tenth

In conclusion, the missing side of the triangle to the nearest tenth is 16.1

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Answer:

c = 108°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × (5 - 2) = 180° × 3 = 540°

since the pentagon is regular then the 5 interior angles are congruent, so

c = 540° ÷ 5 = 108°

First term: degree= 3 coefficient = -2

Second term: degree= 2 coefficient = -5

Third term: degree= 4 coefficient = -5

Fourth term: degree= 1 coefficient = -1

Fifth term: degree= 0 coefficient = 1

The leading coefficient is -5.

The degree of the leading term is 4.

The degree of the polynomial is 4.

A polynomial is an expression comprising components and coefficients, which are combined utilizing number juggling operations like extension, subtraction, and increment, but not division.

The degree of a term in a polynomial is the illustration of its variable. The coefficient of a term is the numerical figure that increments the variable.

For the case, inside the polynomial,  [tex]2x^5 - 3x^3 + x - 4 - 2x^-2,[/tex] the degree of the essential term[tex](2x^5)[/tex] is 5, and its coefficient is 2. So moreover, the degree of the third term (x) is 1, and its coefficient is 1.

The degree of the fourth term (-4) is 0, and its coefficient is -4. The degree of the fifth term [tex](2x^-2)[/tex] is -2, and its coefficient is 2. 

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The full question is
Given the polynomial,

-2x³- 5x²-[tex]5x4[/tex]+1-x

identify the coefficients and degree of each term:

First term: degree=

coefficient =

Second term: degree=

coefficient =

Third term: degree=

coefficient =

Fourth term: degree=

coefficient =

Fifth term: degree=

coefficient =

What is the leading coefficient?

What is the degree of the leading term?

What is the degree of the polynomial?

The figure you described can be a line segment or a line, depending on whether the arrows indicate that it has a finite length or extends infinitely in both directions.

Assuming that the arrows indicate a line segment, the geometric terms that describe the figure are

Line segment is a part of a line that has two endpoints, in this case, the segment RT or ST. Points are The individual locations on the line segment, in this case, R, T, and S. Length is the distance between the endpoints of the line segment, which can be found by measuring RT or ST

If the arrows indicate that the line extends infinitely in both directions, the geometric terms that describe the figure are Line is a straight path of points that extends infinitely in both directions.  Points are the individual locations on the line, in this case, R, T, and S.

Length is the line has no finite length but can be measured by finding the distance between any two points on the line.

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Answer:

To write a system of equations for this problem, we need to define two variables:

Let x be the number of hours the worker worked.

Let y be the number of shirts the worker made.

We can use the given information to write two equations:

The first equation relates the total expenses to the labor and material costs:

144 = 28x + 2y

The second equation relates the number of shirts to the number of hours and the average rate:

y = 4x

This is the system of equations we need to solve:

{144=28x+2yy=4x​

Simplify and solve for x:

144 = 28x + 8x

144 = 36x

x = 4

Now we can plug x = 4 into either equation to find y:

y = 4(4)

y = 16

So the worker worked for 4 hours and made 16 shirts.

Answer:

Step-by-step explanation:

C = [tex]\pi d[/tex]

  = [tex]\pi (7.09)[/tex]

  = =22.27 m

Answer:

The rectangle is 7 cm x 18 cm

Step-by-step explanation:

w = width

l = length

(1)  A = wl = 126 cm²

(2) P = 2w + 2l = 50 cm

Solve equation (2) for w:

2w = 50 - 2l

w = (50 - 2l) / 2 = 25 - l         plug this in to equation (1)

(25 - l)(l) = 126

-l² + 25l - 126

Use quadratic formula to find the 2 roots of l:  a = -1, b = 25. c = -126

l = 7, 18

Since l > w, then l = 18

Solve for w:

w = 126/18 = 7

Answer: D

Step-by-step explanation:

That line on the right is x=2 but the shaded area is less than 2 so one part is: x≤2

which eliminates A and C

then the line on top has a y-intercept at 2 and has a slope of 1, i plug that into y=mx+b  where m=1 and b=2

y=x+2 and the shaded area is under that line so y<x+2

Which would eliminate B

so D is my answer

Answer: The fourth / bottom answer.

Step-by-step explanation:

         To find the answer to this question, we will see which inequalities graphed represent the graph, as asked. We will write equations for the lines in the graph, then see which answer option lines up with the equations we find.

The vertical line can be represented by x ≤ 2

  ➜ The solid line tells us it will be a ≤ or ≥ symbol because it's also equal to. Since the shading is left of the line, it's less than or equal to.

