need help with this rational functions homework question

Answer:

The length of AB is

[tex] \sqrt{ {5}^{2} + {5}^{2} + {5}^{2} } = \sqrt{75} = 3 \sqrt{5} [/tex]

3√5 cm is about 6.7 cm.

Answer:

inflationary expenditure gap of $500

Step-by-step explanation:

At AE2 there is an inflationary expenditure gap of $500 (assuming full-employment output is $2000). The fiscal authority could increase taxes or decrease expenditures, which will shift the aggregate expenditures schedule down to AE0.

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The three statements that are true about the function and its graph are:

The graph of the function is a parabola.

The graph opens downwards, since the coefficient of x² is positive.

The graph contains the point (0, 12), which can be obtained by substituting x=0 in the function.

To check the other statements:

To find f(-10), we substitute x=-10 in the function:

f(-10) = 1/5*(-10)² - 5*(-10) + 12 = 82. So the statement "The value of f(–10) = 82" is true.

To check if the graph contains the point (20,-8), we substitute x=20 in the function:

f(20) = 1/5*(20)² - 5*(20) + 12 = -68. This means the point (20,-8) does not lie on the graph of the function.

To check if the graph contains the point (0,0), we substitute x=0 in the function:

f(0) = 1/5*(0)² - 5*(0) + 12 = 12. This means the point (0,0) does not lie on the graph of the function.

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Answer:

66 because 10 percent of 60 is 6 so add 60 and 6

The option that interchanges the hypothesis with the conclusion is the Converse.

In logic and mathematics, the Converse of an if-then statement switches the positions of the hypothesis (the "if" part) and the conclusion (the "then" part).

It is formed by flipping the original statement.

For example, let's consider the statement: "If it is raining, then the ground is wet."

The hypothesis is "it is raining," and the conclusion is "the ground is wet."

The Converse of this statement would be: "If the ground is wet, then it is raining."

Here, the positions of the hypothesis and the conclusion are interchanged.

It's important to note that the Converse is not always true.

In some cases, the original statement and its converse may have different truth values.

A statement and its converse can be both true, both false, or one true while the other false.

The Converse is a distinct logical operation from other concepts such as the Biconditional and the Inverse.

The Biconditional establishes a two-way relationship between two statements, while the Inverse negates both the hypothesis and the conclusion of the original statement.

Therefore, the option that interchanges the hypothesis with the conclusion is the Converse.

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Answer: Converse

Step-by-step explanation: Took the exam answer above correct

A. not continuous

Continuous functions have no jumps or vertical asymptotes.

Continuity

For a function to be continuous, each point on the function must be defined. This means that there cannot be points on the graph where there is no value or coordinate point. Additionally, all points must be connected by the graph. Sudden jumps in the graph that are not connected by anything are not continuous.

Determining Continuity

The graph above is not continuous. We know this for 2 reasons. Firstly, the graph is not defined at x = -3. Since there is an open circle at x = -3, the value is not defined. Thus, the function cannot be considered continuous. Additionally, there are multiple jumps. At x = -3, the function suddenly jumps to x = -2 without the points being connected. The same thing happens again at x = 1. This also shows that the graph is not continuous.

Answer:

The center is (9, -4), and the radius is

√36 = 6.

The equation that represents a linear function is D 4x - 2 = 6.

A linear function is a function whose graph is a straight line. In general, the equation of a linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Option A (x = 1) represents a vertical line passing through x = 1. Since the slope of a vertical line is undefined

Option B (y = 12²) represents a horizontal line passing through y = 144. Since the slope of a horizontal line is zero

Option C (y = 12-1) represents a horizontal line passing through y = 11. Since the slope of a horizontal line is zero

Option D (4x - 2 = 6) can be rewritten as 4x = 8 or x = 2. This is the equation of a vertical line passing through x = 2.

Therefore, the only equation that represents a linear function is D 4x - 2 = 6.

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The balance in the account after the given period is [tex]\$6,872.74[/tex]  

we know that

The compound interest formula is equal to  

[tex]\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}[/tex]

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]\text{t}= 8 \ \text{years}[/tex]

[tex]\text{P}=\$4,000[/tex]

[tex]\text{r}=0.07[/tex]

[tex]\text{n}=1[/tex]

substitute in the formula above

[tex]\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74[/tex]  

Answer:

Okay, based on your previous question and the analysis, the 3 statements that are true about the function f(x) = x2 – 5x + 12 and its graph are:

   The graph of the function is a parabola.

