find the equation of a line passing through two points (1,-1, 2) and (0,2-3).​

Answer:

Step-by-step explanation:

To solve the equation c = 3/7(wm + a) for m, we can isolate m on one side of the equation.

Here's the step-by-step process:

Distribute the 3/7:

c = 3/7 * wm + 3/7 * a

Subtract 3/7 * a from both sides:

c - 3/7 * a = 3/7 * wm

Divide both sides by 3/7 * w:

(c - 3/7 * a) / (3/7 * w) = m

And that's it! m is the value you're looking for. Just remember to use the values of c, w, and a that you have in your specific problem when you evaluate the expression.

[tex]m=\frac{7 c-a}{3w}.[/tex]

[tex]c=\frac{3}{7} (wm+a)[/tex]

Remember that dividing by a fraction is the same as multiplying by its multiplicative reciprocate. Hence, we may multiply by [tex]\frac{7}{3}[/tex] on both sides and it'd have the same efect as dividing by [tex]\frac{3}{7}[/tex].

[tex]\frac{7}{3} c=\frac{3}{7} (wm+a)*\frac{7}{3}[/tex]

The two fractions on the right side cancel each other out and we're left with:

[tex]\frac{7}{3} c=(wm+a)[/tex]

[tex]\frac{7}{3} c=wm+a[/tex]

[tex]\frac{7}{3} c-a=wm+a-a\\ \\\frac{7}{3} c-a=wm[/tex]

[tex]\frac{\frac{7}{3} c-a}{w} =\frac{wm}{w} \\ \\\frac{7 c-a}{3w} =m[/tex]

[tex]m=\frac{7 c-a}{3w}.[/tex]

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If you want to verify whether the answer is correct or not, you may take the original equation and plug the calculated value of "m" in the place of said variable. Then, if the equation returns the same value after simplifying completely, the solution is correct!

This step is show on the attached image.

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Answer:

A and C are the correct answers

Step-by-step explanation:

Answer:

And C is the answer to the question

The factors in the factored form represents the value of the function when x = 0.

Quadratic functions are defined as the polynomial functions consisting of variables and exponents with the degree of the variable being 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given is a quadratic function,

y = x² + 2x - 15

This can be factorized as (x + p)(x + q) such that p × q = -15 and p + q = 2.

Two such numbers are -3 and 5.

-3 × 5 = -15 and -3 + 5 = 2

y = x² + 2x - 15

y = (x - 3) (x + 5)

Factors are x - 3 and x + 5

Here, the numbers 3 and -5 represents the input values of the function when the output value or the value of the function equals 0 or they are the x intercepts of the function.

Hence the factors in the factored form are the x intercepts of the function.

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The complete question is as follows :

What do the factors in the factored form represent?

y = x² + 2x - 15

Answer:

y=b+5+k/2

Step-by-step explanation:

2y-k=b+5

2y=b+5+k

2y/2=b+5+k/2

y=b+5+k/2

Answer:

y = b+ 5 + k/2.

Step-by-step explanation:

2y - k = b + 5

the subject for y

[tex]2y - k = b + 5 \\ 2y = b + 5 + k \\ \frac{2y}{2} = \frac{b + 5 + k}{2} \\ y = \frac{b + 5 + k}{2}. [/tex]

Answer: To find the height of the embankment, we need to first find the volume of the well and then the volume of the embankment.

Volume of the well = πr^2h = π * (d/2)^2 * h = π * (5/2)^2 * 24 = 157.08 cubic meters

Volume of the embankment = π * (R^2 - r^2) * h, where R is the outer radius of the embankment and r is the inner radius.

Outer radius of the embankment = (5 + 3)/2 = 4 m

Inner radius of the embankment = (5 - 3)/2 = 1 m

Volume of the embankment = π * (4^2 - 1^2) * h = π * 15 * h

We know that the volume of the well is equal to the volume of the embankment, so we can write:

157.08 = π * 15 * h

Solving for h, we get:

h = 157.08 / (π * 15) = 157.08 / 47.12 ≈ 3.32 m

So, the height of the embankment is approximately 3.32 meters.

Step-by-step explanation:

The mean number of hours the students spent listening to music is 31.25 hours.

In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.

Mean = (sum of all values) / (number of values)

For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:

Mean = 9

Therefore, the mean of this data set is 9.