  ➜ This rules out the first and third answer options.

Next, we will look at the two diagonal lines. These equations are written in slope-intercept form. The line graphed on top can be represented with y < x + 2

  ➜ The dashed line tells us it will be a < or > symbol because it's not equal to. Since the shading is below the line, it is less than or equal to.

  ➜ This rules out the second option.

The line graphed on top can be represented with y > -[tex]\frac{1}{4}[/tex]x - 3

  ➜ The dashed line tells us it will be a < or > symbol because it's not equal to. Since the shading is above the line, it is greater than or equal to.

  ➜ This leaves us with the fourth answer option as our answer.

The only answer option that aligns with the equations we found above is;

             The fourth / bottom answer.

x ≤ 2

y < x + 2

y > -[tex]\frac{1}{4}[/tex]x - 3

The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function [tex]f(x) = 2x + 4x^{(-1)}.[/tex]

First, we find the derivative of f(x):

[tex]f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2[/tex]

Setting f'(x) = 0 to find the critical points:

[tex]2 - 4/x^2 = 0[/tex]

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

[tex]f''(x) = 8x^{(-3)}[/tex]

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

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To multiply 3/4 by 16/9, you can multiply the numerators (top numbers) together to get the new numerator, and multiply the denominators (bottom numbers) together to get the new denominator. Then, simplify the resulting fraction if possible.

So,

(3/4) x (16/9) = (3 x 16) / (4 x 9)

= 48/36

= 4/3

Therefore, 3/4 multiplied by 16/9 is equal to 4/3.

A. The growth rate k is approximately 0.013, which means that the home value is increasing by about 1.3% per year

B.  The exponential model for the value of the home is V(t) = $95,000e^(0.013t).

C. The predicted value of the home in 2022 is approximately $123,539.

D. The value of the home reached $130,000 approximately 11.91 years after 2011, which is in 2023.

An exponential model is a mathematical model that describes exponential growth or decay. It is a function of the form [tex]y = ab^x[/tex], where a and b are constants, and x is the variable that represents time or another independent variable.

(a) To find the growth rate k, we can use the initial and final values of the home and the time period in between:

V(0) = $95,000 (the initial value in 2011)

V(7) = $105,000 (the final value in 2018, 7 years later)

Using the exponential model V(t) = V0ekt, we can set up the following equation:

V(7)[tex]= V(0)e^(k7)[/tex] = $105,000

$105,000/$95,000 = [tex]e^(k7)[/tex]

ln($105,000/$95,000) = k7ln(e)

k = ln($105,000/$95,000)/7 ≈ 0.013

The growth rate k is approximately 0.013, which means that the home value is increasing by about 1.3% per year.

(b) The exponential model for the value of the home is V(t) = $95,000e^(0.013t).

(c) To predict the value of the home in 2022, we can use t = 11 (since 2022 is 11 years after 2011) in the exponential model:

V(11) = $95,000e^(0.013*11) ≈ $123,539

The predicted value of the home in 2022 is approximately $123,539.

(d) To find the year when the value of the home reached $130,000, we can set up the following equation:

$130,000 = $95,000e^(0.013t)

ln($130,000/$95,000) = 0.013t

t ≈ 11.91

The value of the home reached $130,000 approximately 11.91 years after 2011, which is in 2023.

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A. The growth rate k is approximately 0.013, which means that the home value is increasing by about 1.3% per year

B.  The exponential model for the value of the home is V(t) = [tex]$95,000e^{(0.013t)[/tex]

C. The predicted value of the home in 2022 is approximately $123,539.

D. The value of the home reached $130,000 approximately 11.91 years after 2011, which is in 2023.

What is exponential model?

An exponential model is a mathematical model that describes exponential growth or decay. It is a function of the form , where a and b are constants, and x is the variable that represents time or another independent variable.

(a) To find the growth rate k, we can use the initial and final values of the home and the time period in between:

V(0) = $95,000 (the initial value in 2011)

V(7) = $105,000 (the final value in 2018, 7 years later)

Using the exponential model V(t) = V0ekt, we can set up the following equation:

V(7) = $105,000 = [tex]V(0)e^{(k7)[/tex]

$105,000/$95,000 = [tex]e^{(k7)[/tex]

ln($105,000/$95,000) = k7ln(e)

k = ln($105,000/$95,000)/7 ≈ 0.013

The growth rate k is approximately 0.013, which means that the home value is increasing by about 1.3% per year.

(b) The exponential model for the value of the home is V(t) = [tex]$95,000e^{(0.013t)[/tex].