   The graph contains the point (0, 0).

So the options you should select are:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

Let me know if selecting options 2 and 5 makes sense! I can provide any additional details or clarification if needed.

Please let me know if you have any other questions! I'm happy to help explain any other concepts related to this quadratic function and its graph.

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 .The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Okay, just to reiterate, based on the previous analysis, the 3 statements that are TRUE about the quadratic function f(x) = x2 – 5x + 12 and its graph are:

   The graph of the function is a parabola. (true)

   The graph contains the point (0, 0). (true)

   The graph of the function opens down. (false, unknown without seeing graph)

   The value of f(–10) = 82 (false)

   The graph contains the point (20, –8). (false)

So you should select options:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

Please let me know if selecting these 3 options makes sense and matches the analysis. I can re-explain anything if needed.

Your selected options should be:

2) The graph of the function is a parabola.

   The graph contains the point (0, 0).

   The graph of the function opens down.

Let me know if these look correct or if you have any other questions! I'm happy to help explain further or go over any part of the analysis.

Please select options 2, 5 and 3 as the statements that are true about the quadratic function and its graph.

Step-by-step explanation:

The probability that the science teacher trips over the cords for the first time during the 4th period of the day is 0.0279.

A discrete probability distribution has countable alternative values for the random variable and a stated probability for each one. Since the potential values are 0, 1, or 2, and the probability of each conceivable value can be determined, the probability distribution of the number of heads acquired after two coin flips is an example of a discrete probability distribution.

In contrast, a continuous probability distribution has a continuous range of possible values for the random variable and a probability of zero for any given value.

Given that, the probability of tripping is given as: 0.35.

Now, the probability of tripping on the 4th period is given by:

[tex]P(X=k) = (1-p)^{(k-1)} * p[/tex]

Now, for k = 4 and p = 0.35 we have:

[tex]P(X=4) = (1-0.35)^{(4-1)} * 0.35[/tex]

P(X=4) = 0.0279

Hence, the probability that the science teacher trips over the cords for the first time during the 4th period of the day is 0.0279.

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The left-hand side simplifies to 14, and the right-hand side is also 14. Therefore, the equation is true when m = 4.

"LHS = RHS" stands for "left-hand side equals right-hand side". It is a notation commonly used in mathematics to show that two expressions are equal to each other.

In mathematics, to substitute means to replace a variable or expression in an equation or function with a specific value or expression.

To substitute the value 4 for m in the given equation, we replace every occurrence of m:

m + 2(m + 1) = 14

4 + 2(4 + 1) = 14

4 + 2(5) = 14

4 + 10 = 14

14 = 14

14 is the result of simplifying the left and right sides, respectively. Consequently, when m = 4, the equation is accurate.

So, the value 4 is a solution to the given equation.

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2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

What is scatterplot?

A scatter plot is a particular type of plot or mathematical diagram by using Cartesian coordinates to display values for typically two variables for a set of values. It represents the correlation between two sets of data which may be linear or non linear sometimes strongly positive linear sometimes it may be curvilinear sometimes it may be null.

In the first plot it visibly showing a graph for straight line that is strong positive linear scatter plot. Same for the last but there is a little difference that it is negative linear scatter plot.

For the second one there is a null scatter plot. So there is no correlation.

For the 3rd graph there is a curvilinear relation in the scatterplot.

Hence, 2nd and 3rd scatterplot do not suggest a linear relationship between x and y.

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The Simplification of the algebraic expression gives:

a. -2/3x² - (4/15)xy +  (11/4)y²

b. -(12/7)x³ + (20/9)y

Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression

a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

To simplify this, add or subtract like terms. That is:

(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

     = (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y²  + (3/4)y²

     = -2/3x² - (4/15)xy +  (11/4)y²

b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y

To simplify this, add or subtract like terms. That is:

(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y

                                                    = -(12/7)x³ + (20/9)y

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There are 100 cookies.

To find the number of cookies, we can set up a proportion using the given ratio of cookies to glasses of milk, which is 4:1. Let x be the number of cookies:

4/1 = x/25

Now, cross-multiply and solve for x:

1 * x = 4 * 25

x = 100

Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

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The distribution of snowfall amounts is best described as bimodal, with modes at 2 inches and 7 inches. So, the range is a more appropriate measure of variation than the standard deviation.

