A library has 500 books. There were history, maths and science books. The ratio of the history to maths
to science books is 2:3:5. If 20 history, 40 maths, and 10 science books were added in the library,
find the new ratio of the history to the maths to the science books.

Pls help

force f as a Cartesian vector: F = (59.40i - 88.18j - 83.18k) lb

A three-dimensional plane may be used to represent the geometric objects in the cartesian plane; this representation is known as the cartesian form. The X, Y, and Z axes are used to depict it in three dimensions. A point, a line, or a plane can also be shown in a cartesian form in addition to this.

The co-ordinates of pints A and B is: (0,0,0) ft

A(-10cos70°sin30°, 10cos70°cos30°, 10sin70°)ft

B(5, -7)ft

so, the position vector from origin to the point A:

r(OA) = A - O

= (-10cos70°sin30°i + 10cos70°cos30°j + 10sin70°k) - (0i + 0j + 0k)

= (-10cos70°sin30°i + 10cos70°cos30°j + 10sin70°k)

the position vector from origin to the point B:

r(OB) = B - O

= (5i - 7j) - (0i + 0j)

= (5i - 7j)

next, the position vector from A to B:

r(AB) = r(OB) - r(OA)

r(AB) = (5i - 7j) - (-10cos70°sin30°i + 10cos70°cos30°j + 10sin70°k)

r(AB) = (6.710i - 9.962j -9.937k) ft

magnitude of the position vector:

|r(AB)| = √(6.710)² + (-9.962)² + (-9.937)²

|r(AB)| = 15.25 ft

the force vector acting from the point A to B:

F = F r(AB) / |r(AB)|

F = 135 × {(6.710i - 9.962j -9.937k)}/  15.25

F = (59.40i - 88.18j - 83.18k) lb

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The complete question is as follows:

The room tax is 18%. Total cost fo the motel room to stay 3 days including the tax is  $361.08.

A percent represents a fraction of a hundred.

For example:

60% = 60/100

Percent is usually used to denote a portion of a whole. For example, 20% of 30, means:

20% x 30 = 20/100 x 30 = 6

In this problem:

The motel room costs $102.00 per day.

The cost for 3 days before tax is:

Cost = 3 x $102 = $306

The tax rate is 8%, it means the amount of tax is:

tax = 18% x $306 = $55.08

Total cost after tax = $306 + $55.08 = $361.08

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The values of x, y and z are 33 degrees, 35 degrees and 109 degrees

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

The parallelogram

By the alternate interior angle theorem, we have

x = 33 degrees

Also, we have

z = 109 degrees

The sum of angles in a triangle is 180

So, we have

33 + y + 109 = 180

Evaluate

y = 38 degrees

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The double integral of the given equation is -0.983

What is meant by integral?

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

The integrals of a function in two variables over a region in R², or the real number plane, are referred to as double integrals in mathematics.

The surface area of a 2D figure can be determined primarily using the double integral, which is indicated by the symbol "∫∫". By using double integration, we may quickly determine the area of a rectangular region. Double integration challenges will be easier to address if we are familiar with simple integration.

We have to find the double integral of ∫∫(7x + 6y) dA over region D.

D is bounded by y = x and y = x²

From the graph below, we can see the region is bounded between x = 0 and 1

So the equation becomes

[tex]\int\limits^1_0\int\limits^{x}_{x^2} (7x+6y)dydx[/tex]

The lower limit of y is x² because the lower part of the region is x² and the upper part is x.

Evaluating,

[tex]\int\limits^1_0\int\limits^{x}_{x^2} (7x+6y)dydx = \int\limits^1_0[7xy+6y^2/2]^x_x^2dx= \int\limits^1_0[(7x^3+6x^4/2) - ( 7x^2+6x^2/2]dx[/tex]

                                               = [tex]\int\limits^1_0[(7x^3+6x^4/2) -10x^2]dx[/tex]

              =[tex][(7x^4/4+6x^5/10 -10x^3/3]^1_0 = 7/4 + 6/10-10/3 =[/tex]  

   = -0.983

Therefore the double integral of the given equation is -0.983.

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To convert 165 cm to feet  we get 5 feet and 4.96063 inches.

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The entire space or area occupied by an isosceles triangle's sides in a two-dimensional space is known as the triangle's area. Thus the area will be "112.5 cm²".

what is the maximum possible area of an isosceles triangle if the two equal sides are each 15 cm long?

The area is a function of the apex angle β according to

Area = (1/2)(2 cm)²×sin(β)

This will be a maximum for β = 90°. The corresponding length of the third side is  2√2 cm ≈ 2.2828 cm.

