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Which polar coordinates represent the point plotted on the graph? Select all that apply and explain your answer.

The sum of the first 97 terms of the arithmetic progression is 153761.

What is arithmetic progression?

Arithmetic progression (AP) is a sequence of numbers in which each term is obtained by adding a constant value (known as the common difference) to the previous term. In other words, an arithmetic progression is a sequence of numbers where each term is a fixed distance apart.

To find the sum of the first 97 terms of an arithmetic progression with the nth term given as 2 + n/3, we use the formula:

S_n = n/2 [2a + (n-1)d]

We first find the first term, a, by substituting n = 1 into the nth term equation to get a = 7/3. Then, we find the common difference, d, by subtracting the (n-1)th term from the nth term, which gives us d = n/3.

Substituting these values into the S_n formula, we get:

S_97 = 97/2 [2(7/3) + (97-1)(97/3)]

Simplifying this expression, we get:

S_97 = 47(14 + 96 × 97/3)

S_97 = 47(3263)

S_97 = 153761

Therefore, the sum of the first 97 terms of the arithmetic progression is 153761.

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The group contains all possible isometries of the polygon onto itself and can be used to describe and analyze the symmetries and properties of the polygon.

What is rotational symmetry in a hexagon?

Rotational symmetry in a hexagon is a type of symmetry where the hexagon can be rotated by a certain angle about its center, and the resulting figure coincides with the original hexagon. The angle of rotation that produces this symmetry is called the angle of rotational symmetry, and it depends on the number of sides or vertices of the hexagon.

In the context of the dihedral group D of a regular polygon with n vertices, this statement means that the isometries (rigid transformations that preserve distances and angles) of the polygon onto itself are composed of n symmetries about the n axes of symmetry that intersect at the center of the polygon, and n rotations about the center by multiples of 2π/n radians.

The n symmetries are denoted by s0, s1, ..., sn-1, where si is the symmetry about axis i (with axis 0 being the axis passing through the center and vertex 0). These symmetries reflect the polygon across each axis of symmetry, producing a total of n reflections.

The n rotations are denoted by r0, r1, ..., rn-1, where ri is the rotation by 2πi/n radians about the center of the polygon. These rotations rotate the polygon counterclockwise around its center by a fraction of a full turn, with the fraction being i/n. This produces a total of n rotations, with r0 being the identity rotation (i.e., not rotating at all).

Together, the n symmetries and n rotations form the dihedral group D of the regular polygon with n vertices. This group contains all possible isometries of the polygon onto itself and can be used to describe and analyze the symmetries and properties of the polygon.

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Samuel has a total of 45 toy cars in his collection. Let's assume that Samuel has x toy cars in total. We know that 60% of his collection consists of red toy cars, which means that he has 0.6x red toy cars.

According to the problem, he has 27 red toy cars, so we can set up the following equation:

0.6x = 27

To solve for x, we can divide both sides by 0.6:

x = 27 / 0.6

x = 45

Therefore, Samuel has a total of 45 toy cars in his collection.

It's important to note that this solution assumes that the only colors of toy cars in Samuel's collection are red and non-red. If there are other colors present, then the total number of cars in his collection may be different. Additionally, we assumed that the problem is referring to whole numbers of toy cars, so if the collection includes fractional parts of cars, the answer may be different as well.

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Hence, the normal octagon has a space of about 310.8 square feet. with a radius of 10.5 feet and a circumference of 64 feet. The area of the normal octagon is roughly 310.8 square feet, while the length of the apothem is roughly 9.7 feet.

Each side of the octagon is 64/8 = 8 feet long because the circumference of an octagon is equal to the sum of its side lengths.

From the octagon's centre to one of its sides' midpoints, draw a line. The radius of a triangle produced by the octagon's centre and two consecutive vertices is this line segment, which is also known as the apothem. This triangle is isosceles and has an apothem of 10.5, with a base length of 8. The Pythagorean theorem can be used to determine the triangle's height.

[tex]height^2= \frac{apothem^2 - base^2}{4}[/tex]

[tex]height^2= \frac{10.5^2 - 8^2}{4}\\height^2= \frac{110.25 - 64}{4} \\height^2 = \frac{46.25}{4}[/tex]

height ≈ 9.7

Hence, the apothem is around 9.7 feet long.

A = (1/2)ap, where an is the apothem and p is the perimeter, gives the area of an octagon. By substituting our current values, we get:

A = (1/2) x 9.7 x 64

A ≈ 9.7 x 32

A ≈ 310.8 [tex]ft^2[/tex]

Hence, the normal octagon has a space of about 310.8 square feet.

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Answer:

A rectangular octagon is shown in the ceiling of a cathedral. The radius is 10.5 feet and the perimeter is 64 feet.

The regular octagon in the ceiling of this cathedral has a radius of 10.5 feet and a perimeter of 64 feet.

What is the length of the apothem of the octagon? Round your answer to the nearest tenth of a foot.

Using your answer for the length of the apothem, what is the area of the regular octagon? Round your answer to the nearest tenth of a square foot.

Step-by-step explanation:

Answer: $29.25

(I'm not American)

Step-by-step explanation:

65% of 45 = 65/100 x 45 =  29.25

80 units  is the minimum unit cost.

What is cost and example?

