Determine whether f(x) = 0 has any repeated real solutions

Answers

Answer 1

Answer:

Yes

Step-by-step explanation:

These are the rules regarding polynomial graphs and their real zeros (solutions)

If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero.If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity. That means it will have 2, 4 repeated solutionsIf the graph crosses the x-axis at a zero, it is a zero with odd multiplicity i.e. multiplicity of 3, 5 etcThe sum of the multiplicities cannot be greater than the degree of the polynomial

In the above graph we see that the graph touches the x-axis at x = 3. This means (x - 3)ᵃ is a factor of the polynomial where p is an even number (2, 4, 6 etc)

That means x = 3 is a repeated real solution. It appears that the multiplicity is 2 so one factor of the polynomial is (x - 3)²

More inf o(ignore if you want)

The other real roots are x = -1 and x = 5 because the graph crosses the x axis at these two values of x. So the multiplicity of both factors ( x + 1) and (x - 5) is odd. Since at the crossover point, the graph is almost linear, we can safely assume that the multiplicity of the graph is odd at these points and equal to 1

Therefore the polynomial can be factored as
(x + 1)(x - 5)(x - 3)²

The degree of the polynomial is the sum of the multiplicities and is equal to 1 + 1 + 2 = 4 so it is a quartic polynomial of the form ax⁴ + bx³ + cx² + dx + e

Related Questions

62x2^5x=27 what is the answerr to this question that i cant figure out

Answers

Answer: hello am I solving for x?

Step-by-step explanation:question

As people are living longer and the world's population keeps increasing, there are more and more people ages 65 or older. Over the last 17 years, the number of people ages 65 or older has been growing exponentially, increasing about 2.7% every year. In 2017, there were approximately 656 million people ages 65 or older. If the trend continues, in what year will the population of people 65 or older surpass 1 billion?

Answers

To solve this problem, we can use the exponential growth formula:

Nt = N0 * (1 + r)^t

where Nt is the population at time t, N0 is the initial population, r is the annual growth rate as a decimal, and t is the number of years.

We know that N0 = 656 million, r = 0.027 (since the population is growing at a rate of 2.7% per year), and we want to find the year when Nt = 1 billion.

Substituting in these values, we get:

1 billion = 656 million * (1 + 0.027)^t

Simplifying:

1.524 = 1.027^t

Taking the natural log of both sides:

ln(1.524) = t * ln(1.027)

Dividing by ln(1.027):

t = ln(1.524) / ln(1.027)

Using a calculator:

t ≈ 23.1 years

Therefore, if the trend continues, the population of people ages 65 or older will surpass 1 billion in approximately 23.1 years from 2017.

Answer: 2040 (rounded to the nearest whole year).

Find the equation of the line.
Use exact numbers.

Answers

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = [tex]\frac{1-7}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

Writing the equation of the line in slope-intercept form.

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

Answers

Answer:

Let's start by figuring out how many aliens are captured every four hours. If half of the aliens are captured every four hours, that means the number of remaining aliens is also halved every four hours. So we can use exponential decay to model the number of aliens remaining after t four-hour periods:

N(t) = N₀ (1/2)^t

where N₀ is the initial number of aliens and t is the number of four-hour periods that have passed.

The initial number of aliens is 1,300, and we want to know how many remain after 14 four-hour periods (from 2:00am to 8:00pm, a total of 16 hours with 4-hour intervals):

N(14) = 1,300 (1/2)^14

N(14) ≈ 20.16

So there will be approximately 20 aliens remaining free at 8:00pm on Wednesday. Note that the actual number may be slightly different due to rounding, and also because we assumed that the capture rate remains constant throughout the 16-hour period.

Step-by-step explanation:

N(t) = N₀ (1/2)^t

where N₀ is the initial number of aliens and t is the number of four-hour periods that have passed.