The entire space or area occupied by an isosceles triangle's sides in a two-dimensional space is known as the triangle's area. A triangle with two equal sides, which also means two equal angles, is referred to as an isosceles triangle. The following characteristics of an isosceles triangle set it apart from other kinds of triangles: The vertex angle, also known as the apex angle, is the angle formed by the two equal sides of an isosceles triangle. The base is the side that the vertex angle faces, and the base angles are equal.

The vertex angle and the base are both divided in half by the perpendicular from the vertex angle.

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The quadrilateral ABCD has the vertices B (2, 5) and D (0,-3). If ABCD is a square, the coordinates of the other two vertices are (5, 0) and (-3, 2). So option C is correct

Distance is a numerical measurement of how far apart two or more points are in space, typically in one, two, or three dimensions. It is used to describe the separation between objects, locations, or events.

Given that,

The quadrilateral ABCD,

whose two opposite vertices B (2, 5) and D (0,-3)

other two vertices = ?

This problem can be solved by hit and trial method,

It is known that,

all the sides of square has equal length,

lets take,

A =  (5, 0)

C =  (-3, 2)

Now, by calculating the length of each side, we can check

Distance between A & B

AB = √[(-3-0)²+(2+3)]

     = √34

BC = √34

CD = √34

DA = √34

Hence, A & B are respectively,  (5, 0) and (-3, 2)

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Mikos is required to repay it on September 13 of the same year based on simple interest.

When there is only one compounding every time period, simple interest is applied.

Following t years, the amount of money is predicted by:

A(t) = A(0) (1 + rt)

That where:

The initial amount is A(0).

The interest rate in decimal form is r.

In this issue:

The starting sum is A(0) = 100000.

R = 0.105 is the interest rate.

The maturity value is 104375 for A(t).

Therefore, we must find t; as a result,

A(t) = A(0)(1 + rt)

104375 = 100000(1 + 0.105t)

1 + 0.105t = 104375 / 100000

1 + 0.105t = 1.04375

0.105t = 1.04375

t = 0.04375 / 0.105

t = 0.4166

The time in years, then in days, is as follows:

On September 13, which is 152 days after April 14 (0.4166 x 365).

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statistics is the study of statistics is the science of conducting studies to collect, , , analyze, and draw conclusions from data. It involves using mathematical concepts such as probability and regression analysis to analyze data and make predictions.

Statistical methods are used in a wide variety of fields, including economics, medicine, engineering, and social sciences. Statisticians use data to make decisions, test hypotheses, and evaluate the effectiveness of policies and programs. Statistical techniques are also widely used in business, finance, and marketing to help make decisions and understand customer behavior.

1. Statistics is the science of collecting, organizing, analyzing, and interpreting data to draw conclusions.

2. Statisticians use mathematical concepts such as probability and regression analysis to analyze data and make predictions.

3. Statistical methods are used in a variety of fields, including economics, medicine, engineering, and social sciences.

4. Statistical techniques are used in business, finance, and marketing to understand customer behavior and make decisions.

5. Statisticians use data to test hypotheses, evaluate the effectiveness of policies and programs, and make decisions.

Statistics is a science that uses mathematical concepts such as probability and regression analysis to analyze data and make predictions. It is used in a variety of fields, including economics, medicine, engineering, and social sciences, as well as in business, finance, and marketing to understand customer behavior and make decisions. Statistical methods are used to test hypotheses, evaluate the effectiveness of policies and programs, and make decisions.

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The theoretical probability of the spinner not landing on blue is 0.625.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given A spinner with repeated colors numbered from 1 to 8 is shown,

total outcome = 8

a favorable outcome for blue = 3

a favorable outcome for red = 1

a favorable outcome for purple = 2

a favorable outcome for yellow =  2

probability =  favorable outcome/total outcome

P(blue) = 3/8

P(blue) = 0.375

P(not blue) = 1 - P(blue)

P(not blue) = 1 - 0.375

P(not blue) = 0.625

Hence option B is correct.

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Answer:

NO

Step-by-step explanation:

In the pythagorean theorem,

[tex]{a}^{2} + {b}^{2} = {c}^{2} [/tex]

So it should be

[tex] {10}^{2} + {24}^{2} = {28}^{2} [/tex]

But,

[tex]100 + 576 = 676 \: and \: {28}^{2} = 784[/tex]

The approximation of √0.96 using the linearization of f(x) = √(1/x) at x = 1 is 0.6836.

To find the linearization of f(x) = √(1/x) at x = 0  use the tangent line of f(x) at x = 0. To do this, we first need to find the derivative of f(x) at x = 0, which is f'(0).