The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.

We can find the mean number of hours spent listening to music using the formula:

mean = (sum of (midpoint of each class) * (frequency of each class)) / (sum of frequencies)

The midpoint of each class can be found by taking the average of the upper and lower class limits.

Using this formula, we get:

mean = ((1.25 + 3.75 + 6.25 + 8.75 + 11.25) * (22 + 15 + 3 + 3 + 1)) / (22 + 15 + 3 + 3 + 1)

mean = (31.25 * 44) / 44

mean = 31.25

Therefore, the mean number of hours the students spent listening to music is 31.25 hours.

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The mathematical Expression is 5x- 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given:

We have the unknown variable x.

4 is subtracted from the product of 5 and a number.

Now, Translating the word problem (sentence) into an algebraic expression, we get

= 5x - 4

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The area of the parallelogram that is shown above would be = 9 yd².

A parallelogram is defined as the quadrilateral that has four sides whose sides are also parallel to each other.

The formula that can be used to calculate the area of the parallelogram = base × height ( diagonal)

The base = 4½ yd

height = 2 yd (diagonal)

Area = 4½× 2 = 9yd².

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If x and y vary inversely, we can write their relationship then the function that models the inverse variation is y = 80/x.

What is Function?

In mathematics, a function is a rule or mapping that associates each input value (also called the independent variable) with a unique output value (also called the dependent variable). Functions are often represented using an equation, formula, or a graph, and are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and more.

They can take different forms and have different properties, such as being linear, quadratic, exponential, periodic, or more complex. Some common notation used to represent functions includes f(x), y = f(x), or simply y.

If x and y vary inversely, we can write their relationship as:

x * y = k

where k is a constant of proportionality. We can use the given initial values of x and y to solve for k:

10 * 8 = k

k = 80

Therefore, the function that models the inverse variation is:

x * y = 80

or

y = 80/x

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The values of x and y are 30 and 80

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

The parallel line and the transversal

The value of y is calculated as

y + 25 = 105 ---- alternate angle theorem

So, we have

y = 80

For x, we have

3x - 15 + 105 = 180 --- coresponding angle

So, we have

3x = 90

Divide

x = 30

Here, we make use of

2x + 54 = 180 --- sum of alternate interior angles

So, we have

2x = 126

Divide

x = 63

This is calculated as

Slope = (y2 - y1)/(x2 - x1)

So, we have

Slope = (6 - 6)/(5 - 2)

Slope = 0

Hence, the slope is 0

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Answer: To find the distance between the tops of two buildings, we first need to find the horizontal distance between the two buildings. This distance can be found using the Pythagorean theorem.

Let's call the horizontal distance between the two buildings "d".

d^2 = 12^2 + (34 - 29)^2

d^2 = 144 + 25

d^2 = 169

d = 13

So, the horizontal distance between the two buildings is 13 meters.

To find the distance between their tops, we simply add the height of each building:

distance = 34 + 29 = 63 meters

So, the distance between the tops of the two buildings is 63 meters.

Step-by-step explanation:

a) The standard deviation of  1.45 mpg.

b)The margin of error for the mean estimate 3.03 mpg

c) A 95% confidence interval for μμ is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg, the mean highway mpg for this vehicle is  27 mpg.

a) Using the formula for the standard error of the mean, σx¯ = σ/√n, where σ is the standard deviation of the population, n is the sample size, we can calculate σx¯ = 6.5/√20 ≈ 1.45 mpg.

b) Using a 95% confidence level, we can find the critical value for the t-distribution with 19 degrees of freedom (n-1), which is 2.093. The margin of error for the mean estimate is then t*σx¯ = 2.093 x 1.45 ≈ 3.03 mpg.

c) The 95% confidence interval for μ is given by x¯ ± margin of error, which is (28.1 - 3.03, 28.1 + 3.03) or (25.07, 31.13) mpg. Since the vehicle sticker information states a highway average of 27 mpg, the results of this experiment are not consistent with the vehicle sticker, as the 95% confidence interval does not contain the value of 27 mpg. This suggests that the vehicle may not be performing as well as expected, or that the sample of mpg readings was not representative of the overall population.

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Answer:

(-4, -1)

Step-by-step explanation:

The system has one solution

The slope of the graph of this function is 1/2, the correct option is C.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

We are given that;

The x input and y output of function.

Input x -2 -1 0 1 2

Output y -3 -1 1 3 5

Now

m=y2-y1/x2-x1

m= 2-1/5-3

m=1/2

Also, m=-1+2/-1+3

m=1/2

Therefore, the slope of the function will be 1/2

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The amount of federal state tax Selina owes if her gross pay for two weeks is $840 is  $14.11, which is closest to option A: $16.17. so the best answer is A as it is the closest.

To calculate Selina's federal tax contribution, we first need to determine her taxable income. From her gross pay of $840, we can subtract the biweekly standard deduction for a single person, which is $191.15 (based on the federal tax table provided). This gives us a taxable income of $648.85.

Using the federal tax table for biweekly earnings of a single person, we can see that the federal tax on this amount is $67.25.

Selina's state tax deduction is 21% of her federal tax contribution, which is 0.21 x $67.25 = $14.11.

Therefore, the amount of state tax Selina owes is $14.11, which is closest to option A: $16.17. However, none of the given options match the calculated amount exactly, so the best answer is A as it is the closest.

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Actual distance from Spokane to Missoula = 100 miles

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Given,

On map one inch represents 20 miles

Distance between Spokane to Missoula on map = 5 inches

Actual distance = 5 × 20 = 100 miles

Hence, 100 miles is the actual distance from Spokane to Missoula.

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Answer:

The solution of the equation is B. 4

Step-by-step explanation:

√x + 2 = x

√x = x - 2

(√x)² = (x-2)²

x = (x-2) (x-2)

x = x² - 4x + 4

x moves to the right

0 = x² - 4x - x + 4

0 = x² - 5x + 4

0 = (x-1) and (x-4)

x-1 = 0 x-4 = 0

x = 1 (not) x = 4

So, the solution to the equation is B. 4

The correct option is A {-5, 0, 3, 4}.

In mathematics, the domain of a function is the set of all possible input values (independent variable) for which the function is defined. In other words, the domain is the set of values that we can substitute for the independent variable in a function to produce a meaningful output.

For example, consider the function f(x) = 2x. Here, we can substitute any real number for x and get a meaningful output. Therefore, the domain of this function is all real numbers, or (-∞, ∞). However, if we consider the function g(x) = 1/x, we can see that we cannot substitute 0 for x because division by 0 is undefined. Therefore, the domain of this function is all real numbers except 0, or (-∞, 0) U (0, ∞).

The domain of a relation is the set of all possible values for the independent variable (x) for which there exists a corresponding value of the dependent variable (y). In this case, the given coordinates are (1,3), (4,1), and (-5,-4).

The domain of the relation would be the set of x-values that correspond to the given coordinates. So, the domain of this relation is {-5, 1, 4}.

Therefore, the correct answer is A: {-5, 0, 3, 4}.

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Answer:

Step-by-step explanation:

a) The tree diagram for the results of tossing a fair two-sided coin four times would look like this:

     (1)

    /   \

 (H)     (T)

/   \   /   \

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

b) There are four stages in the tree diagram.

c) The possible outcomes (the sample space) would be all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times. The possible outcomes are:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTTT

d) There are 2^4 = 16 outcomes in the sample space.

ALSO:

a) Draw the Tree Diagram

Start with a root node labeled with the first toss (toss 1)

From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.

Repeat this process for each of the next tosses (toss 2, 3, and 4)

Continue until all the possible outcomes of the four tosses have been represented.

Here is an example of the tree diagram:

(1)

/

(H) (T)

/ \ /

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

/ \ / \ /

(4-HHH) (4-HHT) (4-THH) (4-TTT)

b) Number of Stages in the Tree Diagram

There are four stages in the tree diagram, one for each toss of the coin.

c) Possible Outcomes (Sample Space)

The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.

There are 16 possible outcomes in the sample space, as shown below:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTHH

TTTTH

TTTTT

d) Number of Outcomes in the Sample Space

There are 2^4 = 16 outcomes in the sample space.

This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.

ALSO:

a) Draw the Tree Diagram

Start with a root node labeled with the first toss (toss 1).

From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.

Repeat this process for each of the next tosses (toss 2, 3, and 4).

Continue until all the possible outcomes of the four tosses have been represented.

Here is an example of the tree diagram:

(1)

/

(H) (T)

/ \ /

(2-H) (2-T) (2-H) (2-T)

/ \ / \ /

(3-HH) (3-HT) (3-TH) (3-TT)

/ \ / \ /

(4-HHH) (4-HHT) (4-THH) (4-TTT)

b) Number of Stages in the Tree Diagram

There are four stages in the tree diagram, one for each toss of the coin.

c) Possible Outcomes (Sample Space)

The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.

There are 16 possible outcomes in the sample space, as shown below:

HHHHH

HHHTT

HHTHT

HHTTH

HTTHH

HTHHT

HTHTH

THHHH

THHTT

THTHT

TTHHT

TTHTH

TTTHH

TTTTH

TTTTT

d) Number of Outcomes in the Sample Space

There are 2^4 = 16 outcomes in the sample space.

This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.

I hope this step-by-step explanation with the diagram helps! Let me know if you need further clarification.

Answer:

[B]. (1,-5)

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]

Solve:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]        Since 2y - 2y = 0 we take that away now we have;

[tex]4x=-6\\3x=13[/tex]        Add 4x + 3x = 7x

[tex]\frac{7x}{7} =\frac{7}{7}[/tex] Divide both sides by 7.

[tex]x=1[/tex]

Now substitute x to find y.

[tex]4(1)+2y=-6[/tex]

[tex]4 + 2y =-6[/tex]  Add 6 to the other side.

[tex]10 = 2y[/tex] Divide both sides by 2.

[tex]\frac{10}{2} =\frac{2y}{2}[/tex]

[tex]y = 5[/tex]

Hence, the answer is [B]. (1,-5)

RevyBreeze

The mortgage of A is $110158.2.

The mortgage of B is $137494.8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Mortgage A:

15 years at 4.5% with monthly payments of $611.99.

15 years = 15 x 12 = 180 months

Total paycheck.

= 180 x 611.99

= $110158.2

Mortgage B:

30 years at 4% with monthly payments of $381.93

30 years = 360 months

Total paycheck.

= 360 x 381.93

= $137494.8

Thus,

Mortgage A = $110158.2

Mortgage B = $137494.8

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Answer:

Derek's mango juice will last for 10 days.

Step-by-step explanation:

Derek buys 5 small bottles of mango juice, so he has 5 bottles in total.

He plans to drink half the contents of each bottle every morning, which means he will drink 1/2 * 1 bottle = 1/2 bottle of mango juice every day.

Since Derek drinks 1/2 bottle of mango juice every day, the 5 bottles of mango juice will last for 5 bottles / (1/2 bottle per day) = 10 days.

So, the answer is that the 5 bottles of mango juice will last for 10 days.

Hi there, here's your answer:

Given Derek buys 5 small bottles of Mango Juice
Also given that Derek drinks half a bottle every morning.

So taking the number of days to be 'x'

We get an equation [tex]\frac{1}{2} x = 5[/tex]

Upon cross multiplication, we get 1 × x = 5 × 2 = 10 days.

Therefore, the mango juice will last for 10 days.

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Answer: To verify the identity, we need to convert both sides into sines and cosines and see if they are equal.

Starting with the left side:

cotx = 1/tanx

So,

cotx - tanx = 1/tanx - tanx

Using the identity tan^2x = sec^2x - 1, we get

cotx - tanx = (sec^2x - 1) / tanx

Expanding the right side using the definition of cscx and sinx, we get:

cotx - tanx = secx(1/sinx - 2sinx)

So,

cotx - tanx = secx(cscx - 2sinx)

Since both sides are equal, we can conclude that the identity is verified.

Step-by-step explanation:

Answer:(A=πr2).

Step-by-step explanation:The cubic feet, or volume, of a cylindrical log is given by the volume of a cylinder V=πhr2. A log with radius of 2 feet and height of 10 feet would have a volume of about 125.66 cubic feet (or ft3). The volume can also be thought of as the area of the base times height with the base area being the area of a circle (A=πr2).

