Consider the transformation.

2 trapezoids have identical angle measures but different side lengths. The first trapezoid has side lengths of 4, 2, 6, 2 and the second trapezoid has side lengths of 8, 4, 12, 4.
Which statement about the transformation is true?

Answer:

B) 1/2

Step-by-step explanation:

Note that pi=180.

Then we have 180/3=60 and so 5*60=300.

Thus cos 300=1/2.

Therefore, cos 5pi/3=1/2.

Answer: B

Step-by-step explanation:

Answer:

Blank A:  (17, 0)

Blank B:  (-2, 19)

Step-by-step explanation:

Blank A:

Step 1:  Find the slope of AB:

Before we can find the equation of CD, we'll first need to find the slope of AB

We can do this using the slope formula, which is given by:

m = (y2 - y1) / (x2 - x1), where

Thus, we can plug in (-10, -3) for (x1, y1) and (7, 14) for (x2, y2) in the slope formula to find m, the slope of AB:

m = (14 - (-3)) / (7 - (-10))

m = (14 + 3) / (7 + 10)

m = 17 / 17

m = 1

Thus, the slope of AB is 1.

Step 2:  Find the slope of CD:

The slope of perpendicular lines are negative reciprocals of each other as shown by the following formula:

m2 = -1 / m1, where

Thus, we can plug in 1 for m1 in the perpendicular slope formula to find m2, the slope of CD:

m2 = -1 / 1

m2 = -1

Thus, the slope of CD is -1.

Step 3:  Find the y-intercept of CD:

One of the equations we can use when looking for intercepts is the slope-intercept form of a line, whose general equation is given by:

y = mx + b, where

Thus, we can plug in (5, 12) for (x, y) and -1 for m to find b, the y-intercept of the line, allowing us to have the full equation in slope-intercept of CD:

12 = -1(5) + b

12 = -5 + b

17 = b

Thus, the equation of CD is y = -x + 17

For any x-intercept, the y-coordinate will always be 0 since the line is intersecting the x-axis.

Thus, we can find the x-coordinate of the x-intercept by plugging in 0 for y in y = -x + 17 and solving for x:

0 = -x + 17

-17 = -x

17 = x

Thus, the x-coordinate of the x-intercept of CD is 17.

Thus, the coordinates of the x-intercept of CD are (17, 0)

Blank B:

We can see that (-2, 19) lies on CD when we plug in (-2, 19) for (x, y) in y = -x + 17, as we get 19 on both sides of the equation when simplifying:

19 = -(-2) + 17

19 = 2 + 17

19 = 19

Thus, (-2, 19) lies on CD.

Answer:

(- 7, 4 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

P (- 7, - 4 ) → (- 7, - (- 4) ) → (- 7, 4 )

Answer:

x = -1, 1

Step-by-step explanation:

The function h(x) is given below:

[tex]\displaystyle{h(x)=\dfrac{x-9}{x^2-1}}[/tex]

The denominator must not equal to 0. Therefore,

[tex]\displaystyle{x^2-1\neq 0}[/tex]

Solve the inequality; factor the expression:

[tex]\displaystyle{(x-1)(x+1) \neq 0}[/tex]

Hence,

[tex]\displaystyle{x \neq 1,-1}[/tex]

Therefore, x = -1, 1 both are not in the domain of h.

The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.

To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.

Assuming we have a simplified progressive tax system with three tax brackets:

For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.

For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.

For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.

To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:

Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.

Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.

The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.

Now, we can sum up the taxes for each bracket:

Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket

Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840

Total Tax = Ksh 3,340

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Answer:

[tex]\frac{2.5}{1}[/tex]

Step-by-step explanation:

To express it as a fraction, divide 250 by 100 first to get 2.5. Then put that over 1.

Hope this helps!

The interval for the graphed function that has a local minimum of 0 is [-2, 0].

To determine the interval for the graphed function that has a local minimum of 0, we need to examine the behavior of the graph around the x-values where it crosses the x-axis.

We know that the graph crosses the x-axis at -2.5, 0, and 3. Since the local minimum occurs at 0, we need to find the interval where the graph is decreasing to the left of 0 and increasing to the right of 0.

From the given information, we can determine the following:

The graph is decreasing between -2.5 and 0 because it crosses the x-axis at -2.5 and 0, and the minimum value is at (-1.56, -6).

The graph is increasing between 0 and 3 because it crosses the x-axis at 3, and the maximum value is at (1.2, 2.9).

The correct option is [–2, 0].

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Question

On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0). Which interval for the graphed function has a local minimum of 0? [–3, –2] [–2, 0] [1, 2] [2, 4]

The measure of the indicated arc angle is 134 degrees.