Using the power rule for derivatives, we have:

f(x) = √(1/x)

f'(x) = -1/([tex]2x^{(3/2)[/tex])

Now, we can use f'(0) to find the tangent line at x = 0. The equation for the tangent line is given by:

y = f'(0)(x - 0) + f(0)

Since f(0) is undefined (since the square root of zero is undefined), we can't use the equation above. However, we can still find the slope of the tangent line at x = 0. The slope is given by f'(0), which is:

f'(0) = -1/(2(0)[tex]^{(3/2)[/tex]) = undefined

So, we can conclude that the linearization of f(x) = √(1/x) at x = 0 is undefined.

To approximate √0.96, we can use the linearization of f(x) = √(1/x) at x = 1, since 0.96 is close to 1. The linearization of f(x) = √(1/x) at x = 1 is given by:

y = f'(1)(x - 1) + f(1)

f'(1) = -1/([tex]2(1)^{(3/2)[/tex]) = -1/√2

y = -1/√2(x - 1) + √1/1 = -1/√2x + √2

Now, we can use this linearization to approximate √0.96:

y = -1/√2 * 0.96 + √2 = 0.96 * -1/√2 + √2

y = 0.96 * -1/√2 + √2 = 0.96 * -0.7071 + 1.41

y ≈ 0.6836

So, the approximation of √0.96 using the linearization of f(x) = √(1/x) at x = 1 is 0.6836.

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The total  fencing they required = 38x + 10.

The family needs yards of  fencing of the home = 160 yards

The family needs yards of fencing of the pool = 40 yards

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Perimeter of a rectangle = 2(length + width)

Perimeter of a square = 4(side length).

Given that,

A rectangle labeled home has its right side labeled (2 + 5 x) yards

And bottom side labeled (3 + 10 x) yards

Perimeter for the rectangular fencing of the home = 2(3 + 10x + 2 + 5x) = 2(15x + 5) = 30x + 10

Perimeter for the square fencing of the pool = 4(2x) = 8x

The total amount of fencing they need = 30x + 10 + 8x = 38x + 10.

If x = 5, then:

Perimeter for the rectangular fencing of the home = 30x + 10 = 30(5) + 10 = 160 yards

Perimeter for the square fencing of the pool = 4(2x) = 8x = 8(5) = 40 yards.

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For a uniform distribution, the probability of any given value is the same across the entire range of the distribution. Therefore, for the given random variable Y, the probability of Y being less than or equal to 0.4 (P(Y <= 0.4)) is 0.4. The probability of Y being less than 0.4 (P(Y < 0.4)) is also 0.4.

For the third probability, P(0.1 < Y <= 0.15 or 0.77 ≤ Y < 0.88), the probability is the sum of the probabilities of the two ranges. The probability of Y being between 0.1 and 0.15 is 0.05, and the probability of Y being between 0.77 and 0.88 is 0.11. Therefore, the total probability is 0.05 + 0.11 = 0.16.

In conclusion, the probabilities of the given random variable Y are P(Y <= 0.4) = 0.4, P(Y < 0.4) = 0.4, and P(0.1 < Y <= 0.15 or 0.77 ≤ Y < 0.88) = 0.16.

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Answer:

39.2

Step-by-step explanation:

Always true. The sum of the measures of the interior angles of any triangle is 180 degrees, so when one angle is 120 degrees, the remaining two angles must add to 60 degrees.

The sum of the measures of the interior angles of any triangle is 180 degrees. This is because the angles of a triangle add up to form a straight line, which is 180 degrees. Therefore, if one angle has a measure of 120 degrees, the remaining two angles must add up to the remaining 60 degrees to make 180 degrees in total. This means that the measure of angle 1 must be 60 degrees. Therefore, it is always true that when the measure of angle 4 is 120 degrees, the measure of angle 1 is 60 degrees. This is because the total sum of the interior angles of a triangle must add up to 180 degrees, so the other two angles must add up to the remaining 60 degrees.

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The total number of two-person tents taken on the camping trip was 0, and the total number of four-person tents taken on the camping trip was 50.

The total number of tents taken on the camping trip was 60, and the total number of people was 202. We want to determine how many of each type of tent were taken. Let x represent the number of two-person tents and y represent the number of four-person tents. We can use the following equation to solve for x and y:

2x + 4y = 202

After rearranging the equation to solve for x, we get x = (202 - 4y)/2. Substituting this into the equation, we get 2((202 - 4y)/2) + 4y = 202. Simplifying, we get (202 - 4y) + 4y = 202. Then, 0 + 4y = 202. Dividing both sides by 4, we get y = 50.5. Plugging this value into the equation x = (202 - 4y)/2, we get x = (202 - 202)/2, which simplifies to x = 0.

