The function y = f(a) is graphed below. What is the average rate of change of the
function f(a) on the interval -8 < < 8?

The Function Y = F(a) Is Graphed Below. What Is The Average Rate Of Change Of Thefunction F(a) On The

Answers

Answer 1

Answer: -35/16

Step-by-step explanation:

[tex]f(8)=-5\\\\f(-8)=30\\\\\frac{f(8)-f(-8)}{8-(-8)}=\frac{-5-30}{16}=\boxed{-\frac{35}{16}}[/tex]

The Function Y = F(a) Is Graphed Below. What Is The Average Rate Of Change Of Thefunction F(a) On The

Related Questions

There are 60 students studying Sciences (Biology, Chemistry or Physics). 7 students study Biology, Chemistry and Physics. 12 students study Biology and Chemistry. 15 students study Biology and Physics. 20 students study Chemistry and Physics. 35 students study Biology. 32 students study Physics. B Complete the Venn diagram. E P C There are 60 students studying Sciences ( Biology , Chemistry or Physics ) . 7 students study Biology , Chemistry and Physics . 12 students study Biology and Chemistry . 15 students study Biology and Physics . 20 students study Chemistry and Physics . 35 students study Biology . 32 students study Physics . B Complete the Venn diagram . E P C​

Answers

Answer:

8 in the box.

Step-by-step explanation:

As, it is given that 35 students study Biology.

So, in Biology circle,

15+7+5+x=35

27+x=35

x=35-27

x=8

y=2x^2-4x-3
Solve quadratic questions

Answers

By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.

How to find the roots of a quadratic equation

All quadratic equations of the form a · x² + b · x + c = 0 have two roots that can be found by using the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]     (1)

If we know that a = 2, b = - 4 and c = - 3, then the roots of the quadratic equations are:

[tex]x = \frac{4 \pm \sqrt{(-4)^{2}-4\cdot (2) \cdot (- 3)}}{2\cdot (2)}[/tex]

[tex]x = 1 \pm \frac{\sqrt{40}}{4}[/tex]

[tex]x = 1 \pm \frac{\sqrt{10}}{2}[/tex]

By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.

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[tex]\frac{1}{28} + \frac{1}{70} + \frac{1}{130} + \frac{1}{208} + \frac{1}{304} = ?[/tex]

Evaluate this expression.

Answers

Considering the least common multiple of the denominators, it is found that the result of the expression is given by:

[tex]\frac{9100}{138320}[/tex]

How do we add fractions?

We place all the terms of the addition in "equivalent" fractions, with the same denominator, found from the last common multiple of all the denominators.

In this problem, the denominators are as follows: 28, 70, 130, 208, 304. Using a calculator, their lcm is of 138,320.

Considering equivalent fractions(the numerators are the division of the lcm by the previous denominator), the expression is:

[tex]\frac{4940}{138320} + \frac{1976}{138320} + \frac{1064}{138320} + \frac{665}{138320} + \frac{455}{138320} = \frac{4940 + 1976 + 1064 + 665 + 455}{138320} = \frac{9100}{138320}[/tex]

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Which sequences are geometric? Check all that apply.
5, 10, 20, 50,...
3, 12, 48, 192,...
3, 15, 75, 375,...
8, 15, 75,375,...
14, 21, 28, 35,...
17, 20, 23, 26,...
2, 10, 50, 250,...

Answers

Answer:

The first, third and last sequences

What is the solution to the following system?
4x+3y-z=-6
6x-y+3z=12
8x+2y+4z=6
x= 1, y = -3, z = -1
x= 1, y=-3, z = 1
x = 1, y = 3, z = 19
x = 1, y = 3, z = -2

Answers

The solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have three linear equations in three variable:

4x + 3y - z = -6 ..(1)

6x - y+ 3z = 12 ..(2)

8x + 2y + 4z = 6 ...(3)

From the equation (1)

[tex]\rm x=\dfrac{-6-3y+z}{4}[/tex]

Substitute the above value in the equation (2) and (3):

[tex]\rm 6\cdot \dfrac{-6-3y+z}{4}-y+3z=12\\\\ 8\cdot \dfrac{-6-3y+z}{4}+2y+4z=6[/tex]

After simplification:

[tex]\rm -11y+9z-18=24\\ -4y+6z-12=6[/tex]

After solving the above two equations by substitution method:

z = 1

y = -3

Plug the above two values in the equation (1), we get:

x = 1

Thus, the solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.

