2. Iwo functions t and g are definea on the set R of real numbers by f: x x² - 2x - 4. g: x → X - 1 Find the value fx for which f(x) = (x) = m - 4.​

The measure of ∠O in ΔMNO is approximately 41.5°.

To find the measure of ∠O, we can use the Law of Cosines in ΔMNO, with sides M = 540 inches, N = 330 inches, and O = 600 inches. The Law of Cosines states:

O² = M² + N² - 2MN * cos(∠O)

Rearrange the equation to solve for cos(∠O):

cos(∠O) = (M² + N² - O²) / (2MN)

Substitute the values:

cos(∠O) = (540² + 330² - 600²) / (2 * 540 * 330)

cos(∠O) ≈ -0.7944

Now, find the angle using the inverse cosine function:

∠O ≈ arccos(-0.7944) ≈ 141.5°

Since ∠O is an obtuse angle, we need to find its supplement to the nearest 10th:

180° - 141.5° ≈ 38.5°

Thus, the measure of ∠O is approximately 38.5°.

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Answer:

y = 11x/13 + 36/13

Step-by-step explanation:

We can write the line using y = mx + b form.

To find the slope, m, we can use the formula (y1 - y2) / (x1 - x2):

(7-(-4)) / (5-(-8)) = (7+4) / (5+8) = 11 / 13.

To find b, we can plug in one of the points. Lets use (5, 7).

y = 11/13 * x + b

7 = 11/13 * 5 + b

7 - 55/13 = b

b = 91/13 - 55/13 = (91-55)/13 = 36/13.

Your equation is:

y = 11x/13 + 36/13.

Answer: y = [tex]\frac{11}{13}[/tex]x + [tex]\frac{36}{13}[/tex]

Step-by-step explanation:

First, we will find the slope.

       [tex]m=\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{-4-7}{-8-5} =\frac{-11}{-13} =\frac{11}{13}[/tex]

Next, we will substitute this slope and a given point in and solve for our y-intercept (b).

       y = [tex]\frac{11}{13}[/tex]x + b

       (7) = [tex]\frac{11}{13}[/tex](5) + b

       (7) = [tex]\frac{11}{13}[/tex](5) + b

       7 = [tex]\frac{55}{13}[/tex] + b

       b = 7 - [tex]\frac{55}{13}[/tex]

       b = [tex]\frac{36}{13}[/tex]

Final equation:

       y = mx + b

     y = [tex]\frac{11}{13}[/tex]x + [tex]\frac{36}{13}[/tex]

The piecewise function that represents the situation is therefore:

Costs                                           Possible hours

13                                                     0 < x ≤ 1

20                                                 1 < x ≤ 3

50                                                   3 < x ≤ 10

We see that up to one hour, the cost to Marshall would be $ 13 so the possible hours at that price is 0 < x ≤ 1 .

Likewise from one hour, the price goes up to $ 20 which means that possible hours become  1 < x ≤ 3 because the price will increase at 3 hours again.

From 3 hours, the price becomes $ 50 and there are a maximum of 10 hours so the hours become 3 < x ≤ 10 .

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The statement that explains the negative and nonlinear relationship between group size and percent woodland is given by the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly.

This statement suggests that as the amount of woodland id increases, when the number of deer in a group decreases.

However, the rate of decrease is not constant, but rather decreases more slowly as the percent of woodland increases.

This suggests that there may be some threshold or tipping point.

At which the relationship between group size and percent woodland becomes less pronounced.

This kind of relationship is not uncommon in ecological studies.

Where factors like habitat availability, food availability, and predation risk can all influence animal behavior and population dynamics.

Nonlinear relationships like this one can help researchers better understand complex interplay between these factors and behavior of animals they study.