Therefore, the total number of two-person tents taken on the camping trip was 0, and the total number of four-person tents taken on the camping trip was 50.

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The next term in the given pattern is 36.

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

The number of squares in the given pattern is as follows is 9, 16, 25,....

So, the pattern is 3², 4², 5², 6², 7², 8²,.....

9, 16, 25, 36, 49, 64,....

Hence, the next term in the given pattern is 36.

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This is the equation of the line with a slope of 1/3 and a point of (12, 5).

The slope of a line is a measure of its steepness and direction. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope can be positive (the line rises from left to right), negative (the line falls from left to right), or zero (the line is horizontal).

The point-slope formula for a line is given by:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) is any other point on the line.

In this case, the slope is 1/3 and the point is (12, 5). Substituting these values into the formula:

y - 5 = 1/3(x - 12)

Expanding the right-hand side:

y - 5 = 1/3x - 4

Adding 5 to both sides:

y = 1/3x - 4 + 5

Simplifying:

y = 1/3x + 1

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Calculating the probability of a mean time watching television falling between 2 and 3 hours requires knowledge of the population's distribution of time spent watching television.

The probability that a random sample of adults will result in a mean time watching television on a weekday of between 2 and 3 hours can be determined by using the standard normal distribution. This requires knowledge of the population's mean and standard deviation for time spent watching television. If these values are not known, they can be estimated using a sample from the population. The calculated probability assumes that the population's distribution of time spent watching television is normal. If this assumption is not met, alternative methods may be used to estimate the probability.

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Answer:

28.5

Brainly is probably going to take this down because of the picture but here you go anyway

Step-by-step explanation:

You're welcome.

a) No, a single spray of 10 grams of butter would not be enough to entirely cover the area of 4 slices of toast at 2 meters. The area of 4 slices of toast is larger than the area of 1 slice of toast, meaning that it would require more butter than 10 grams to cover the entire area.

b) A single spray of 10 grams of butter would be enough to cover the area of 8 slices of toast at 3 meters.

c) These changes would affect the amount of butter on each piece of toast in that there would be more butter on each piece with a larger rack and further distance from the "butter gun".

d) At 5 meters from the gun, our up-and-coming chef would be able to spray 16 slices of toast with a single burst of 10 grams of butter. Each piece of toast would also have more butter than it would if it was sprayed at a closer distance.

e) To duplicate the original single-slice toast at 5 meters from the gun, the chef would need to reduce the amount of butter being sprayed. He could do this by simply reducing the distance between the gun and the toast rack.

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Complete question :

A harried chef can't keep up with his breakfast orders and decides to automate the process with a "butter gun." The gun provides a 10 gram burst of butter spray with each hit of the trigger. He starts with a rack that holds one piece of toast 1 meter away. The demand again exceeds supply and he realizes he can use the same gun to produce more toast by placing a larger rack at a greater distance. He finds that a four-slice rack works at a distance of 2 meters. Pleased with profits he carries the idea a step further and puts a holder 3 meters away, maintaining a 10 gram spray. See figure below.a) If 1 spray entirely covers the area of a single slice at 1 meter, can it entirely cover the area of 4 slices at 2 meters? Why or why not?b) How many slices can one spray cover with a 3 meter arragnement?c) How do these changes affect the amount of butter on each piece of toastd) Our up-and-coming chef moves the fun back to 5 meters. Predict how much toast he can spray and how much better each piece gets.e) Explain how he could duplicate the original single-slice toast at 5 meters from the gun.

Answer:

Step-by-step explanation:

This is an arithmetic sequence with a common difference of -12. To find the recursive formula, let's start by finding a general formula for the nth term.

Let a be the first term (3 in this case) and d be the common difference (-12 in this case). The nth term of the sequence can be found using the formula:

an = a + (n-1)d

Using this formula, the first four terms of the sequence are:

a1 = a + (1-1)d = 3 + (1-1)(-12) = 3

a2 = a + (2-1)d = 3 + (2-1)(-12) = 3 - 12 = -9

a3 = a + (3-1)d = 3 + (3-1)(-12) = 3 - 24 = -21

a4 = a + (4-1)d = 3 + (4-1)(-12) = 3 - 36 = -33

So, the sequence is: 3, -9, -21, -33, ...