The angle subtended by the arc at the centre of the circle is the angle of the arc.

Therefore, the central angle of an arc is the angle at the centre of the circle between the two radii subtended by the arc.

Hence, the central angle is also known as the arc's angular distance.

Therefore, the measure of an arc is the measure of its central angle.

Hence, the measure of the indicated arc is 134 degrees.

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Answer:

Jana is likely trying to solve option B:

"A person can afford a $290-per-month loan payment. If he is being offered a 4-year loan with an APR of 0.6%, compounded monthly, what is the most money that he can borrow?"

Step-by-step explanation:

Option B is the correct choice because it aligns with the values entered by Jana into the TVM Solver. Jana set the loan term (N) to 48, which represents 48 months (4 years). The APR value of 0.6% also matches what Jana inputted.

By selecting option B, Jana is attempting to find out the maximum amount of money she can borrow given that she can afford a $290-per-month loan payment and is offered a 4-year loan with an APR of 0.6%, compounded monthly.

This calculation will help Jana determine the loan amount that corresponds to her desired monthly payment and the given loan terms.

Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

Answer:

arc LKF = 208°

Step-by-step explanation:

the angle FLX between the tangent and the secant is half the measure of the intercepted arc LKF , then intercepted arc is twice angle FLX , so

arc LKF = 2 × 104° = 208°

To solve this problem, we can set up a system of equations based on the given information.

Let's assume the amount of money Ralph Chase will receive through the short-term note is represented by "x" and the amount through the long-term note is represented by "y".

According to the problem, the total amount Ralph plans to sell the property for is $145,000. Therefore, we have the equation:

[tex]\displaystyle x+y=145000[/tex] ...(1)

Now let's consider the interest paid annually. The interest paid on the short-term note at 10% is calculated as [tex]\displaystyle 0.10x[/tex], and the interest paid on the long-term note at 8% is [tex]\displaystyle 0.08y[/tex]. The total annual interest paid is given as $13,100. Therefore, we have the equation:

[tex]\displaystyle 0.10x+0.08y=13100[/tex] ...(2)

We now have a system of two equations (1) and (2). We can solve this system to find the values of "x" and "y".

Multiplying equation (2) by 100 to eliminate decimals, we get:

[tex]\displaystyle 10x+8y=1310000[/tex] ...(3)

Now we can solve equations (1) and (3) simultaneously using any method such as substitution or elimination.

Multiplying equation (1) by 10, we get:

[tex]\displaystyle 10x+10y=1450000[/tex] ...(4)

Subtracting equation (3) from equation (4), we can eliminate "x" and solve for "y":

[tex]\displaystyle 2y=140000[/tex]

Dividing both sides by 2, we find:

[tex]\displaystyle y=70000[/tex]

Now substituting the value of "y" back into equation (1), we can solve for "x":

[tex]\displaystyle x+70000=145000[/tex]

Subtracting 70000 from both sides, we have:

[tex]\displaystyle x=75000[/tex]

Therefore, the amount of money Ralph Chase will receive through the short-term note is 75,000 and through the long-term note is $70,000.

Answer:

A) [tex]y-7=\frac{3}{4}(x+1)[/tex]

Step-by-step explanation:

[tex]y-y_1=m(x-x_1)\\y-7=\frac{3}{4}(x-(-1))\\y-7=\frac{3}{4}(x+1)[/tex]

Parallel lines must have the same slope, and then plugging in [tex](x_1,y_1)=(-1,7)[/tex], we easily get our equation.

Answer:

the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.

Step-by-step explanation:

To find the equation of a line parallel to another line, we need to use the same slope. The given line has a slope of 3/4.

Using the point-slope form of a line, which is given by:

y - y₁ = m(x - x₁)

where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line, we can substitute the values (-1, 7) for (x₁, y₁) and 3/4 for m:

y - 7 = (3/4)(x - (-1))

Simplifying further:

y - 7 = (3/4)(x + 1)

Multiplying through by 4 to eliminate the fraction:

4(y - 7) = 3(x + 1)

Expanding:

4y - 28 = 3x + 3

Rearranging the equation to put it in standard form:

3x - 4y = -31

So, the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.

The number of CDs Ahmed has: The expression (1/2) * c + 5 represents the number of CDs Ahmed has, as we derived earlier. Therefore, this option is correct. Option A

According to the given information, Ahmed has five more CDs than one-half the number of CDs Julia has. One-half of the number of CDs Julia has can be represented as (1/2) * c. Ahmed has five more CDs than this value, so we can express the number of CDs Ahmed has as:

Ahmed's CDs = (1/2) * c + 5

Now, let's analyze the options provided:

A. The number of CDs Ahmed has:

The expression (1/2) * c + 5 represents the number of CDs Ahmed has, as we derived earlier. Therefore, this option is correct.

B. The number of CDs Julia has:

The expression (1/2) * c + 5 does not directly represent the number of CDs Julia has. It represents the number of CDs Ahmed has. Therefore, this option is incorrect.

C. The number of CDs Ahmed has more than Julia:

This option is incorrect because the expression (1/2) * c + 5 represents the absolute number of CDs Ahmed has, not the difference between the number of CDs Ahmed and Julia have.

D. The number of CDs Ahmed and Julia have altogether:

The expression (1/2) * c + 5 represents only the number of CDs Ahmed has. It does not include Julia's CDs. Therefore, this option is incorrect.

In conclusion, the expression (1/2) * c + 5 represents the number of CDs Ahmed has.

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The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.

To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.

From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).

Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).

Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.

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The value of 12 remains 12.

The value of X cannot be determined without additional information.

The value of 25° remains 25°.

To find the values of the variables in the given information, we have:

12: This is a given value and does not require calculation. Therefore, the value of 12 remains as it is.

X: Without additional information or an equation to solve, we cannot determine the value of X. It could represent any unknown quantity or variable, and its specific value would depend on the context or problem being solved.

25°: This is an angle measure in degrees. The value of 25° remains as it is.

To summarize:

The value of 12 remains 12.

The value of X cannot be determined without additional information.

The value of 25° remains 25°.

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By analyzing the temperature-altitude relationship on a mountain, we can establish a linear model that describes how temperature changes with varying altitudes.

Step-by-step explanation:

a) Knowing the altitude and temperature data, we can use the formula for the slope of a line:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are two points on the line.

Using the altitude and temperature values provided:

(x1, y1) = (4800, 79) and (x2, y2) = (6400, 67),

we can calculate the slope:

m = (67 - 79) / (6400 - 4800)

= -12 / 1600

= -0.0075.

Now, to find the y-intercept (b), we can substitute one of the points (4800, 79) into the equation:

79 = (-0.0075)(4800) + b.

Solving for b, we have:

b = 79 + 0.0075(4800)

= 79 + 36

= 115.

Therefore, the linear model is T(x) = -0.0075x + 115.

b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.

c) To find T(5800), we can substitute x = 5800 into the linear model:

T(5800) = -0.0075(5800) + 115

= -43.5 + 115

= 71.5.

Answers:

a) T(x) = -0.0075x + 115.

b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.

c) 71.5 degrees.

Step-by-step explanation:

a linear relationship or function is described in general as

y = f(x) = ax + b

Because the variable term has the variable x only with the exponent 1, this makes this a straight line - hence the name "linear".

here f(x) is P(x) :

P(x) = ax + b

now we are using both given points (ordered pairs) to calculate a and b :

20 = a×170 + b

2820 = a×220 + b

to eliminate first one variable we subtract equation 1 from equation 2 :

2800 = a×50

a = 2800/50 = 280/5 = 56

now, we use that in any of the 2 original equations to get b :

20 = 56×170 + b

b = 20 - 56×170 = 20 - 9520 = -9500

so,

P(x) = 56x - 9500

33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)

To calculate the volume of a triangular prism, the formula that should be used is given as follows;

Volume= BH

where;

B= area of base = 1/2 × base×height

= 1/2×4×3

= 6

H= 6

Volume= 6×6= 36.

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a. The interval of time between eruptions if the previous eruption lasted 4 minutes is 86.51 minutes.

b. The residual for this cycle is 2.07 minutes.

c. The interval of time between eruptions lasted for 2.07 minutes than the regression line equation predicted.

d. The slope of the regression line means that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

e. No, the value of the y-intercept doesn't have meaning in the context of the problem.

Based on the information provided above, the relationship between the duration of the previous eruption (x in minutes) and the interval of time between eruptions (y in minutes) is modeled by this regression line equation:

ÿ = 33.35 + 13.29x

Part a.

When x = 4 minutes, the value of is given by:

ÿ = 33.35 + 13.29(4)

ÿ = 86.51 minutes.

Part b.

The residual for the given cycle can be calculated as follows;

Residual = y - ÿ

Residual = 62 - (33.35 + 13.29(2))

Residual = 62 - 59.93

Residual = 2.07 minutes.

Part c.

Based on the calculation above, we can logically deduce that the interval of time between eruptions lasted for 2.07 minutes than the equation of regression line predicted.

Part d.

The slope of the regression line is equal to 13.29 and it implies that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

Part e.