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The work done on the displacement is 301.95J

To determine the work done, we need to find the displacement in which the box moved.

cos θ = adjacent / hypothenuse

cos 33 = adjacent / 80

adjacent = 80 * cos 33

adjacent = 67.1 lbs

The force applied is 67.1lbs

The displacement on the ramp;

sin θ = opposite / hypothenuse

sin 10 = opposite / 26

opposite = 26 * sin 10

opposite = 4.5 ft

The work done in moving the object can be calculated as;

work done = force * displacement

work done = 67.1 * 4.5

work done = 301.95 J

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None of the options presented represent the same function as the given equation 8x − 2y = 25.

The equation 8x − 2y = 25 represents a linear function in terms of variables x and y. To determine which equation represents the same function, we need to look for an equation that has a similar form.

A. "The number of minutes m to cook c cups of rice" does not have the same form as the given equation, so it does not represent the same function.

B. "The volume V of a cube with side length s" also does not have the same form as the given equation, so it does not represent the same function.

C. "The distance walked after m minutes at r feet per minute" does not match the given equation, so it does not represent the same function.

D. "The cost C for t tickets to a museum does not have the same form as the given equation, so it does not represent the same function.

Therefore, none of the given options represent the same function as the  equation 8x − 2y = 25.

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The slope of the tangent line to the function [tex]s(t) = 8 - 41t^2[/tex] at t = -3 is 246.

1. Differentiate the function s(t) with respect to the independent variable t: [tex]s(t) = 8 - 41t^2[/tex].
2. Calculate the derivative s'(t).
3. Evaluate the derivative at the given value of t.
Step 1: Differentiate the function [tex]s(t) = 8 - 41t^2[/tex].
To differentiate this function, we apply the power rule for differentiation.

The derivative of a constant (8) is 0, and the derivative of 41t^2 is -82t

(since we multiply the exponent 2 by the coefficient 41 and then subtract 1 from the exponent).
Step 2: Calculate the derivative s'(t).
s'(t) = 0 - 82t
Step 3: Evaluate the derivative at the given value of t (t = -3).
s'(-3) = -82(-3) = 246
The slope of the tangent line to the function [tex]s(t) = 8 - 41t^2[/tex] at t = -3 is 246.

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The solution of the given differential equation is y = x + Cx⁴ - x²/4, where C is a constant.

We begin by rearranging the terms as follows:

(4y + x³ - 7)dx = (4x)dy

Integrating both sides, we get:

4xy + (1/4)x⁴ - 7x = 2y² + C

where C is the constant of integration.

Next, we can rearrange this equation to solve for y:

y² = 2xy + (1/8)x⁴ - (7/2)x - C/2

y² - 2xy = (1/8)x⁴ - (7/2)x - C/2

We can complete the square to obtain a more useful expression:

(y - x)² = (1/8)x⁴ - (7/2)x - C/2 + x²

y - x = ±sqrt((1/8)x⁴ - (7/2)x - C/2 + x²)

Simplifying this expression, we get:

y = x ±sqrt(Cx⁴ - (1/4)x⁴ + 7x - C)

Taking the positive sign for simplicity, we get the final solution as:

y = x + sqrt(Cx⁴ - (1/4)x⁴ + 7x - C)

where C is the constant of integration.

We can also simplify this solution further by using the identity (a + b)² = a² + 2ab + b² to get:

y = x + Cx⁴ - x²/4

where C is a constant, as desired.

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The cafe served 12 regular coffees.

Out of the 30 coffees served at Molly's cafe this morning, 40% were regular coffee. To determine the number of regular coffees, we can calculate 40% of 30.

To find the value,

Step 1: Convert the percentage to a decimal by dividing it by 100. So, 40% = 40/100 = 0.4.
Step 2: Multiply the total number of coffees served by the decimal. So, 30 * 0.4 = 12.