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Select the correct answer.

Choose the system of inequalities that best matches the graph below.

Answers

Answer:

Its A

Step-by-step explanation:

I said so

Alaric wants to determine if he can get a better grade in math by studying for longer periods of time.
He plans to experiment for 4 weeks.
Which statement is true of this experiment?
a.) The duration of Alaric's experiment is the explanatory variable.
b.) Alaric's math grade is the explanatory variable.
c.) The amount of time Alaric spends studying is the response variable.
d.) Alaric's math grade is the response variable.

Answers

The statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.

What is an explanatory variable?

It is defined as the variable which is independent. They show the expected results and the result is known as the response variable which is dependent on the explanatory variable.

We have given:

Alaric wants to determine if he can get a better grade in maths by studying for longer periods of time.

The duration of the experiment is 4 weeks which is known or constant.

But the number of hours she studied is a variable, and it is independent.

The maths grade is the dependent variable which is on the number of hours Alaric study variable.

Thus, the statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.

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One positive number is 8 times another number. Their difference is 70.
Which of the following equations could be used to find the numbers?

Answers

Answer:

X equals 10.

8x - x = 70

Step-by-step explanation:

8 x 10 = 80

80 - 10 = 70

Which function is represented by this graph? A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line falls through (negative 6, 10), (0, 4), (4, 0) to (7, negative 3), and then it rises through (10, 0). A. f(x) = |x + 7| − 3 B. f(x) = |x − 7| − 3 C. f(x) = |x + 3| − 7 D. f(x) = |x − 3| − 7

Answers

The line that represents the graph satisfying all condition is  f(x) = |x − 7| − 3.

What is graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

As, the points are given.

We have to find which equation  satisfies all the points.

f(x) = |x − 7| − 3

put x= -6

y=  13-3 = 10

Similarly by putting all the values the only condition that satisfies is

f(x) = |x − 7| − 3

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The formula M = 5/8 K gives the approximate distance in miles as a function of kilometers. Use the inverse to express 25 miles in kilometers.​

Answers

M = 5/8 K
8/5 M = 8/5 x 5/8 K = K
K = 8/5 x 25 = 40 km

The slope of the line below is 0.8. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side. Coordinates (-2,-3)

Answers

The equation of the line is y = 0.8x - 1.4 if the  slope of the line is 0.8 and line passes through coordinates (-2,-3)

What is a straight line?

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope m = 0.8

The line passing through coordinates (-2,-3)

y = mx + c

y = 0.8x + c

Plug the point in the equation.

-3 = 0.8(-2) + c

c = -1.4

y = 0.8x - 1.4

Thus, the equation of the line is y = 0.8x - 1.4 if the  slope of the line is 0.8 and line passes through coordinates (-2,-3)

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Select the correct answer.

A system of equations and its solution are given below.

System A
x + y = 8
4x - 6y = 2
Solution: (5,3)

Choose the correct option that explains what steps were followed to obtain the system of equations below.

System B
x + y = 8
10x = 50

Answers

Answer:

B will be the answer...

Step-by-step explanation:

The second equation in system B is only in terms of y, so we need to use elimination to eliminate the x term from the second equation in system A.

To do that, we need to multiply the first equation by 5.

5 (-x − 2y = 7)

-5x − 10y = 35

Add to the second equation.  Notice the x terms cancel out.