The initial number of aliens is 1,300, and we want to know how many remain after 14 four-hour periods (from 2:00am to 8:00pm, a total of 16 hours with 4-hour intervals):

N(14) = 1,300 (1/2)^14

N(14) ≈ 20.16

The question is in the first picture, the other two pictures should help you solve the question. Certain parts of it won't make sense in the pictures two and three since its a multiple part test. Please answer this as soon as possible if you can, thank you in advance

Answers

The logo that fits the requirement is the circle logo i.e. logo 1

Calculating the area and the width in meters?

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

The figures that represent the logos

For the circle logo, we have

Area = 3.14 * 1/2 * 1/2

Convert units to feet using the scale

Area = 22/7 * 1/2 * 1/2 * 7 * 7

Evaluate

Area = 38.5 sq feet

Also, we have

Width = 1/2 feet *7

Width = 3.5 feet

For the plus sign, we have

Area = 5 * 1/2 * 1/2

Convert units to feet using the scale

Area = 5 * 1/2 * 1/2 * 6 * 6

Evaluate

Area = 45 sq feet

Also, we have

Width = 3 * 1/2 * 6

Width = 9 feet

Hence, the logo that fits the requirement is the circle logo i.e. logo 1

Answers

The maximum value of z = 4x + 4y, subject to the given constraints, is 92/3, which occurs when x = 14/3 and y = 4.

To maximize the objective function z = 4x + 4y subject to the given constraints, we can solve this linear programming problem using the graphical method.

First, let's graph the feasible region determined by the constraints:

1. Graph the line 2x + 4y = 28:

Rewrite the equation in slope-intercept form: y = -0.5x + 7

Plot two points on the line: (0, 7) and (14, 0), and draw a line through them.

2. Graph the line 5x + 6y = 50:

Rewrite the equation in slope-intercept form: y = (-5/6)x + (25/3)

Plot two points on the line: (0, 25/3) and (10, 5/3), and draw a line through them.

3. Shade the region that satisfies the constraints:

Shade the region below the line 2x + 4y ≤ 28.

Shade the region below the line 5x + 6y ≤ 50.

The feasible region is the intersection of the shaded regions.

Next, we evaluate the objective function at the corner points of the feasible region to determine the maximum value.

The corner points of the feasible region are:

A: (0, 7)

B: (0, 25/6)

C: (14/3, 4)

D: (10, 5/3)

Evaluate the objective function at each corner point:

z(A) = 4(0) + 4(7) = 28

z(B) = 4(0) + 4(25/6) = 50/3

z(C) = 4(14/3) + 4(4) = 92/3

z(D) = 4(10) + 4(5/3) = 140/3

The maximum value of z is obtained at z(C) = 92/3.

Therefore, the maximum value of z = 4x + 4y, subject to the given constraints, is 92/3, which occurs when x = 14/3 and y = 4.

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100 Points! Algebra question. Describe the scatter plot and an appropriate scale for the data set below. Photo attached. Please show as much work as possible. Thank you!

Answers

Strength: TThe strength of the scatterplot refers to how closely the data points cluster around a line or curve. Direction: The direction of the scatterplot refers to the general trend or pattern exhibited by the data points.

Answers to the aforementioned questions

To describe the scatterplot and determine an appropriate scale, we can analyze the given data set:

x: 0, 2, -5, 3, 1, -4, 8, -6, -1

y: -3, -1, -13, 3, -1, -11, 12, -15, -5

Strength: TThe strength of the scatterplot refers to how closely the data points cluster around a line or curve.

Direction: The direction of the scatterplot refers to the general trend or pattern exhibited by the data points.

Scale: The appropriate scale for the scatterplot depends on the range of values for the x and y variables. To determine the scale, we need to consider the minimum and maximum values for each variable.

For x: The minimum value is -6 and the maximum value is 8.

For y: The minimum value is -15 and the maximum value is 12.

Based on these ranges, an appropriate scale for both x and y could be chosen with intervals of 2 or 5 units, depending on the desired level of detail.