Hence, the cafe served 12 regular coffees. The remaining 60% (or 18 coffees) would be decaffeinated. It is important to note that percentages represent proportions or fractions of a whole. In this case, 40% indicates that 40 out of 100 parts (or 40/100) are regular coffees. By applying this proportion to the total number of coffees served (30), we can determine the specific quantity. This method can be used in various scenarios involving percentages to find a portion of a whole. Therefore, Molly's cafe served 12 regular coffees and 18 decaffeinated coffees, making a total of 30 coffees.

Your answer: Molly's cafe served 12 regular coffees this morning.

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The correct option is D, the statement that best describes the expression 4+3x means "4 plus 3 times x".

An expression is a combination of numbers, symbols, and/or variables that represents a mathematical or logical statement. It can be as simple as a single number or letter, or as complex as a series of operations that involve multiple variables and functions. Expressions can be used to represent equations, inequalities, functions, and other mathematical concepts. They can be evaluated to produce a numerical value or a boolean value (true or false) depending on the values of the variables involved.

Expressions are used to represent calculations or logical conditions. They can be used to assign values to variables, manipulate data, and control the flow of a program. expressions are a fundamental concept in both mathematics and computer science, and play a critical role in solving problems and building complex systems.

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We know that the total mass of 5 polished stones would be 7 grams according to this equation

Sure! The equation m = 1.4p represents the mass, m, in grams, of p polished stones.

This means that if you know the number of polished stones, p, you can use this equation to calculate their total mass, m, in grams. For example, if you have 5 polished stones, you can plug in p = 5 and solve for m: m = 1.4 x 5 = 7 grams.

So the total mass of 5 polished stones would be 7 grams according to this equation.

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Based on the equation, the number of grams which the mass increase for every 7 polished stones is: D. 9.8 g.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided above, a linear equation that models the mass in grams is given by;

y = mx + c

m = 1.4p

By substituting the given parameter (x = 7 polished stones), we have the following:

m = 1.4(7)

m = 9.8 g

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)

A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.

Given coordinates of points A, B and C

A(6, 10), B(2, -8), C(-4 , -7)

After reflection  (x, y) ---> (-x, y).

Thus,  Coordinates of image of points A', B' and C' are-

A'(-6, 10), B'(-2, -8), C'(4 , -7)

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the ∠sqr is 4y= 4*29=116° we can get this answer with supplementary angle fact and  sum of angle in triangle is 180 degree

what is supplementary angle ?

In geometry, two angles are called supplementary angles if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, Supplementary angles are commonly found in many geometric shapes, such as triangles and quadrilaterals, as well as in other applications of geometry. When two angles are supplementary, they form a straight line or a straight angle, which is an angle that measures exactly 180 degrees. For example, if one angle of a triangle measures 80 degrees, then the other two angles are supplementary and together measure 100 degrees (180 degrees - 80 degrees).

In the given question,

with the fact of complimentary angles we can write as follows

angle trq+ angle qrs  =180

angle qrs=180-145=35 degree

so in triangle we have sum of all angle is 180 degree so we can write as follows

∠r+∠q+∠s=180

35+4y+y=180

5y=180-35

y=145/5

y=29 degree

so the ∠sqr is 4y= 4*29=116°

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The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).

To find the coordinates of the points on the curve x(t) = 3t^2 + 1 and y(t) = t^3 - 1, where the tangent line has a slope of 1/2, follow these steps:

1. Calculate the derivatives of x(t) and y(t) with respect to t:

dx/dt = 6t
dy/dt = 3t^2

2. The slope of the tangent line is given by dy/dx, so calculate dy/dx using the chain rule:

dy/dx = (dy/dt) / (dx/dt) = (3t^2) / (6t) = t/2

3. Set the slope equal to 1/2 and solve for t:

t/2 = 1/2
t = 1

4. Plug the value of t back into the original equations for x(t) and y(t) to find the coordinates of the point:

x(1) = 3(1)^2 + 1 = 4
y(1) = (1)^3 - 1 = 0

The coordinates of the point on the curve where the tangent line has a slope of 1/2 are (4, 0).