(-5x − 10y) + (5x − 6y) = 35 + (-3)

-16y = 32

Combining this new equation with the first equation from system A will get us system B.

-x − 2y = 7

-16y = 32

Answer:

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution to system A.

Step-by-step explanation:

exact answer

one interior angle of a polygon is a right angle and each of the other interior angles is 126°. Calculate the number of sides of the polygon​

Answers

Answer:

There are 7 sides.

Step-by-step explanation:

Let's Use the formula that states that the sum of the angles of an n-sided polygon is given by.

S=(n−2)180

Since we are given that the two angles are right, the angles and each of the remaining angles is 144.

And Therefore, the sum is:

S=90

(n−2)144

(n−2)180

=90

+90

+(n−2)144

⇒(n−2)180

−(n−2)144

=180

⇒(n−2)(180

−144

)=180

⇒(n−2)(36

=180

⇒n−2=

36

180

​⇒n−2=5

⇒n=5+2=7

Hence, the polygon has 7 sides.

The number of sides of the polygon such that one angle is the right angle will be 6.

What is an angle?

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

In any closed polygon, the number of sides is equal to the number of interior angles.

Suppose the number of sides is n in the given polygon.

Sum of angles = 90° + 126° × (n - 1)

The sum of angles is given as, 180(n - 2)

90° + 126° × (n - 1) = 180(n - 2)

90 + 126n - 126 = 180n - 360

180n - 126n = 90 - 126 + 360

54n = 324

n = 6

Hence "The number of sides of the polygon such that one angle is the right angle will be 6".

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Complete the recursive formula of the geometric sequence 56, -28, 14, -7,....

Answers

Step-by-step explanation:

each term in the sequence is half of the value of the previous term, and in the opposite sign.

therfore, the quotient between terms is (-2)

so, to get one term from the previous term, we multiply by 1/(-2), so:

d(n) = d(n-1) × 1/(-2)

the first term is 56 so d(1)=56

Answer:

56 and -1/2

Step-by-step explanation:

khan

Solve the equation x³ - 5x²+2x+8 = 0 given that - 1 is a zero of f(x)= x3 - 5x²+2x+8.
The solution set is? (Use a comma to separate answers as needed.)

Answers

Answer:

added in the picture

Step-by-step explanation:

added in the picture

need help with this question im stuck

Answers

Answer:

answer is B. 100°

Step-by-step explanation:

if correct please I need brainlist

Answer:

100°

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary, i.e., they add up to 180°.

The 80° angle and angle x are opposite each other, so:
x + 80° = 180°

x = 180° - 80°

  x = 100°

Can y’all please help me with this ! Everybody have a good day!

Answers

Answer: A. She substituted incorrectly into the distance formula


She should be subtracting x from x and y from y but she is subtracting y from x.

Answer is A they are supposed to minus one set of x and y but Helen subtracted the x values and y values

The exterior angles of a triangle are (2x+10),(3x+15)and (4x+20). What is the value of x and what is the largest interior angle of the triangle?

Answers

Answer:

x = 35 and 100°

Step-by-step explanation:

the sum of the exterior angles of a triangle = 360° , then

2x + 10 + 3x + 15 + 4x + 20 = 360 , that is

9x + 45 = 360 ( subtract 45 from both sides )

9x = 315 ( divide both sides by 9 )

x = 35

then each exterior angle is

2x + 10 = 2(35) + 10 = 70 + 10 = 80°

3x + 15 = 3(35) + 15 = 105 + 15 = 120°

4x + 20 = 4(35) + 20 = 140 + 20 = 160°

the sum of an exterior angle and corresponding interior angle = 180°

then

180° - 80° = 100°

180° - 120° = 60°

180° - 160° = 20°

the largest interior angle of the triangle is 100°

Answer:

x = 35

largest interior angle = 100°

Step-by-step explanation:

The exterior angles of a triangle sum to 360°

⇒ (2x + 10) + (3x + 15) + (4x + 20) = 360

⇒ 2x + 10 + 3x + 15 + 4x + 20 = 360

⇒ 9x + 45 = 360

⇒ 9x = 315

x = 35

Therefore, the three exterior angles are:

(2x + 10) = 2(35) + 10 = 80°(3x + 15) = 3(35) + 15 = 120°(4x + 20) = 4(35) + 20 = 160°

If the side of a triangle is extended, the angle formed outside the triangle is the exterior angle.  As angles on a straight line sum to 180°:

⇒ interior angle + exterior = 180°

So the largest interior angle will be the supplementary angle to the smallest exterior angle.