A bimodal distribution can be identified in a histogram when two distinct groups can be seen there. A bimodal distribution actually has two modes or two different data clusters.

In a bimodal distribution, no particular data value has the highest frequency of occurrence, rather two data values have the highest frequency.

The line plot of the distribution by Damon has two modes and is, therefore, bimodal.

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The condensed form of the expression abc x abc x abc is (abc)^3

When we have the same base raised to different exponents that are being multiplied together, we can simplify or condense the expression by adding the exponents.

In this case, we have the same base "abc" being raised to the exponent of 1 three times, so we can write it as:

abc x abc x abc

To condense this expression, we add the exponents 1+1+1=3, and write it as:

(abc)^3

So, the condensed form of the expression "abc x abc x abc" is "(abc)^3".

This is an example of the exponent rule for multiplying powers with the same base.

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The function with y-intercept as 1 is h(x) = 0.5(2)ˣ + 0.5.

The y-intercept is the point where the graph intersects the y-axis. In other words, the y-intercept of a function is the value of y when x = 0.

Therefore, let's find the function with y-intercept as 1.

Hence,

h(x) = 0.5(2)ˣ + 0.5

Let's make x = 0 to check if the value of y = 1

Therefore,

h(x) = 0.5(2)ˣ + 0.5

h(0) = 0.5(2)⁰ + 0.5

h(0) = 0.5(1) + 0.5

h(x) = 0.5 + 0.5

h(x) = 1

Therefore, the function with y-intercept as 1 is h(x) = 0.5(2)ˣ + 0.5

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The height of the triangle is 6 inches and the base of the triangle is 30 inches.

Let's denote the height of the triangle as h inches. According to the given information, the base of the triangle is 6 inches more than 4 times the height, which can be expressed as 4h + 6 inches.

The formula for the area of a triangle is given by the formula A = (1/2) * base * height. Substituting the given values, we have:

90 = (1/2) * (4h + 6) * h

To solve for h, we can first multiply both sides of the equation by 2 to eliminate the fraction:

180 = (4h + 6) * h

Next, we can distribute the h on the right-hand side:

[tex]180 = 4h^2 + 6h[/tex]

Rearranging the equation to form a quadratic equation in standard form:

[tex]4h^2 + 6h - 180 = 0[/tex]

Now, we can solve this quadratic equation for h using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

[tex]x = (-b ± \sqrt{(b^2 - 4ac)) / (2a)}[/tex]

In our equation, a = 4, b = 6, and c = -180. Plugging in these values, we get:

[tex]h = (-6 ± \sqrt{(6^2 - 4 * 4 * -180)} ) / (2 * 4)[/tex]

Simplifying further:

[tex]h = (-6 ± \sqrt{(36 + 2880)} ) / 8h = (-6 ± \sqrt{(2916)} ) / 8[/tex]

h = (-6 ± 54) / 8

Now we can find the two possible values for h:

h1 = (-6 + 54) / 8 = 48 / 8 = 6

h2 = (-6 - 54) / 8 = -60 / 8 = -7.5

Since height cannot be negative in this context, we discard the solution h2 = -7.5.

So, the height of the triangle is 6 inches.

Now, we can use this value of h to find the base of the triangle:

Base = 4h + 6 = 4 * 6 + 6 = 24 + 6 = 30 inches.

So, the height of the triangle is 6 inches and the base of the triangle is 30 inches.

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Answer:

There are 2598960 different ways to choose 5 cards from a standard 52-card deck.

Answer:

(52−5)5 = 2598960 different ways to choose 5 cards from the available 52 cards.

Step-by-step explanation:

Answer:

Step-by-step explanation:

125 pounds decreased by 4%  it would be 120 because 4% of 125 is 5, so you subtract 5 from 125 and then you get 120.

Using equations, we can find the required equation for each of the cases as follows:

1. t = cd

2. t = qh

3. t = wm

Equations are mathematical expressions that have two algebraic expressions on either side of the equals (=) symbol. It proves that the expressions printed on the left and right sides are equally valid. In each mathematical equation, we have LHS = RHS (left hand side = right hand side). Equations can be solved to find the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation. We'll consider that to be a term.

As per the question,

The total number of caps per day = c

Total number of caps made = t

Total number of days = d.

Now, the required equation will be:

t = c × d

⇒ t = cd

Coming to the next question,

Quizzes graded per hour = q.

Total number of quizzes = t.