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The allowable MACRS depreciation on Convers’s property in the current year assuming Convers does not elect §179 expense and elects out of bonus depreciation is $39,805.

To calculate the allowable MACRS depreciation, we need to determine the depreciation for each asset using the MACRS tables:

Placed in service in October, which is in the fourth quarter

Depreciation method: 5-year property

Percentage from Table 1: 20.00%

Basis for depreciation: $92,000

Depreciation for the current year: 20.00% x $92,000 x 0.5 = $9,200

Placed in service in February, which is in the first quarter

Depreciation method: 5-year property

Percentage from Table 1: 20.00%

Basis for depreciation: $32,000

Depreciation for the current year: 20.00% x $32,000 x 0.75 = $4,800

Placed in service in March, which is in the first quarter

Depreciation method: 5-year property

Percentage from Table 1: 20.00%

Basis for depreciation: $45,000

Depreciation for the current year: 20.00% x $45,000 x 0.75 = $6,750

Placed in service in April, which is in the second quarter

Depreciation method: 7-year property

Percentage from Table 2: 14.29%

Basis for depreciation: $172,000

Depreciation for the current year: 14.29% x $172,000 x 0.5 = $12,285

Placed in service in May, which is in the second quarter

Depreciation method: 39-year property

Percentage from Table 5: 2.564%

Basis for depreciation: $520,000

Depreciation for the current year: 2.564% x $520,000 x 0.5 = $6,670

The total allowable MACRS depreciation for Convers Corporation in the current year is the sum of the depreciation for each asset:

$9,200 + $4,800 + $6,750 + $12,285 + $6,670 = $39,805

Therefore, the allowable MACRS depreciation on Convers’s property in the current year is $39,805.

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The number of different combo meals possible in a restaurant that is serving a special dinner combo meal is 90.

We are given that the customers can choose from 5 drinks, 6 main dishes, and 3 desserts. We have to find that how many different combos are possible. It means that we have to do an arrangement for such a situation. Arrangement of things means to group them in a systematic order, in all the possible ways.

We know that the number of possible ways to arrange is n! where n is the number of objects. As we know that the dinner includes 5 drinks, 6 main types of dishes, and 3 types of desserts. The number of different combo meals possible can be found by simply multiplying all the meals. Thus,

n = 5 * 6 * 3

n = 90

Therefore, the number of different combo meals possible in a restaurant that is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 90.

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Based on the information, the equilibrium price is $56.67

Using the first data point, we have:

25 = a - 40b

Using the second data point, we have:

185 = a - 20b

Solving these two equations simultaneously, we get:

a = 325

b = 5/2

So the demand function is:

Qd = 325 - 5/2 P

the supply function is:

Qs = -100 + 5P

325 - 5/2 P = -100 + 5P

425 = 15/2 P

P = $56.67

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Answer:

We can use the formula for simple interest to calculate the interest earned by Henry:

Simple Interest = (Principal * Rate * Time)

where,

Principal = $850 (initial amount)

Rate = 5% per year (as given)

Time = 4 years (as given)

Substituting the values, we get:

Simple Interest = (850 * 0.05 * 4) = $170

Therefore, Henry will have earned $170 in interest after 4 years of keeping his money in the savings account.

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The volume of air that the beach ball will hold is 36000π cubic cm

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

The radius of the beach ball is 30 cm.

This means that

r = 30

The volume of air that the beach ball will hold is calculated as

V = 4/3πr³

Substitute the known values in the above equation, so, we have the following representation

V = 4/3π * 30³

Evaluate

V = 36000π

Hence, the volume of air that the beach ball will hold is 36000π cubic cm

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Answer: The answer is (C

Step-by-step explanation:

To find f-1(6), we need to find the value of x that gives f(x) = 6. However, we don't have enough information about the function f to do this. We need to know whether f is a linear function or not.

When the function and its inverse intersect, we have f(x) = f-1(x). Substituting y for both f(x) and f-1(x), we get y = f(y). To find the value of y when this is true, we need to solve for y:
y = f(y)
y = f-1(y)
Substituting y = f(x), we get:
f(x) = f-1(f(x))
f(x) = x

So the function and its inverse intersect when y = x.
If a = 0, then the linear function is f(x) = b, which is a constant function. Constant functions do not have inverses, so the inverse of f(x) = b does not exist.

If a ≠ 0, then the inverse of f(x) = ax + b is given by:
f-'(x) = (x - b) / a
This is also a linear function, so the inverse of a linear function is always a linear function when a ≠ 0.
(a) To find the inverse of a linear function, you need to swap the x and y values. Given that f(4) = 6, the inverse function f^(-1)(6) would yield the value of x when y = 6. Since we know that f(4) = 6, it implies that f^(-1)(6) = 4.
A function and its inverse intersect when the input value (x) is equal to the output value (y). In other words, they intersect when y = x.

(c) Yes, the inverse of a linear function is always a linear function. If f(x) = ax + b, where a ≠ 0, then the inverse function, f^(-1)(x), can be found by swapping x and y values and solving for y. In this case, x = ay + b. Solving for y, we get y = (x - b) / a, which is also a linear function.

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Tip: When writing math questions, the coefficient would go in front of variables: 7b*[tex]b^2[/tex]

Anyways, in this case, since we cannot mutiply 7 by b, the 7 will stay put

But.... we can mutiply b by b

[tex]b^2[/tex][tex]*b[/tex]=b^3

Tip: B's with no exponent has an exponent with one

Questions?

So,7 will stay put and b and b^2 will simply to b^3

[tex]7b^3[/tex]=Answer

The common ratio for the geometric series 1, 1/2, 1/4, 1/8, ... is 1/2 and the sum of series is 2 which is finite.

To determine whether the series has an infinite sum, we can use the formula for the sum of an infinite geometric series, which is:

S = a/(1-r),

where a is the first term and r is the common ratio.

In this case, a = 1 and r = 1/2, so

S = 1/(1 - 1/2) = 2.

Since the value of S is finite and not infinite, we can conclude that the given geometric series has a finite sum of 2.

The common ratio of a geometric series is the ratio between consecutive terms. For example, in the series 1, 2, 4, 8, 16, ..., the common ratio is 2 because each term is obtained by multiplying the previous term by 2.

To determine whether a geometric series has an infinite sum, we can use the formula for the sum of an infinite geometric series, which is S = a/(1-r), where a is the first term and r is the common ratio.

If the value of r is between -1 and 1 (excluding -1), then the series has a finite sum. If the value of r is greater than 1 or less than -1, then the series has an infinite sum.

In the given series 1, 1/2, 1/4, 1/8, ..., the common ratio is 1/2. To find the sum of the series, we can use the formula S = a/(1-r) with a=1 and r=1/2, which gives S=2. Since the value of S is finite and not infinite, we can conclude that the given geometric series has a finite sum of 2.

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complete question:

Determine the common ratio for each of the following geometric series and determine which ones have an infinite sum 1,1/2,1/4,1/8....

The value of x is calculated as x = 3, while the length of segment JL is calculated as 18 units.

Create an equation based on the fact that the diagonals of the shape shown bisects each other to form equal segments such as:

JN = LN

Plug in the values to find x:

15 - 2x = 4x - 3

Combine like terms:

15 + 3 = 4x + 2x

18 = 6x

18/6 = x

x = 3

Length of JL = 15 - 2x + 4x - 3 = 12 + 2x

Plug in the value of x:

Length of JL = 12 + 2(3) = 18 units

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The statement about the chances of occurrence of nonmoving violations more on a weekend than on a weekday in past ten years is cannot be answered using only the information in the database. So, option(b) is provide the right answer.

Database: The database is a large collection of data and it is used to store and retrieve the accordingly. It has an organization of a certain amount of data that needs and it contains. We have a database of all traffic tickets that were issued over the past ten years in a city. The informations including are

2) nonmoving violations

We have to recongise the statement which is not answering by the above informations in database. First statement is can be answerable, because we have data of year in which tickets are issued. Similarly, statements third and fourth related to data of tickets issued in month and year in past ten years. So, both are answerable statements. Therefore, the second statement

is cannot be answerable here.

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Complete question:

a city maintains a database of all traffic tickets that were issued over the past ten years. the tickets are divided into the following two categories. moving violations nonmoving violations the data recorded for each ticket include only the following information. the month and year in which the ticket was issued the category of the ticket which of the following questions cannot be answered using only the information in the database? responses

a) have the total number of traffic tickets per year increased each year over the past ten years?

b) in the past ten years, were nonmoving violations more likely to occur on a weekend than on a weekday?

c) in the past ten years, were there any months when moving violations occurred more often than nonmoving violations?

d) in how many of the past ten years were there more than one million moving violations?

1. Myla bought an item for P2,500 and decided to sell it with a 2% markup. The selling price will be P2,500 + (2% of P2,500) = P2,500 + P50 = P2,550.

2. Joan sold her old iPhone for P5,000 at an 8% markdown rate. To find the markdown and the original cost, we first calculate the markdown: P5,000 = 92% of original price. So, the original price was P5,000 ÷ 0.92 ≈ P5,434.78. The markdown is P5,434.78 - P5,000 = P434.78.

3. The student assistant bought an item for P520 and sold it for P550. The markup is P550 - P520 = P30.

4. Mother earned P120 on an item at a 60% markdown. Let X be the original price, then X * 60% = P120. X = P120 ÷ 0.60 = P200. So, the mother bought the item for P200.

5. The cost of a t-shirt from the manufacturer is P400. If Loan wants a 30% markup based on the selling price, we'll let X be the selling price, then X - 30% of X = P400. So, 0.7X = P400. X = P400 ÷ 0.7 ≈ P571.43. Loan's selling price will be P571.43.

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The paper airplane will not hit the ground within the given time frame.

To find the equation for h( t), we need to find the rate of change or the  pitch of the function. We can do this by chancing  the difference in height and time for any two points on the line. Let's choose the first two points,( 0,200) and( 1,208).  

pitch = ( change in height)/( change in time)  

pitch = ( 208- 200)/( 1- 0) =  8  

So, the equation for h( t) can be written in  pitch- intercept form as   h( t) =  8t b  

To find the value of b, we can use any of the given points.

Let's use( 0,200)   200 =  8( 0) b  b =  200  

So, the equation for h( t) is   h( t) =  8t 200  

To find how long it'll take the aeroplane to hit the ground, we need to find when h( t) =  0,

since that would mean the height is 0  bases or the ground  position.   0 =  8t 200   working for t,

we get   t = -25

Since time cannot be negative the paper airplane will not hit the ground within the given time frame.

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Solving the equation, Joshua will reach 100,000 miles after approximately 1,760 days of work.

To model Joshua's truck mileage as a function of the number of days he has worked, we can use the following equation:

Mileage (M) = 14 * Number of days worked (D) + Initial Mileage (I)

First, we need to determine the initial mileage on the mail truck. To do this, we can use the information given for his 100th day of work:

76,762 = 14 * 100 + Initial Mileage
76,762 = 1,400 + Initial Mileage
Initial Mileage (I) = 76,762 - 1,400
Initial Mileage (I) = 75,362

Now we can rewrite the equation as:

Mileage (M) = 14 * Number of days worked (D) + 75,362

To find when Joshua will reach 100,000 miles, we can set M equal to 100,000 and solve for D:

100,000 = 14 * D + 75,362
24,638 = 14 * D
D ≈ 24,638 / 14
D ≈ 1,759.857

Since Joshua cannot work a fraction of a day, he will reach 100,000 miles after approximately 1,760 days of work.

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