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sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2

Answers

Answer:

sin( 3pi/4 ) = -√2/2

So, B.

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 70 cm/s. Find the rate (in cm2/s) at which the area within the circle is increasing after each of the following.
(a) after 1 s

Answers

Let's start by using the formula for the area of a circle:

A = πr^2

where A is the area and r is the radius.

We are given that a circular ripple is created in a lake and it travels outward at a speed of 70 cm/s. This means that the radius of the circle is increasing at a rate of 70 cm/s.

(a) After 1 second, the radius of the circle is:

r = 70 cm/s × 1 s = 70 cm

Now we can use the formula for the area of a circle to find the rate at which the area within the circle is increasing:

A = πr^2

A = π(70 cm)^2

A ≈ 15,400 cm^2

To find the rate at which the area within the circle is increasing, we need to take the derivative of the area with respect to time:

dA/dt = 2πr(dr/dt)

where dA/dt is the rate at which the area is increasing, and dr/dt is the rate at which the radius is increasing (which we know is 70 cm/s).

Plugging in the values we have:

dA/dt = 2π(70 cm)(70 cm/s)

dA/dt ≈ 9,800 cm^2/s

So after 1 second, the area within the circle is increasing at a rate of approximately 9,800 cm^2/s.

HELP DUE!! HELP ASAP!!

Answers

The time needed before the doctor administers the medication again is given as follows:

d) 22.2 hours.

How to model the situation?

The exponential function giving the amount of the medicine in the patient's bloodstream after t hours is given as follows:

[tex]A(t) = 500(0.93)^t[/tex]

The medication will be applied when the amount is given as follows:

A(t) = 100.

Hence the time needed is obtained solving the exponential function as follows:

[tex]100 = 500(0.93)^t[/tex]

[tex](0.93)^t = \frac{100}{500}[/tex]

[tex](0.93)^t = 0.2[/tex]

The logarithm of base 10 is the inverse of the exponential, hence:

[tex]t = \frac{\log{0.2}}{\log{0.93}}[/tex]

t = 22.2 hours.

Which is the time needed before the doctor administers the medication again.

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Which of the following would you see on a circle graph?
OA. Percentages
OB. Bars
C. Points
OD. A y-axis

Answers

A, percentages

You would see percentages on a circle graph, because it's how many parts of the whole that they take up.

Happy to help, have a great day! :)

Help please and thank u

Answers

Answer:

A=6cm

D=11,66cm

Step-by-step explanation:

A=6cm

D=6²+10²=136

D=√136

D=11,66

Find x and the measurement of each angle.

Answers

Answer:

x = 8, m2 = 78, m4 = 102, m6 = 78, m7 = 78,

Step-by-step explanation:

In 2004, a school population was 2122. By 2009 the population had grown to 2647.

1) How much did the population grow between the year 2004 and 2009?

Answers

The population grow by 24.7% between the years 2004 and 2009

Calculating how much the population grow between the years

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

Population in 2004 = 2122

Population in 2009 = 2647

The growth of the population between the years is calculated as

Percentage = Population in 2009/Population in 2004 - 1

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

Percentage = 2647/2122 - 1

Evaluate

Percentage = 24.7%

Hence, the population grow between the years by 24.7%

Answers

He could buy 7 hamburgers

When you order a salad from Nelly's Deli, you can choose from 5 different base salads, 3 different proteins, and 6 different dressings. How many different combinations for a salad are possible?

Answers

Answer:

Step-by-step explanation:

This type of problem is an example of combinations. In this case, in one salad, it states that you can chose between 5 bases, 3 proteins, and 6 dressings.

In this problem, you would have to multiply all numbers together.

In this case, 5(bases)x3(protiens)x6(dressings)=90

I hope this helps you!

Urgent! A home décor store donated a percent of every sale to hospitals. The total sales were $8,400 so the store donated $672. What percent of $8,400 was donated to hospitals?