Total number of hours = h.

So, the required equation will be:

t = q × h

⇒ t = qh.

Coming to the final question,

Words typed per minute = w.

Total number of words = t.

Total number of minutes = m

So, the required equation will be:

t = w × m

⇒ t = wm.

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Therefore, Janelle would need 1872 square inches of plywood to make the chest.

A square inch (sometimes known as an in2 or sq. in.) is a unit of area measurement. A square with sides that are one inch long has an area of one square inch: Two lengths are used to measure a square area.

The areas of all the sides must be added up in order to determine the surface area of the chest. For instance, if we use 1/2 inch plywood and the chest is 24 inches by 12 inches by 18 inches, the surface area of the chest would be:

Top and bottom: 2 * (24 inches * 12 inches) = 576 square inches

Front and back: 2 * (18 inches * 12 inches) = 432 square inches

Sides: 2 * (24 inches * 18 inches) = 864 square inches

Total surface area = 576 + 432 + 864 = 1872 square inches

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Total stored energy = (1/625) ∞

Voltage, also known as electric potential difference, is the measure of the electric potential energy per unit of charge in an electric circuit. It is the force that drives the electric charge in a circuit, similar to how pressure drives water through a pipe. Voltage is measured in volts (V) and is usually represented by the symbol "V". Voltage can be either positive or negative, depending on the direction of current flow and the orientation of the voltage source.

A. The voltage across an inductor is proportional to the time derivative of the current through it, according to Faraday's law of electromagnetic induction. This can be expressed mathematically as:

v(t) = L di/dt

where v(t) is the voltage across the inductor, L is the inductance in henries, and di/dt is the time derivative of the current through the inductor.

In this case, we have [tex]v(t) = 8e^{(-4t)[/tex] V and L = 250 H. Integrating both sides of the above equation with respect to time gives:

∫v(t) dt = L ∫di/dt dt

∫[tex]8e^{(-4t)} dt = 250[/tex] ∫di/dt dt

[tex]-2e^{(-4t)[/tex]= 250i(t) + C

where C is the constant of integration. We can assume that the initial current is zero, so at t = 0, i(0) = 0. This means that C = -2. Substituting this into the equation above, we get:

[tex]-2e^{(-4t)[/tex]= 250i(t) - 2

Solving for i(t), we get:

i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]

B. The power absorbed by an inductor is given by:

P = i² R

where P is the power, i is the current, and R is the resistance of the circuit. In an ideal inductor, the resistance is zero, so the power absorbed is also zero.

However, the energy stored in an inductor can be calculated using the following formula:

E = 1/2 L i²

where E is the energy stored, L is the inductance, and i is the current.

In this case, we have L = 250 H and i(t) = (2/250) [tex]- (2/250)e^{(4t)[/tex]Substituting these values into the above equation, we get:

E = 1/2 (250) [(2/250) [tex]- (2/250)e^{(4t)]^2[/tex]

Simplifying this expression, we get:

E = (1/625) [tex]- (2/625)e^{(4t)[/tex]+ (2/625)e^(8t)

To determine the total stored energy, we need to integrate this expression over the interval 0 to infinity, since the voltage and current are given for all values of t. This gives:

Total stored energy = ∫E dt from 0 to infinity

Total stored energy = (1/625) ∫1 dt from 0 to infinity[tex]- (2/625) ∫e^{(4t)[/tex]dt from 0 to infinity + (2/625) ∫e^(8t) dt from 0 to infinity

Total stored energy = (1/625) ∞ [tex]- (2/625) [1/4 e^{(4t)][/tex]from 0 to infinity + (2/625) [1/8 e^(8t)] from 0 to infinity

Since the integrals involving exponential functions go to infinity as t goes to infinity, these terms become zero. Therefore, we are left with:

Total stored energy = (1/625) ∞

which is an infinite value. This is because the energy stored in an inductor is not finite, but rather is dependent on the magnetic field generated by the inductor, which can extend infinitely far.

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Answer: To calculate the amount of money you will have in the account after 40 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money in the account after t years, P is the principal (the initial amount of money deposited), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $2000, r = 0.02 (since the interest rate is 2%), n = 12 (since the interest is compounded monthly), and t = 40. Plugging these values into the formula, we get:

A = 2000(1 + 0.02/12)^(12*40)

A = $5,837.85

So you will have $5,837.85 in the account after 40 years.