We can now use this information to write the recursive formula for the sequence:

an = a(n-1) + d

So, for the sequence 3, -9, -21, -33, ... the recursive formula is:

an = an-1 + (-12)

This formula tells us how to find the nth term of the sequence given the (n-1)th term. The sequence starts with the first term a1 = 3 and the common difference is d = -12. By repeatedly applying the formula, we can find the values for the subsequent terms in the sequence.

The expression for the electric field strength at 1/2 R is E = 8 * π * k * q * r^2 / (1/2R)^2, and the expression for the electric field strength at 2R is E = 2 * π * k * q * r^2 / (2R)^2.

What is the spherical shell?

In geometry, a spherical shell is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing radii.

(A) Electric field strength at 1/2R:

The electric field strength at a point P due to a charge q located at point O is given by:

E = k * q / r^2

where k is the Coulomb constant, q is the charge at point O, and r is the distance between points P and O.

For a spherical shell of radius R carrying charge 2q spread uniformly over its surface, the electric field at any point inside the shell is zero, since the charges on the shell produce equal and opposite electric field vectors that cancel each other out.

Therefore, the electric field strength at 1/2R is zero.

(B) Electric field strength at 2R:

At a distance of 2R from the center of the spherical shell, the electric field due to the entire shell can be calculated as if all the charge were concentrated at the center of the shell.

The electric field strength at a point P due to a point charge q located at the center of the spherical shell is given by:

E = k * q / r^2

where k is the Coulomb constant, q is the total charge on the shell (2q), and r is the distance between points P and the center of the shell (2R).

So, the electric field strength at 2R is:

E = k * (2q) / (2R)^2 = k * q / R^2

Hence, the expression for the electric field strength at 1/2 R is E = 8 * π * k * q * r^2 / (1/2R)^2, and the expression for the electric field strength at 2R is E = 2 * π * k * q * r^2 / (2R)^2.

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The branch of statistics that draws conclusions about a large set of data based on a smaller set of data is often referred to as sampling statistics.

Sampling statistics involve taking a small subset of data from a larger population, and then making inferences about the population based on the sample. For example, if you wanted to determine the average height of people in a given population, you could take a sample of a few hundred people and calculate the average height of the sample. Then, you could use that information to make inferences about the average height of the entire population. The formula for calculating the sample mean, which is the average of the sample, is: X = Σx/n, where x is the sample data, Σx is the sum of the sample data, and n is the sample size. For example, if a sample of five people had heights of 165, 192, 186, 154, and 176 cm, then the sample mean would be (165+192+186+154+176)/5 = 175 cm.

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Answer:

Rounded it's 37 mph but the exact answer is 37.28 mph

Answer:

a³ + b³ = (a+b) (a² - ab + b²)

Step-by-step explanation:

(a+b) (a² - ab + b²) =

(a+b)*a² - (a+b)*ab + (a+b)*b² =

(a³+ba²) - (a²b+ab²) + (ab²+b³) =

a³ + ba² - a²b - ab² + ab² + b³ =

a³ + ba² - a²b - ab² + ab² + b³ =

a³ + 0 - 0 + b³ = a³ + b³

The required order of who came in the first second and so on the place is A1, Edgarr, Filomena, Courtney, and Brad respectively.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Time is taken by A1 to finish the marathon in seconds
Total =  2 hours * 60 minutes/hour * 60 seconds/minute  +120 minutes * 60 seconds/minute + 60 seconds

Total = 14,560 seconds

Similarly,

Brad: takes 21,720 seconds

Courtney: takes 18,333 seconds

Edgar: takes 14,800 seconds

Filomena: takes 17,601 seconds

Comparing the total times, we can see that the order of the runners is:

A1 with 14,560 seconds

Edgar with 14,800 seconds

Filomena with 17,601 seconds

Courtney with 18,333 seconds

Brad with 21,720 seconds

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Therefore , the solution of the given problem of rectangle comes out to be there are only four values for this circumstance.

A rectangle is just a cube with quartet right angles in the Euclidean plane. It is also known as a quadrant that appears to have equal angles, or an equiangular quadrilateral. A straight angle is an additional alternative for the parallelogram. A square has four sides that are the same length. A quadrilateral with four 90° vertices and four equal sides is rectangular in shape.

Here,

Given :

=> Perimeter = 18cm

the length and width are of whole numbers,

The length is always greater than the width:

Let x be the length and y be the width,

using

=> 2x+2 y = 18

=> x =8 , y =1

=> x =7 , y =2

=> x= 6 , y =3

=> x = 5 , y =4

Thus , it can be the only the value for length where length is greater than the width.

Therefore , the solution of the given problem of rectangle comes out to be there are only four values for this circumstance.

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