In the context of the problem, we can logically deduce that the value of the y-intercept doesn't have any meaning because the duration of the previous eruption cannot be equal to 0 minutes.

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The calculated value of x to the nearest degree is 56

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

The triangle

The value of x can be caluclated using the following cosine rule

So, we have

cos(x) = 5/9

Evaluate the quotient

cos(x) = 0.5556

Take the arc cos of both sides

x = 56

Hence, the value of x to the nearest degree is 56

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The perimeter of the rectangle is 140 inches.

Let's denote the width of the rectangle as w. According to the given information, the length of the rectangle is six times its width, so we can express the length as 6w.

The area of a rectangle is given by the formula A = length × width. Substituting the values we have:

A = (6w) × w

600 = 6w^2

To solve for w, we divide both sides of the equation by 6:

w^2 = 100

Taking the square root of both sides:

w = ±10

Since width cannot be negative in this context, we discard the negative value and consider the positive value, w = 10.

Now that we have the width, we can find the length of the rectangle:

Length = 6w = 6 × 10 = 60

The perimeter of a rectangle is given by the formula P = 2(length + width). Substituting the values:

P = 2(60 + 10)

P = 2(70)

P = 140

Therefore, the perimeter of the rectangle is 140 inches.

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(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

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a) Brooke's monthly income is $3,166.67 from her full-time job as a cook, and an additional $532.59 from her part-time job, resulting in a total monthly income of $3,699.26.

b) Yes, the rent of $975 per month for the new apartment falls within the housing guideline of spending 30% or less of her monthly income on housing.

a) To determine Brooke's monthly income, we need to calculate her earnings from both her full-time and part-time jobs.

Full-time job income: Brooke earns $38,000 per year as a cook.

To find her monthly income from this job, we divide her annual salary by 12:

Monthly income from full-time job = $38,000 / 12 = $3,166.67

Part-time job income: Brooke earns $10.25 per hour and works 12 hours per week.

To find her weekly income from this job, we multiply her hourly rate by the number of hours she works:

Weekly income from part-time job = $10.25/hour x 12 hours/week = $123

To find her monthly income, we multiply her weekly income by the average number of weeks in a month (approximately 4.33):

Monthly income from part-time job = $123/week x 4.33 weeks/month = $532.59 (rounded to the nearest cent)

To calculate Brooke's total monthly income, we add her full-time and part-time job incomes:

Total monthly income = $3,166.67 + $532.59 = $3,699.26 (rounded to the nearest cent)

b) The rent for the new apartment is $975 per month, including utilities. To determine if it falls within the housing guidelines, we need to compare it to a percentage of Brooke's monthly income.

Typically, a common guideline is to spend no more than 30% of your monthly income on housing.

Percentage of monthly income for housing = 30% of total monthly income

= 30/100 x $3,699.26

= $1,109.78 (rounded to the nearest cent)

Since the rent of $975 is lower than the guideline of $1,109.78, if Brooke takes this apartment, it will fall within the housing guidelines.

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Step-by-step explanation:

Perimeter =  pi * diameter

  radius = 1  1/3  yard   then diameter =  2  2/3 yd

perimter = pi *  2 2/3   yds = 8.38 yds

By completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.

(a) To plot the lines y = 2x + 1 and y = 10 - x, we need to complete the tables of values and then plot the points on the axes.

For the line y = 2x + 1, we can choose some values of x and calculate the corresponding y values:

x | y

0 | 1

1 | 3

2 | 5

For the line y = 10 - x, we can also choose some values of x and calculate the corresponding y values:

x | y

0 | 10

1 | 9

2 | 8

Plot the points (0, 1), (1, 3), and (2, 5) for the line y = 2x + 1, and the points (0, 10), (1, 9), and (2, 8) for the line y = 10 - x on the provided axes.

(b) To find the solution to the simultaneous equations y = 2x + 1 and y = 10 - x,

we need to identify the point(s) where the two lines intersect on the graph.

From the plotted lines, we can see that they intersect at the point (3, 7). Therefore, the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7.

In conclusion, by completing the tables of values and plotting the lines, we can determine that the solution to the simultaneous equations y = 2x + 1 and y = 10 - x is x = 3 and y = 7, which corresponds to the point (3, 7) on the graph.

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Answer:

(a) To find the average cost in 2011, substitute 11 for x in the function.

g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64

The average cost in 2011 was $2,247.64.

(b) Using the graphing calculator, graph the function in the viewing window

[6, 15] by [1,000, 3,000].

The correct graph is B.

(c) A. The average cost increases at a slower rate as time goes on.

The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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