The smallest exterior angle is 80°, so:

⇒ largest interior angle + 80° = 180°

⇒ largest interior angle = 180° - 80°

largest interior angle = 100°

Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.5 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number.

Answers

Answer:

6.3 *30= 189; so 4 cotton swabs

Two vertical angles are complementary. Statement is always, sometimes, or never true. Explain your reasoning

Answers

Answer:

depends upon the degree of the angle

Step-by-step explanation:

vertically opposite angles are always equal like

80 = 80 sum is equal to 160 degrees not equal to 90

45 = 45 , sums equal to 90 degrees ,equal to 90

30 = 30 sum is equal to 60 degrees, not equal to 90

so we can say it depends what is the no of degrees if it is  45 only we can say  the vertically opposite angles are  complementary angle

Ella wants to buy a home. The maximum loan she can get from the bank is $445,000
If Ella has $55,000 available to make a down payment, what is the highest valued home she can purchase?

Answers

Ella can buy a house worth $5 million

What is a Loan ?

Loan is the amount of money borrowed from a bank or any other person , The amount has to be returned back with a Interest.

It is given that

The maximum loan Ella can get from the bank is $445,000

Ella has $55,000 available to make the down payment.

The highest value home that she can purchase is the sum of money she has and the maximum amount of money she can get from the bank.

It is given by

$445,000 +  $55,000

$500,000

Therefore Ella can buy a house worth $5 million

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look at the picture

Answers

Answer:

The x-intercept is 2.

Step-by-step explanation:

[tex]2 \sqrt[3]{x - 10} + 4 = 0[/tex]

[tex]2 \sqrt[3]{x - 10} = - 4[/tex]

[tex] \sqrt[3]{x - 10 } = - 2[/tex]

[tex]x - 10 = - 8[/tex]

[tex]x = 2[/tex]

Assume that the function f is a one-to-one function.
a. if f(3)=9, find ^-1 (9)

b. if f^-1(-8)=-9 , find f(-9)

Answers

Answer:

a. 3

b. -8

Step-by-step explanation:

let me know if you want an explanation

Solve 8x + c = k for x.
A. x=8(k-c)
OB. x=
_k+c
8
O C. x = 8(k+c)
O D. x=
k-c
8

Answers

Answer: [tex]x=\frac{c-k}{8}[/tex]

Step-by-step explanation:

[tex]1) \text { } 8x+c=k \text{ (given)}\\\\2) \text { }8x=c-k \text{ (subtract } k \text{ from both sides)}\\\\3) \text { } \boxed{x=\frac{c-k}{8}} \text{ (divide both sides by 8)}[/tex]

PLEASE HELP I WILL GIVE BRAINLEST!!!!!!

Below is the graph of a polynomial function with real comedic fangs. All local extreme of the function are shown in the graph.
Use the graph to answer the following questions.

(a) over which intervals is the function decreasing? Choose all that apply.
(-∞,-8) (-8,-4) (-4,0) (0,5) (-4,5) (9, ∞)

(b) At which x-values does the function have local minima? If there is more than one value seepage them with commas.

(C) what is the sign of the function’s leading coefficient?
Answers are positive, negative, not enough time

(D) which of the following is a possibility for the degree of the function? Choose all that apply
4 , 5 , 6 , 7 , 8 , 9

Answers

Part (a)

Decreasing means that as x increases, y decreases.

So the intervals are [tex](-8, -4), (0, 5), (9, \infty)[/tex]

Part (b)

A local minimum is where the function changes from decreasing to increasing.

So, the local minima are at [tex]x=-4, 5[/tex]

Part (c)

The function is approaching negative infinity as x approaches both positive and negative infinity, so the leading coefficient is negative

Part (d)

The degree is given by the number of roots (including multiplicity).

From the graph, we see there is a single root at x = -6, a single root at x = -1, a single root at x = 1, a single root between x=6 and x=8, and a single root at around x = 10.

Thus, there are a minimum of 5 roots for the graph (there could be more outside of the given section)

However, since the graph has the same end behavior in both directions, the degree must be even.

So, the possible answers are any even number that is at least 6

X -6,-3,0,3,6 y 0 1 2 3 4 which equation contains the coordinate parts given in the table

Answers

The linear equation that contains the coordinate parts in the given table is: y = 1/3x + 2.

How to Find the Equation of a Linear Equation?

To find the linear equation that contains the coordinate parts in the table given, find the slope (m) and y-intercept (b), then substitute the values into y = mx + b.

Slope (m) using two coordinate parts, (0, 2) and (3, 3):

Slope (m) = change in y / change in x = (3 - 2)/(3 - 0)

Slope (m) = 1/3

y-intercept (b) = 2 [this is the value of y when x = 0)

Substitute the values into y = mx + b

y = 1/3x + 2.

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Write a function rule for the table.

Days

1
2
3
4

Cost to Rent a Truck

29
47
65
83

Answers

Answer:

can you give upload the pictures

For every day that passes the cost to rent a truck increases 18

Here it is: y = 18x + 11


An electrical resistor is rated at 4500 ohms ± 3%. Express this tolerance in ohms and state the
actual range of resistance.

Answers

Answer:

Range =  4365-4635

Step-by-step explanation:

4500 * 3/100 = 135

4500 + 135  = 4635

4500 - 135  = 4365

Range =  4365-4635

The actual range of resistance is from 4365 ohms to 4635 ohms.

How to determine the tolerance in ohms and state the actual range of resistance.

To express the tolerance in ohms, we need to calculate 3% of the rated resistance, which is 4500 ohms.

Tolerance in ohms = 3% of 4500 ohms

Tolerance in ohms = 0.03 * 4500

Tolerance in ohms = 135 ohms

The actual range of resistance can be found by adding and subtracting the tolerance from the rated resistance:

Lower limit = Rated resistance - Tolerance

Lower limit = 4500 ohms - 135 ohms

Lower limit = 4365 ohms

Upper limit = Rated resistance + Tolerance

Upper limit = 4500 ohms + 135 ohms

Upper limit = 4635 ohms

So, the actual range of resistance is from 4365 ohms to 4635 ohms.

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determine weather y varies directly with x. if so, find the constant variation and write the equation

Answers

Answer:

Yes, k = 1/3 and y = 1/3x

Step-by-step explanation:

[tex]\text{The given line passes through the origin, hence it has equation of the form:}\\y=kx[/tex]

[tex]\text{Therefore y varies directly as x.}The line passes through the point (3,1)}[/tex]

[tex]\text{This implies that,}[/tex]

[tex]1=k(3)\\k=\frac{1}{3}[/tex][tex]\text{Hence the constant of variation is}[/tex] ⇒ [tex]\frac{1}{3}[/tex]

The equation would be ⇒ [tex]y=\frac{1}{3} x[/tex]

The assets (in billions of dollars) for a financial firm can be approximated by the function A(x)=318e^0.27x, where x=7 corresponds to the year 2007. Find the assets in each following years. A)2012 B) 2014 C) 2017

Answers

The value of the asset in 2012, 2014, and 2017 are 8119.72, 13933.55 and, 31321.23, respectively. A function assigns the values.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given the assets (in billions of dollars) for a financial firm can be approximated by the function [tex]A(x)=318e^{0.27x}[/tex], where x=7 corresponds to the year 2007. Therefore, the assets value in the following years will be,

A.) 2012 - [tex]A(12)=318e^{0.27\times 12} = 8,119.72[/tex]

B.) 2014 - [tex]A(14)=318e^{0.27\times 14} = 13,933.5[/tex]

C.) 2012 - [tex]A(17)=318e^{0.27\times 17} = 31,321.23[/tex]

Hence, the value of the asset in 2012, 2014, and 2017 are 8119.72, 13933.55 and, 31321.23, respectively.

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X-6-103y-719-2What is the domain of the given function?O {x|x = -6, -1, 0, 3}(y ly=-7, -2, 1, 9}{x|x=-7, -6, -2, -1, 0, 1, 3, 9}(y ly=-7, -6, -2, -1, 0, 1, 3, 9}1 match each histotical period with the main type of art market that existed at that time Construct a truth table for the following symbolic statement.Use the type of truth table where each variable or operator in the given expression has its own column. Fill in the rows of the truth table one at a time. what is the 10th term for sequence 4; 8; 13; 19; 26 Given two points of a line, find its slope.(3, 1), (7,4) When is your breathing likely to speed up?A. When your heart cells need more carbon dioxideB. When your white blood cells increaseC. When your blood cells have too much oxygenD. When your cells need more energy If you were a policy maker in country lt, how would you ensure that the ideals of free enterprise are preserved while protecting the citizens of your nation? explain your answer in three to four sentences. which condition is consistent with a client's report of posterior leg pain while walking that worsens upon rest evaluate-4x + 2y - z if x = - 2, y = 3, and z = -4 An uncharged spherical conductor hangs by an insulating thread. You bring a negatively charged rod nearfrom the left side. The net charge on the hanging conductors left side is (choose one):a. Positiveb. Negativec. Neutral A truck accelerating at 0.0083 meters/second2 covers a distance of 5.8 104 meters. If the truck's mass is 7,000 kilograms, what is the work done to reach this distance? What role are you, as a Muslim, playing in the requirements of faith in the beloved Prophet in the present age? Write a paragraph in your own words Find the value of x. Round the length to the nearest tenth. What are 2 ways to send a message to your client when signed in as an accountant user?. a nurse administers albuterol (proventil), as ordered, to a client with emphysema. which finding indicates that the drug is producing a therapeutic effect? 25:50=4x:8. What is the value of X find the total surface area of this triangular prism 21cm 29cm 20cm 22cm Which of these choices was an effect of the Emancipation Proclamation? what is the measure of Read the passage from Sugar Changed the World.You could date a great change in the world to a visit one Madame Villeneuve made to France in 1714. That year, Pauline, an enslaved woman from the Caribbean, arrived in France as the personal servant of her mistress. When Madame Villeneuve set off from the coast to visit Paris, she left Pauline in a convent. The young woman spent her time studying with the nuns and went so far in her training that she asked to become a nun herself and remain in the convent. The nuns agreed, which enraged Madame Villeneuve. She rushed to a judge, demanding to have her property back. Was Pauline a free woman, a bride of Christ, or an item to be bought, sold, and warehoused when she was not in use?Twenty-three years earlier, King Louis XIV had issued a set of rules that defined slavery as legal in the French sugar islands. But when two slaves managed to reach France, he freed themsaying they became free "as soon as they [touched] the soil" of France. The judges sided with Paulineshe was real to them, human, not a piece of property. For Pauline's judges, as for King Louis, slavery far off across the seas was completely different from enslaved individuals in France.What claim do the authors make in this passage?Madame Villeneuve deserves credit for persuading the judges that enslaved people should not be property.Freeing Pauline would have a significant effect on how people viewed involuntary servitude.Because so many other people remained enslaved, Pauline's specific case was not very important.The disagreement between King Louis XIV and the judges would have major effects on laws.