(c) To predict the value of the home in 2022, we can use t = 11 (since 2022 is 11 years after 2011) in the exponential model:

[tex]V(11) = $95,000e^{(0.013*11)[/tex] ≈ $123,539

The predicted value of the home in 2022 is approximately $123,539.

(d) To find the year when the value of the home reached $130,000, we can set up the following equation:

[tex]130,000 = $95,000e^{(0.013t)[/tex]

ln($130,000/$95,000) = 0.013t

t ≈ 11.91

The value of the home reached $130,000 approximately 11.91 years after 2011, which is in 2023.

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The directed distance from point A to the curve at the angle theta = 5[tex]\pi[/tex]/6 is:

[tex]\sqrt(192 + 48\sqrt(3))[/tex]

To find the directed distance from point A to the curve at the angle theta = 5[tex]\pi[/tex]/6, we first need to find the equation of the tangent line to the curve at point A.

To do this, we can take the derivative of the curve equation with respect to x:

[tex]2x + 2y * dy/dx + 8 = 0[/tex]

Solving for dy/dx, we get:

[tex]dy/dx = -x / (y + 4)[/tex]

At point A, we have x = -4 and y = 4, so:

[tex]dy/dx = -(-4) / (4 + 4) = 1/2[/tex]

Therefore, the equation of the tangent line to the curve at point A is:

[tex]y - 4 = (1/2) * (x + 4)[/tex]

Simplifying, we get:

[tex]y = (1/2) * x + 6[/tex]

Now we can find the intersection point of the tangent line with the line passing through point A and making an angle of 5π/6 with the positive x-axis.

The line passing through point A with angle 5π/6 has slope:

[tex]tan(5\pi /6) = -\sqrt(3)[/tex]

So the equation of this line is:

[tex]y - 4 = -\sqrt(3) * (x + 4)[/tex]

Simplifying, we get:

[tex]y = -\sqrt(3) * x + 4\sqrt(3) + 4[/tex]

Now we can solve for the intersection point of the two lines. Setting the equations for y equal to each other, we get:

[tex](1/2) * x + 6 = -\sqrt(3) * x + 4\sqrt(3) + 4[/tex]

Solving for x, we get:

[tex]x = -8 / (2 + \sqrt(3))[/tex]

Now we can find the corresponding value of y using either equation for the tangent line or the line with angle 5π/6. Using the equation for the tangent line, we get:

[tex]y = (1/2) * (-8 / (2 + \sqrt(3))) + 6 = 11 - 4\sqrt(3) / (2 + \sqrt(3))[/tex]

The directed distance from point A to this intersection point is the distance between these two points along the line with angle 5π/6. This distance can be found using the distance formula:

[tex]d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

Plugging in the values, we get:

[tex]d = \sqrt((-4 - (-8 / (2 + \sqrt(3))))^2 + (4 - (11 - 4\sqrt(3) / (2 + \sqrt(3))))^2)[/tex]

Simplifying, we get:

[tex]d = \sqrt(192 + 48\sqrt(3))[/tex]

Therefore, the directed distance from point A to the curve at the angle theta = 5π/6 is:

[tex]\sqrt(192 + 48\sqrt(3))[/tex]

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The directed distance from point A to the point on the curve corresponding to θ = 5π/6 is 4 units.

What is curve?

In mathematics, a curve refers to a continuous and smooth line that has no corners or edges. Curves can be described using equations or parametric equations, and they can be represented in a two-dimensional or three-dimensional space.

To find the directed distance when θ = 5π/6, we first need to find the corresponding point on the curve.

The equation [tex]x^2 + y^2 + 8x = 0[/tex] can be rewritten as [tex](x + 4)^2 + y^2 = 16[/tex], completing the square. This is the equation of a circle with center (-4, 0) and radius 4.

To find the point on the circle corresponding to θ = 5π/6, we can use polar coordinates. Let r be the radius of the circle (r = 4), and let θ be the angle from the positive x-axis to the point we want to find. Then we have:

x = r cos(θ) = 4 cos(5π/6) = -2√3

y = r sin(θ) = 4 sin(5π/6) = 2

So the point on the curve corresponding to θ = 5π/6 is (-2√3, 2).

To find the directed distance from point A (-4, 4) to this point, we can use the distance formula:

distance = √[[tex](x2 - x1)^2 + (y2 - y1)^2[/tex]]

= √[[tex](-2\sqrt3 - (-4))^2 + (2 - 4)^2[/tex]]

= √[12 + 4]

= 2√4

= 4

Therefore, the directed distance from point A to the point on the curve corresponding to θ = 5π/6 is 4 units.

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