Answer:

1 pound of jelly beans cost $1.75 , 1 pound of trail mix cost $3.75

Step-by-step explanation:

let j represent 1 pound of jelly beans and t represent 1 pound of trail mix , then

5j + 3t = 20 → (1)

7j + 9t = 46 → (2)

multiplying (1) by - 3 and adding to (2) will eliminate t

- 15j - 9t = - 60 → (3)

add (2) and (3) term by term to eliminate t

(7j - 15j) + (9t - 9t) = 46 - 60

- 8j + 0 = - 14

- 8j = - 14 ( divide both sides by - 8 )

j = [tex]\frac{-14}{-8}[/tex] = 1.75

substitute j = 1.75 into either of the 2 equations and solve for t

substituting into (1)

5(1.75) + 3t = 20

8.75 + 3t = 20 ( subtract 8.75 from both sides )

3t = 11.25 ( divide both sides by 3 )

t = 3.75

then

cost of 1 pound of jelly beans = $1.75

cost of 1 pound of trail mix = $3.75

Answer:

Cost for each pound of jelly beans:  $1.75

Cost for each pound of trail mix:  $3.75

Step-by-step explanation:

Define the variables:

Using the given information and defined variables, create a system of equations:

[tex]\begin{cases}5J+3T=20\\7J+9T=46\end{cases}[/tex]

To solve the system of equations, multiply the first equation by 3 to create a third equation:

[tex]5J \cdot 3+3T \cdot 3=20\cdot 3[/tex]

[tex]15J+9T=60[/tex]

Subtract the second equation from the third equation to eliminate the term in T:

[tex]\begin{array}{crcrcl}&15J & + & 9T & = & 60\\\vphantom{\dfrac12}- & (7J & + & 9T & = & 46)\\\cline{2-6}\vphantom{\dfrac12} &8J&&&=&14\end{array}[/tex]

Solve the equation for J by dividing both sides by 8:

[tex]\dfrac{8J}{8}=\dfrac{14}{8}[/tex]

[tex]J=1.75[/tex]

Therefore, the cost of each pound of jelly beans is $1.75.

To find the cost of one pound of trail mix, substitute the found value of J into one of the original equations and solve for T.

Using the second equation:

[tex]7(1.75)+9T=46[/tex]

[tex]12.25+9T=46[/tex]

[tex]12.25+9T-12.25=46-12.25[/tex]

[tex]9T=33.75[/tex]

[tex]\dfrac{9T}{9}=\dfrac{33.75}{9}[/tex]

[tex]T=3.75[/tex]

Therefore, the cost of each pound of jelly beans is $3.75.

Answer: 20.64 miles.

Step-by-step explanation: The assignment of nomenclature to the location of the boat's initiation as point A, the termination of the first course of the excursion as point B, and the termination of the second course of the journey as point C is proposed. The present study reveals that the spatial positioning of point A and point B is separated by a distance of precisely 15 miles in an eastward direction. Similarly, point B and point C are separated by a distance of 15 miles, but oriented along the vector of N 20° E.

The application of trigonometry provides a means to determine the spatial separation between point B and point C. Based on computations, the distance from point B to point C has been estimated to be approximately 7.83 miles along the northward direction and approximately 14.16 miles along the eastward direction.

Henceforth, the computation of the distance between point A and point C (i.e., the prevailing separation of the boat from the pier) can be determined by the ensuing method:

The mathematical expression denoting the distance between points A and C, designated as AC, is given by the square root of the sum of the squares of the distances between points A and B, designated as AB, and between points B and C, designated as BC. In formulaic notation, this can be expressed as AC = √((AB)² + (BC)²).

The magnitude of the distance denoted by AC, between two points A and C, can be calculated using the Euclidean distance formula, which involves the square root of the sum of the squares of the differences between the corresponding coordinates of the two points. In this particular case, the calculation results in the expression √(15² + 14.16²).

The distance between points A and C, denoted as AC, can be expressed mathematically as the square root of the sum of the squares of the horizontal and vertical distances between them. Thus, AC = √(225 + 200.89), where 225 and 200.89 represent the square of the horizontal and vertical distance, respectively. This equation can be simplified to yield the measurement of the physical distance between points A and C in the applicable units of length.

The distance between points A and C is determined to be the square root of 425.89 in units of length.

The measurement of the distance between point A and point C is approximately equivalent to 20.64 miles.

Answer: Graph A.

Step-by-step explanation: