Antonina goes on Wheel of Fortune and wins $12,000 after taxes. She decides that she will invest this money with the goal of putting a $20,400 down payment on a house. She puts the money in a mutual fund that has had a historical return of 7.5%.
a. (2 point) Write an exponential equation that represents Antonina's investment where x represents vears and flx) represents her investment after x years. Assume the mutual fund earns a 7.5 annual rate of return.
b. (2 point) Calculate how long it will take to reach her investment goal. Round to 2 decimal places.

Answer:

f(x)  :  exponential growth

g(x);  exponential growth

h(x):  exponential growth

j(x):   exponential decay

Step-by-step explanation:

In an exponential function such as
[tex]m(x) = a \cdot b^x[/tex]

the factor that determines whether it is a growth or decay function depends entirely on the value of b since x cannot be negative

If b > 1, it is a growth function

If b < 1 then it is a decay function

If b = 1 neither growth or decay function values are constant

In this context
f(x) has b = 2 > 1 . Hence it is a growth function
g(x) has b = 3 > 1 hence growth function
h(x) has be = 3/2 > 1; hence growth function
j(x) has be = 0.5 < 1 hence decay function

Answer:

O f(x)  :  exponential growth

O g(x);  exponential growth

O h(x):  exponential growth

O j(x):   exponential decay

Step-by-step explanation: I used to do this before :)

Answer:

Step-by-step explanation:

about 18.7

Answer:

18.7

Step-by-step explanation:

2 gray cars / 15 cars = x gray cars / 140 cars

Solving for x, we get:

x = 2 gray cars * 140 cars / 15 cars

x = 18.67 gray cars

Therefore, the option D is correct [tex]\frac{4dollar}{1lb}[/tex]

The rate of change of a linear function is the slope of the line, which represents the rate at which the output (dependent variable) changes with respect to the input (independent variable).

A line's slope is calculated by dividing the difference in y-coordinates between any two locations on the line by the difference in x-coordinates. Geometrically, the slope is the tangent of the angle that the line makes with the x-axis.

Here in the graph we have x and y values find out the slope,

To calculate the slope of a line from two points (x1, y1) and (x2, y2), we use the formula:

[tex]Slope =\frac{(y2 - y1)}{(x2 - x1)}[/tex] = 4 (for every two points)

So, the line is linear and the rate of change of this linear function is 4/1, which means that for every 1 lb increase in the x-coordinate, the y-coordinate (the output) increases by $4.

Therefor the option D is correct [tex]\frac{4dollar}{1lb}[/tex]

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The electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.

What is an electric field?

An electric field is a region in which an electric charge experiences a force. It is created by an electric charge or a changing magnetic field. Electric fields exist everywhere in nature and are vital to the functioning of many electronic devices. Electric fields are also used to describe the motion of electrons in a conductor and the behavior of electric currents.

The electric field at the origin (x=0, y=0) can be calculated using the equation of electric field,

E = k(q1/r1² + q2/r2²)

Where k is the Coulomb's constant, q1 and q2 are the charges and r1 and r2 are the distances from the charges to the origin.

The electric field at the origin can be calculated by substituting the given values in the equation.

The distance from the charge at y = 4.0 cm to the origin is 5 cm and the distance from the charge at y = -4.0 cm to the origin is also 5 cm.

E = 8.988 X 10⁹ (3.8 X 10⁻⁹/25 + 3.8 X 10⁻⁹/25)

E = 8.99 X 10⁹ (3.8 X 10⁻⁹/25)

E = 1.05 X 10⁷ N/C

Therefore, the electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm is 1.05 X 10⁷ N/C.

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Right Question:-

Two positive charges on the y axis has a charge of 3.8 X 10^-9 are located at y, Find electric field at the origin due to two positive charges on the y axis with a charge of 3.8 X 10⁻⁹ located at y = 4.0 cm and y = -4.0 cm?

Probability of rolling a number greater than 0 but less than 7 is 1.

The probability formula is as follows:

Probability = Favourable outcomes / Total outcomes

Sample space of rolling a dice:

S = {1, 2, 3, 4, 5, 6}

Total outcomes = 6

Favourable outcomes: number greater than 0 but less than 7

Favourable outcomes: 6

Then, probability of rolling a number greater than 0 but less than 7

Probability = Favourable outcomes / Total outcomes

Probability = 6/6

Probability = 1

Thus,  probability of rolling a number greater than 0 but less than 7 is 1.