Answer:

XY = 18

Step-by-step explanation:

In this picture, XD = DW, and YE = EZ, so we are able to use the midline theorem. From the midline theorem, we can easily determine that (XY + WZ)/2 = DE. From this, we can plug in: (XY + [tex]\frac{4}{3}[/tex]XY) = 2 * 21. So, simplifying that equation gets: [tex]\frac{7}{3}[/tex]XY = 42. So, XY = [tex]42 * \frac{3}{7} = 18[/tex].

(if i'm going to be honest, i'm sure your geometry teacher covered this in class. just make sure to pay attention next time.)

Answer:

XY = 18 ft.

Step-by-step explanation:

The perimeter of the figure after a dilation with a scale factor of 4 is

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}\\[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

Given;

The perimeter= 12units

Scale factor=4

Now,

Dilation with the given scale factor;

= 12*1/4

=12/4

=3

Therefore, dilation by the given scale factor will be 3.

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Part A:

[tex]B\cap D[/tex] is asking for what the sets B and D have in common:

   [tex]B\cap D = \{4\}[/tex]

since B and D only have 4 in common.

Now [tex](B \cap D)'[/tex] is asking for all of the things in the universal set [tex]U[/tex] that are not in [tex]B\cap D[/tex].  That's what the little tick mark on the right side means.

   [tex](B \cap D)' = \{2, 3, 6, 7\}[/tex]

Part B:

[tex]B' = \{2, 3, 7\}[/tex] since those are the things not in B.

[tex]D=\{3, 4\}[/tex]

[tex]B'\cup D[/tex] is asking for all the things in either [tex]B'[/tex] or [tex]D[/tex].

    [tex]B'\cup D = \{2, 3, 4, 7\}[/tex]

(We don't need to list 3 twice, even though it was in both sets. )

A more accurate value would be 13.8271643518519

Round it however you need to.

======================================================

Explanation:

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

Let's see how many seconds there are in a day.

[tex]1 \text{ day} = (1 \text{ day})*\frac{24 \text{ hrs}}{1 \text{ day}}*\frac{60 \text{ min}}{1 \text{ hr}}*\frac{60 \text{ sec}}{1 \text{ min}}\\\\=\frac{24*60*60}{1*1*1}\text{ sec}\\\\=86,400\text{ sec}\\[/tex]

I set up those fractions so that the units "day", "hours", "minutes" cancel out. The only unit left over is "seconds".

There are exactly 86,400 seconds in 1 day.

This leads to the fact the sink fills up at a rate of 86,400 drops per day, since the leak rate is 1 drop per second.

----------

1 drop = 0.003 cubic inches approximately

x of those drops give a volume of 0.003x cubic inches, where x is some positive whole number. Set this equal to the volume of the sink and solve for x.

0.003x = 3584

x = 3584/0.003

x = 1,194,666.66666667 approximately

Round up to the nearest whole number to get 1,194,667

The sink starts to overflow when we have 1,194,667 drops of water in it.

Divide this over 86,400 mentioned earlier.

(1,194,667)/(86,400) = 13.8271643518519 approximately.

Round that however you need to. If for instance you round to 3 decimal places, then it would be 13.827

Answer:

Step-by-step explanation:

Step 1: Understanding the Problem

The problem involves finding an equation to approximate the amount of fuel in Jon's semitruck after he drives x miles. Jon started with 240 gallons of fuel and his truck uses 0.15 gallons of fuel for each mile he drives.

Step 2: Writing the Equation

We know that the amount of fuel in Jon's tank decreases as he drives. So, we can write the equation as:

f(x) = 240 - 0.15x

This equation says that the amount of fuel in Jon's tank after he drives x miles is equal to 240 gallons (the amount of fuel he started with), minus 0.15 gallons for each mile he drives.

Step 3: Interpreting the Equation

The function f(x) = 240 - 0.15x is a linear equation, which means that it is a straight line on a graph. The value 240 is the y-intercept, which means that when x = 0, the y-value of the function is 240 (the amount of fuel in Jon's tank when he starts driving). The value -0.15 is the slope of the line, which tells us how much the y-value decreases for each unit increase in x (in this case, how much the fuel decreases for each mile Jon drives).

Step 4: Conclusion

So, the equation f(x) = 240 - 0.15x can be used to approximate the amount of fuel in Jon's semitruck after he drives x miles. The equation is linear and can be written in the form f(x) = mx + b, where m = -0.15 (the slope of the line) and b = 240 (the y-intercept).