Answers

Answer:

here is the answer in the photo

Step-by-step explanation:

mark branliest

Of the $8,400 in sales, the store donated about 8% to hospitals.

To find the percentage of $8,400 that was donated to hospitals, we can set up a proportion using the given information.

Let's represent the percentage of the sales donated as x.

We can set up the proportion:

(x/100) = 672/8400

To solve for x, we can cross-multiply and then divide:

8400 * x = 672 * 100

8400x = 67200

x = 67200 / 8400

x = 8

Therefore, the store donated approximately 8% of $8,400 to hospitals.

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50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

Answer: Answer is seen below (sorry if its confusing, this is what I got though)

Step-by-step explanation:

Which of the following will have a smaller standard deviation, if nine observations are randomly drawn from a population?
The distribution of the individual observations, X

The distribution of the sample means,
x
¯

This cannot be determined from the information given.

Answers

The distribution of the sample means will have a smaller standard deviation

Identifying which will have a smaller standard deviation

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

Observations = 9

The population is not given

However by the theorem of the central limit; we understand that

The distribution of the sample means will always have a smaller standard deviation

This is because the sample mean selected from the population might not totally represent the whole population, but would have smaller standard deviation

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devide 255 in the ratio 3:7:7:10

Answers

Answer:5

Step-by-step explanation:

5098

NO LINKS!!
will give brainliest!!!!!!!!!!!

Answers

The value of the side BC is equal to 10√21 in the simplest rationalized form using the trigonometric ratio of tangent.

What is trigonometric ratios?

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the tangent of angle 60°

tan 60° = BC/(10√7) {opposite/adjacent}

BC = 10√7 × tan 60° {cross multiplication}

BC = 10√7 × √3 {tan 60 = √3}

BC = 10√21

Therefore, the value of the side BC is equal to 10√21 in the simplest rationalized form using the trigonometric ratio of tangent.

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Assume the probability of rain on any given independent day is 0.23. What is the average number of days it rains for the first time?

Answers

The probability that this song will be played on exactly 0 days out of 7 days, if The probability that a particular song is played is 0.23 is 0.008.

We have,

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

The probability that a particular song is played is 0.23,

As can be seen that the problem is of combination, so we have to choose 5 out of 7,

Calculate the combination as shown below,

⁷C₅ = 7! / (5! × 2!) = 7 × 6 / 2

⁷C₅ = 7 × 6 / 2

⁷C₅ = 21

Calculate the probability as shown below,

P = ⁷C₅ × (0.23)⁵ × (0.77)²

P = 0.008

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complete question;

During a single day at radio station WMZH, the probability that a particular song is played is 0.23. What is the probability that this song will be played on exactly 0 days out of 7 days? Round your answer to the nearest thousandth.

The graph shows the cube root parent function.
-5
5
Which statement best describes the function?
A

Answers

The statement of the function is (b) when x > 0, the graph is positive

Describing the transformation of the function f(x)

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

The functions f(x) and g(x)

In the graph, we can see that

The graph of the function passes through (0, 0)

This means that

When x > 0, the graph is positive

When x < 0, the graph is negative

Hence, the statement of the function is (b)

Answers

A. The distributions of the periods is that using the five number summary is that

The 7th Period has higher minimum and lower maximumThe 3rd period is more spread (from the quartiles)The 7th Period has higher median

B. The box and whisker plot of the periods is attached

A. Comparing the distributions of the periods

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

Minimum: 66Lower Quartile Q1: 79.5Median: 88Upper Quartile Q3: 92.25Maximum: 96

3rd Period

Minimum: 52Lower Quartile Q1: 64.75Median: 75.5Upper Quartile Q3: 85.75Maximum: 97

B. Creating a box and whisker plot of the periods

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

Answers

Answer:

m<1 = 47 degrees

m<2 = 43 degrees

m<3 = 90 degrees

m<4 = 43 degrees

Step-by-step explanation:

Corine and Shonda are reading the same book.

The rate at which Corine is reading the book can be represented by the equation y=32x,
where x
is the time in hours and y
is the number of chapters read.

Shonda's rate is represented by this graph.

A graph with the X-axis labeled Time in Hours and the Y-axis labeled Chapters Read. A line begins at the origin and passes through (1, 2), (2, 4), (3, 6), and continues on.

© 2017 StrongMind. Created using GeoGebra.

If the girls read the book at the same time, who will finish first? Why?

Select the option that correctly answers both questions.

Responses

Corine will finish first. Her ratio of chapters to hours is 32.
Shonda's rate of chapters to hours is 21,
and 32
is a greater slope than 21.
Corine will finish first. Her ratio of chapters to hours is Shonda's rate of chapters to hours is 2 over 1 textsf comma and 3 halves is a greater slope than

Shonda will finish first. Her ratio of chapters to hours is 21.
Corine's rate of chapters to hours is 32,
and 21
is a greater slope than 32.
Shonda will finish first. Her ratio of chapters to hours is Corine's rate of chapters to hours is 3 halves textsf comma and 2 over 1 is a greater slope than

Shonda will finish first. Her ratio of chapters to hours is 12.
Corine's rate of chapters to hours is 23,
and 12
is a greater slope than 23.
Shonda will finish first. Her ratio of chapters to hours is Corine's rate of chapters to hours is 2 thirds textsf comma and 1 half is a greater slope than

Corine will finish first. Her ratio of chapters to hours is 23.
Shonda's rate of chapters to hours is 12,
and 23
is a greater slope than 12.

Answers

If the girls read the book at the same time, who will finish first: A. Shonda will finish first. Her ratio of chapters to hours is 2/1. Corine's rate of chapters to hours is 3/2, and 2/1 is a greater slope than 3/2.

How to calculate or determine the slope of a line?

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = 2/1

Slope (m) = 2.

Based on the table, the slope is the change in y-axis with respect to the x-axis and for Shonda it is equal to 2/1 or 2. Therefore, Shonda would finish before Corine because 2/1 > 3/2.

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Missing information:

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

A rectangle floor is 9 yards long and 3 yards wide what is the area of the floor in square feet

Answers

Answer:

1. Find the area of the rectangle in square yards. In this case, the area is 9 yards * 3 yards = 27 square yards.

2. Convert square yards to square feet. There are 9 square feet in 1 square yard. So, the area of the rectangle in square feet is 27 square yards * 9 square feet/square yard = 243 square feet.

Therefore, the area of the rectangle floor in square feet is 243 square feet.

Answer:243

Step-by-step explanation:

(9x3) x (3x3)

27 x 9 = 243

when the football game started, there were twice as many eagle fans as spartan fans. At the end of the first quarter, 500 extra eagle fans came on busses. The total attendance at the game was 4790. How many people attended from each school?

Answers

Answer:

2860 Eagle fans and 1430 Spartan fans

-------------------

Let E represent the number of Eagle fans and S represent the number of Spartan fans at the start of the game.

We can set up two equations using the given information:

1) E = 2S (twice as many Eagle fans as Spartan fans) 2) E + S + 500 = 4790 (total number, including the extra 500 fans)

Now we can solve the equations.

From equation (1), we can replace E in equation (2), the solve for S:

(2S) + S + 500 = 4790 3S + 500 = 47903S = 4290 S = 1430

Now find the number of Eagle fans using equation (1):

E = 2S E = 2(1430) E = 2860

Finding Probabilities
Every person has blood type O, A, B, or AB. A random
group of people are blood-typed, and the results are
shown in the table.
Blood Type
A
B
AB
Number of People
22
20
6
2
Use the table to determine the following probabilities.
The probability that a randomly chosen person from
this group has type B is [
The probability that a randomly chosen person from
this group has type AB is [
The probability that a randomly chosen person from
this group has type B or type AB blood is

Answers

The probability that a randomly chosen person from this group has type B is 0.4.

The probability of type AB is 0.12, and the probability of type B or type AB is 0.52.

We have,

The probability that a randomly chosen person from this group has type B is given by the number of people with blood type B divided by the total number of people in the group:

Probability of type B

= Number of people with type B / Total number of people

In this case, the number of people with blood type B is 20, and the total number of people is 50 (22 + 20 + 6 + 2).

Probability of type B = 20 / 50 = 0.4

Similarly, the probability that a randomly chosen person from this group has type AB is given by the number of people with blood type AB divided by the total number of people:

Probability of type AB = Number of people with type AB / Total number of people

In this case, the number of people with blood type AB is 6, and the total number of people is 50. Therefore,

Probability of type AB = 6 / 50 = 0.12

To find the probability that a randomly chosen person from this group has blood type B or type AB, we need to add the probabilities of both events:

Probability of type B or type AB = Probability of type B + Probability of type AB

Probability of type B or type AB = 0.4 + 0.12 = 0.52

Thus,

The probability that a randomly chosen person from this group has type B is 0.4, the probability of type AB is 0.12, and the probability of type B or type AB is 0.52.

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QUESTIONS 1. Explain and illustrate the difference between and (4) 2. Explain and illustrate the difference between ratio and proportional reasoning. Do not copy definitions from any source but use your own understanding. (4) 3. Illustrate with a drawing or diagram what "fifth" means in each of the following instances: ● ordinal number ● unit fraction 4. Show with a diagram 3, using the following: 1.1 the area model 1.2 set mode 1.3 the length model (3) 2. A rectangular piece of paper has a perimeter of 54 cm. Its length is 1 of its width. Find its dimensions. (3) 3. If the given regular hexagon represents one whole: 3.1 Show three sixths. 3.2 Write the equivalence 6.1 above. 3 Represent+ in the figure given to prove that a set of two halves 6 make a whole. (4) 6.3.1 Draw a number line showing a whole made of six equal parts. Show the sum of two halves on the same number line. (1) (1) (2) (3)

Answers

The difference between 1/5 and 2/10 is that they are different representations of the same value.

The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.

"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.

The diagram can be used to illustrate fraction concepts.

How to solve

1/5 is simple, but 2/10 can be reduced to 1/5 by dividing both numbers by 2. They are both 0.2 or 20%. 1/5 and 2/10 are different fractions with different purposes.

Use 1/5 for 5 parts and 1/5 (simplified from 2/10) for 10 parts. 1/5 and 2/10 = 0.2, ratio reasoning emphasizes ratios between quantities. A 2:3 boys-to-girls ratio compares the constant ratio between changing quantities.

Proportional reasoning maintains constant ratios between quantities, while ratio reasoning uses fractions or ratios to compare relationships. For instance, if distance doubles, so does speed.

Step 3/5: "Fifth" is the ordinal number for the object five places away in a sequence. See diagram. The fifth circle is 1/5 of a whole in unit fraction sequence. Imagine a rectangle divided into five equal parts, each shaded to show 1/5. Shaded part = 1/5 of whole.

To show 25/7 with area model, make 7x25 rectangle and split into 7 equal parts. 25/7 per part.

1.2 The set model:

To represent 25/7, divide 25 objects into 7 equal sets, resulting in 3 objects per set with 1 left over. This represents the fraction of 25/7.

Step 5/5

Let's assume the width of the rectangular piece of paper as x cm. Then the length of the paper would be:

Now we know that the perimeter of the rectangle is given by the formula:

So, for this rectangle:

54 = 2(5x + x)

Simplifying and solving for x, we get:

54 = 2(6x)

27 = 6x

x = 4.5 cm

Therefore, the width of the paper is 4.5 cm and the length is 5 times the width which is 22.5 cm

The difference between 1/5 and 2/10 is that they are different representations of the same value.

The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.

"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.

The diagram can be used to illustrate fraction concepts.