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The complete question is-

A dice is being rolled. Find the probability of rolling a number greater than 0 but less than 7

Answer:

For the lifetime membership to be cheaper than paying $550 in annual membership dues, we need to calculate the present value of the lifetime membership and compare it to the present value of the stream of annual payments.

The present value of the lifetime membership can be calculated using the formula for the present value of a lump sum:

PV = FV / (1 + r)^n

where FV is the future value (which is the cost of the lifetime membership today, $5,000), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.

The present value of the stream of annual payments can be calculated using the formula for the present value of an annuity:

PV = A * [(1 - (1 + r)^-n) / r]

where A is the annual payment ($550), r is the annual interest rate (7.5%), and n is the number of years for which we want to calculate the present value.

We need to find the minimum number of years for which the present value of the lifetime membership is less than the present value of the stream of annual payments. We can do this by setting the two present values equal to each other and solving for n:

5000 / (1 + 0.075)^n = 550 * [(1 - (1 + 0.075)^-n) / 0.075]

Solving this equation gives n ≈ 18.7 years. Rounded up to the nearest year, this means that Lloyd must remain a member of the ADLA for at least 19 years for the lifetime membership to be cheaper than paying $550 in annual membership dues.

Therefore, the answer is 19 years.

For the second question, we can use the formula for the future value of a lump sum:

FV = PV * (1 + r)^n

where PV is the present value ($24), r is the annual interest rate (4.5%), and n is the number of years (392).

Substituting the given values, we get:

FV = 24 * (1 + 0.045)^392

FV ≈ $859,993,041.68

Therefore, the value of the $24 purchase price as of 2018 is approximately $859,993,041.68.

Answer:

38

Step-by-step explanation:

Let x represent the number of days Timmy has been driving his car since he had 3,000 miles on it. Then, his total mileage can be represented as:

Total mileage = 3,000 + (38 × x)

This is a linear model, because the relationship between the total mileage and the number of days driven is a straight line with a constant slope of 38. The y-intercept of this line is 3,000, which represents the initial mileage on Timmy's car. The slope of 38 indicates that the car is being driven 38 miles further each day, which corresponds to the rate of change in the total mileage.

Answer: Since there are 500 tumblers in each batch, there are a total of:

500 tumblers/batch × 3 batches = 1500 tumblers

To make a set of 3 tumblers with one tumbler of each color, we can choose one tumbler from each batch. There are 500 choices for the tumbler from the red batch, 500 choices for the tumbler from the yellow batch, and 500 choices for the tumbler from the purple batch. Therefore, there are:

500 choices for the first tumbler × 500 choices for the second tumbler × 500 choices for the third tumbler = 500^3 = 125,000,000 possible sets of 3 tumblers.

However, we are interested in the number of sets that can be made from the available tumblers. Each set requires one tumbler from each batch, and since there are 500 tumblers in each batch, we can make:

500 sets/batch = 500 sets/batch × 3 batches = 1500 sets

Therefore, we can make a total of 1500 sets of 3 tumblers from the available tumblers.

Step-by-step explanation:

Answer:

If the new cereal box contains 20% more than the original cereal box, then the original cereal box contained 100% - 20% = 80% of the new cereal box.

Let X be the original cereal box amount in ounces, then we can set up the following equation:

X + 0.20X = 18.48

Simplifying and solving for X:

1.20X = 18.48

X = 15.40

Therefore, the original cereal box amount was 15.40 ounces.

One possible solution of this system is Arun has 5 nickels and 15 pennies.

One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system.

x+y≥20

0.05x+0.01y≤0.40

x≥0

y≥0

Inequality: y≥20-x

Inequality: y≥5x-40

x≥0

y≥0

The solution set satisfying the inequality is shown in black area above when x=5 and y=15

So, Arun has 5 nickels and 15 pennies.

Graph of the system of inequalities is attached below.

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Using the data points given, the equation is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].

What is an ellipse?

An ellipse is a locus of a point that moves in such a way that its perpendicular distance from a fixed straight line (directrix) and its distance from a set point (focus) remain constant. which is smaller than unity, i.e. eccentricity(e).

We are given that the center of the ellipse is at (4,-2), and a vertex is at (9,-2).

We know that the distance from the center to a vertex is a, where a is the length of the semi-major axis.

Therefore, we have -

a = 9 - 4 = 5

Since the point (4,3) is on the ellipse, we can use the distance formula to find the length of the semi-minor axis -

c = distance from (4,-2) to (4,3)

c = [tex]\sqrt{((4-4)^2 + (3-(-2))^2}[/tex]

c = 5

Now, we can use the equation of an ellipse -

[tex]\frac{\Big(\frac{(x - h)^2}{a^2}+ (y - k)^2\Big)}{b^2} = 1[/tex]

where (h,k) is the center of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.

Plugging in the values we have found, we get -

[tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex]

Therefore, the equation for the ellipse is [tex]\frac{\Big(\frac{(x - 4)^2}{25}+ (y + 2)^2\Big)}{25} = 1[/tex].

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Using percentage, we can get that 7ml of the 70% solution will be needed.

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form.

In this context, "%" is read as "percent" or "percentage" to represent a percentage. By "division by 100," the percent symbol can always be changed to a fraction or decimal equivalent.

In the given question we get the equation,

35(245) + 0.75x = 0.4(245+x) = 98 + 0.4x

85.75 + 0.75x = 98 + 0.4x

0.35x = 98-85.75 = 12.25

x = 12.25/.35 = 35 mL of 75% solution

mixed with 245 mL of 35% it yields 280 mL of 40% so,

35 is within 5 of 40

75 is within 35 of 40

35/5 = 7

245/35 = 7

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Answer:

79 degrees

Step-by-step explanation:

[tex]x + y = 90 \: degrees \\ 11 + y = 90 \\ y = 90 - 11 \\ y = 79 \: degrees[/tex]

Answer: a. To shift the graph downwards 5 units, we subtract 5 from the function, to shift it left 3 units, we add 3 to the input (the x-value), to stretch the graph vertically by a factor of 4, we multiply the function by 4, and to reflect it about the x-axis, we multiply the entire function by -1. Thus, the new function is:

g(x) = -4(1/2)^(x+3) - 5

b. To find the y-intercept, we set x=0 in the equation and solve for y:

g(0) = -4(1/2)^(0+3) - 5 = -9

Thus, the y-intercept is (0, -9).

c. The domain of the function g(x) is all real numbers, since there are no restrictions on the input x.

d. The range of the function g(x) is (-∞, -5], since the function is shifted downwards 5 units and stretched vertically by a factor of 4, which means that the maximum value of the function is -5, and it can take any value less than or equal to -5. The reflection about the x-axis does not change the range.

Step-by-step explanation:

Using the graph the value of the function (f + g)(-2) = 5

A graph is a diagrammatic representation of a function

Since we have the graphs of the function f(x) and g(x), we desire to find (f + g)(-2). We proceed as follows.

First, we note that (f + g)(x) = f(x) + g(x)

Now, we need to find (f + g)(-2) = f(-2) + g(-2)

So, we use the graph to find these values.

From the graph

f(-2) = 2 and g(-2) = 3

So, substituting the values of the variables into the equation, we have that

(f + g)(-2) = f(-2) + g(-2)

= 2 + 3

= 5

So, (f + g)(-2) = 5

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Anju earned $30 by doing 10 chores. So, if Anju does 10 chores, she can earn money up to $30?

An equation is a mathematical statement that indicates the equality of two expressions. It is made up of one or more variables, constants, and mathematical operations. An equation consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equal sign (=).

The purpose of an equation is to find the value(s) of the variable(s) that satisfy the given conditions. To solve an equation, we need to isolate the variable on one side of the equation and simplify the other side of the equation until we obtain a solution or solutions.

The equation shows that the amount of money Anju earns is directly proportional to the number of chores she does. Each chore is worth $3, so if Anju does c chores, she earns 3c dollars.

For example, if Anju does 5 chores, she can use the equation to find how much money she earned:

3c = d

3(5) = d

15 = d

So, Anju earned $15 by doing 5 chores.

Similarly, if Anju does 10 chores, she can use the same equation to find her earnings:

3c = d

3(10) = d

30 = d

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Answer:  independent variable Dependent variable

if you’re on khan it’s all right MARK AS BRAINLIEST PLS

hi!

first, you have to graph the piecewise function. a piecewise function is basically where there are multiple different lines, but they all have different sections on the graph that they are applicable.

on the graph, graph the first equation, in the piecewise function, which is y= -3x + 2.

then, you have to erase all parts except the segment between x=-1 and x=1. at the endpoints, place a filled in dot to mark the point.

do the same with y = x - 2, however, this time, the restraints are at x=1 and x=3. you'll see that the endpoint at x=1 coincides with the previous equation! for the endpoint on the side of x=3, you should place another filled in dot to mark that it includes x=3.

i've attatched a screenshot below (scroll down a bit!) of what the graph should look like, in case that was confusing :)

next, you can fill in the table by finding what the function outputs for the given x. for the first one, x = -3. first, look at the function. is x between -1 and 1, or between 1 and 3? neither. that means that it is no solution for that point.

continue down the table. it is the same with x=-2.

next, x = -1. this is in the interval of -1<=x<=1, so you should look at the first equation in the piecewise function, which is 2-3x. if we plug in -1 for x, we get 2 - 3(-1) = 2+3 = 5. this means that the point is (-1, 5). you should make sure that this is a point that you plotted on the graph, and if not, the graph is wrong :(

continue down the table and keep doing that!

next question is if there is a min or max. there is! as you can see, the piecewise function only goes from x=-1 through x=3, and all other values give a no solution output. so, the minimum is -1 and the maximum is 3.

next: turning point or vertex. this would be at the point when x = 1, since that would be where the graph changes direction. the vertex is at (1, -1).

the zeroes of the function is where the graph crosses the x-axis. this means that y=0. we can see that this happens when x=2/3 and when x=2.

i hope this was helpful! :)

Answer:13)2,4,6,8

14)x=3

Step-by-step explanation:

13) you should make it equal to numbers inside bracket {}.

for example,

1.-6x+11=-37

-6x=-37-11=-48

x=8

2.-6x+11=-25

-6x=-36

x=6

3.-6x+11=-13

-6x=-24

x=4

4.-6x+11=-1

-6x=-12

x=2

14)f(x)=13

f(x)=3x+4=13

3x=9

x=3

Given:-

To find:-

Solution:-

As we know that in a right angled triangle,

[tex]\implies \sin\theta =\dfrac{p}{h} \\[/tex]

And here;

On substituting the respective values, we have;

[tex]\implies \sin20^o = \dfrac{12}{x} \\[/tex]

[tex]\implies 0.342 =\dfrac{12}{x} \\[/tex]

[tex]\implies x = \dfrac{12}{0.342} \\[/tex]

[tex]\implies \underline{\underline{ x = 35.087}} \\[/tex]

Hence the value of x is 35.087 .

and we are done!

The length of the missing side of the given triangle above which is adjacent to angle 20° is 35.09.

To calculate the length of the missing side of the triangle, the formula given below is used. Such as:

Sin ∅ = opposite/hypothenuse.

Where ∅ = 20°

opposite = 12

hypotenuse = X

That is;

sin 20° = 12/X

make X the subject of formula;

X = 12/sin20°

X = 12/0.342020143

X = 35.09

Therefore the length of the missing part of the given triangle which is adjacent to angle 20° is 35.09.

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The value for the x in the triangle with sides  (4x - 4) and 30 is obtained as x > 6.8.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Assume that the side length 30 is the greatest of the 3 sides.

Using this fact, we can write an inequality based on the lengths of the sides in the given triangle -

(4x - 4) + x > 30

Simplifying this inequality, we get -

4x + x - 4 > 30

Adding x on LHS, we get -

5x > 34

Dividing both sides by 5, we get -

x > 6.8

Therefore, the value of x is greater than 6.8.

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The ratiο οf the amοunt spent οn staff salaries tο the tοtal budget fοr the yοuth prοgrams is 1:5.

A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).

If 80 cents οf every dοllar gοes directly tο prοgram services, then 20 cents οf every dοllar is spent οn staff salaries.

This can be written as a ratiο οf 20 cents tο 100 cents, οr simplified tο 1:5.

Therefοre, the ratiο οf the amοunt spent οn staff salaries tο the tοtal budget fοr the yοuth prοgrams is 1:5.

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The total surface area of the rectangular prism is 94 cm2.

Surface area is the measurement of the total area of a three-dimensional object. It is the sum of all the areas of the faces or surfaces of a 3D shape.

The total surface area of a 3D object is the sum of the areas of all its faces. The formula to calculate the total surface area of a 3D object is:

Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height)

Where Length, Width, and Height are the dimensions of the 3D object.

For example, if you have a rectangular prism with Length = 5 cm, Width = 4 cm, Height = 3 cm, then the total surface area is:

Total Surface Area = 2(5 cm x 4 cm) + 2(5 cm x 3 cm) + 2(4 cm x 3 cm)

 = 40 cm2 + 30 cm2 + 24 cm2

 = 94 cm2

Therefore, the total surface area of the rectangular prism is 94 cm2.

In conclusion, the formula to calculate the total surface area of a 3D object is: Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height). Examples can be used to better understand the concept and apply the formula to solve for the total surface area.

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Answer:

0

Step-by-step explanation:

3r-9=3(r+3)

3r-9=3r+9

collect like terms

3r-3r=9-9

r=0

Answer:

[tex]\large\boxed{\textsf{No Solutions.}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to identify how many solutions are possible for r.}[/tex]

[tex]\textsf{First, we should simplify the given equation.}[/tex]

[tex]\textsf{For one part of the equation, we have to use the \underline{Distributive Property}.}[/tex]

[tex]\Large\underline{\textsf{What is the Distributive Property?}}[/tex]

[tex]\textsf{The \underline{Distributive Property} is a property used to distribute the \underline{multiplier} into}[/tex]

[tex]\textsf{values \underline{inside} the parentheses.}[/tex]

[tex]\textsf{Let's begin simplifying the equation.}[/tex]

[tex]\large\underline{\textsf{Simplify.}}[/tex]

[tex]\mathtt{3r-9=3(r+3)}[/tex]

[tex]\large\underline{\textsf{Distribute:}}[/tex]

[tex]\mathtt{3r-9=(3 \times r)+(3 \times 3)}[/tex]

[tex]\mathtt{3r-9=3r+9}[/tex]

[tex]\large\boxed{\textsf{No Solutions.}}[/tex]

[tex]\large\underline{\textsf{Why?:}}[/tex]

[tex]\textsf{Any value that is substituted into r will \underline{never} make the equation true.}[/tex]

True, The polynomial 32x^2+12x-57 has two real roots.

What is a polynomial, exactly?

A polynomial in mathematics is an expression that consists of variables (also known as indeterminates) and coefficients and uses only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

                             The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

It is an absolutely true statement that the polynomial 32x^2+12x-57 has two real roots. The correct option among all the options that are given in the question is the first option or option "A".

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The complete question is -

The polynomial 32x^2+12x-57 has two real roots.

A. True

B. False The polynomial 32x^2+12x-57 has two real roots.

Therefore, the budgeted production for the year is 69,087 units.

factors

given by the question.

To determine the budgeted production for the year, we need to consider the following factors:

Projected sales for the year: 67,577 bicycles

Estimated January 1 inventory: 6,048 units.

Desired December 31 inventory: 7,558 units

The formula to calculate the budgeted production is:

Budgeted Production = Projected Sales + Desired Ending Inventory - Beginning Inventory

Using the values given in the problem, we can calculate the budgeted production as follows:

Budgeted Production = 67,577 + 7,558 - 6,048

Budgeted Production = 69,087 units

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Answer:

See below.

Step-by-step explanation:

We are asked to round 4.586 cm to the nearest cm.

Rounding is a simple method used to change a number, and all of the numbers behind it to 0. Rounding is similar to an approximation, in order to show you how I should give you an example.

Example:

Round 459 to the hundreds place.

The hundreds place is where the 4 is. We should look at the 5.

Requirements necessary are that 5 needs to be greater than [tex]4.\bar{9}.[/tex]

Because 5 is greater, we can round up to 500.

Rounding is an approximation because it's close to the actual number, in other words, inexact.

Let's use the example as a guide for our problem now.

4.586 to the nearest cm (ones place)

The ones place is the 4. We should look at the 5.

5 is greater than [tex]4.\bar{9}.[/tex]

Because 5 is greater, we can round up to 5.000 cm.

Our final answer is 5.000 cm.

(a) The derivative of the function, dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)

(b) The equation of the tangent line to the curve at (1, 1) is y = (-779/9)x + 778/9.

To find dy/dx, we differentiate both sides of the equation with respect to x using the chain rule and product rule as necessary:

d/dx (57x⁷) + d/dx (10x³⁸y) + d/dx (y⁹) = d/dx (68)

Simplifying each term using the power rule and the chain rule where appropriate, we get:

399x⁶ + 380x³⁷y + 9y⁸(dy/dx) = 0

Now, solving for dy/dx, we get:

dy/dx = (-399x⁶ - 380x³⁷y) / (9y⁸)

To find the equation of the tangent line to the curve at (1, 1), we first need to evaluate dy/dx at that point. Plugging in x = 1 and y = 1 into the expression for dy/dx, we get:

dy/dx = (-399 - 380) / 9 = -779/9

Now we can use the point-slope form of the equation of a line to find the tangent line. The point-slope form is:

y - y1 = m(x - x1)

where;

Plugging in m = -779/9, x1 = 1, and y1 = 1, we get:

y - 1 = (-779/9)(x - 1)

Simplifying, we get:

y = (-779/9)x + 778/9

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Answer:

x=3

Step-by-step explanation

x=7 is an excluded value for the quotient x=3 because 3 is not an integer.