Cost is the price paid, which is typically calculated based on the resources given up to accomplish a specific goal. It entails making a sacrifice in exchange for goods or services. Not all costs translate into expenses. Assets and expenses both have costs associated with them. Expiring costs are called expenses.

it means

the function C(x) = 0.9x² - 144x + 21,053

So, the derived of C(x) respect to "x" is

     C(x)' = 0.9 * 2x - 144

   Now, we make the previous expression equal to zero and clear "x":

       1.8x - 144 = 0

          1.8x = 144

            x = 144/1.8

            x = 80

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Answer:

B. The x values of -6, 0, 2, 4 and 7.

Step-by-step explanation:

The domain of a function is its x-values. Therefore, the points on the graph contain the x-values -6, 0, 2, 4, and 7, so that is the domain.

Answer:

55.5cm^2

Step-by-step explanation:

5×3=15

12-3=9

5+4=9

9×9=81

81÷2=40.5

40.5+15=55.5

answer: 55.5cm^2

The only type of geometric shape that can have two side lengths of 14 ft and exactly one right angle is the isosceles right triangle. So, correct option is C.

Geometric figures are shapes that are defined by their geometric properties, such as size, shape, orientation, position, and other characteristics that are inherent to their structure. These shapes can be two-dimensional or three-dimensional and can be classified into different categories based on their properties. Here are some examples of geometric figures:

Points: A point is a basic element in geometry that has no size, shape, or dimension. It is usually represented by a dot and is used to describe the position of other geometric figures.

Lines: A line is a straight path that extends infinitely in both directions. It has no thickness or width and is usually represented by a straight line with arrows at both ends.

Segments: A segment is a part of a line that has two endpoints. It can be measured by its length.

Rays: A ray is a part of a line that has one endpoint and extends infinitely in one direction.

Angles: An angle is the space between two rays that share a common endpoint, called the vertex. It is usually measured in degrees or radians.

The geometric figures that could describe how the garden might look are quadrilaterals with one right angle. Some examples of such quadrilaterals are:

Out of these options, the only type of geometric shape that can have two side lengths of 14 ft and exactly one right angle is the isosceles right triangle. Therefore, the answer is:

C. Isosceles right triangle.

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The length of the third side is increasing at a rate of 8√3 m/min when the angle between the sides of the fixed length is 60° and increasing at a rate of 2°/min.

An angle is a geometric figure formed by two rays (also known as sides) that share a common endpoint (also known as the vertex). The rays are typically represented as straight lines, and the angle is measured in degrees or radians.

Let's call the two sides of fixed length (9 m and 16 m) sides a and b, respectively, and let's call the variable third side c. Let's also call the angle between sides a and b θ. We want to find how fast the length of side c is changing (dc/dt) when θ is 60° and dθ/dt is 2°/min.

To solve this problem, we can use the law of cosines, which relates the lengths of the sides and the cosine of the angle between them:

c² = a² + b² - 2ab cos θ

We can take the derivative of both sides of this equation with respect to time (t) to get:

2c(dc/dt) = 2a(da/dt) + 2b(db/dt) - 2ab(-sin θ)(dθ/dt)

At the moment when θ = 60°, we know that a = 9 m and b = 16 m. We also know that dθ/dt = 2°/min. To find da/dt and db/dt, we can use the fact that the triangle is isosceles when θ = 60°, so a = b = c/2. Taking the derivative of this equation with respect to time, we get:

da/dt = db/dt = (1/2)(dc/dt)

Substituting these values into the equation we derived earlier, we get:

2c(dc/dt) = 2(9/2)(1/2)(dc/dt) + 2(16/2)(1/2)(dc/dt) - 2(9)(16)(-sin 60°)(2°/min)

Simplifying and solving for dc/dt, we get:

dc/dt = 8√3 m/min

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Answer: A

Step-by-step explanation:

9 + 9 + 5 =23

CONSECUTIVE NUMBERS: 4,5,6,8

The largest number less than 1000 that is equal to sum of 4 natural consecutive numbers is 998.

The natural numbers include the positive integers (also known as non-negative integers) and a few examples include 1, 2, 3, 4, 5, 6, …∞. In other words, natural numbers are a set of all the whole numbers excluding 0. 23, 56, 78, 999, 100202, etc. are all examples of natural numbers.

We have to find the largest natural number less than 1000 that is equal to the sum of 4 natural consecutive.

First number is 999.

So, the sum is =  9 + 9 + 9 = 27

Now, the next number is

= 9 + 9 + 8

= 26

Also, 26 can be represented as sum of 4 Natural number as

= 5 + 6 + 7 + 8 = 26

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The derivative of the expression is: f'(x) = 9132(31x^30) + 6.

The derivative of this function can be obtained by applying the constant multiple rule in which the constant is multiplied by the derivative of the function. Next, we will apply the power rule of differentiation in which the power rule of differentiation. When these are applied, we will have the following:

First, the principle of linear differentiation is applied to all the values on the right as follows:

f'(x) = d/dx [9132x^31 + x + x + x + x + x + x]

     = d/dx [9132x^31] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x]  

When we apply the constant multiple rule, this then equals:

     9132 d/dx [x^31] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x] + d/dx [x]

Finally, we apply the power rule of differentiation to obtain:

     = 9132 (31x^30) + 1 + 1 + 1 + 1 + 1

     = 9132 (31x^30) + 6

So, the derivative of the function is f'(x) = 9132(31x^30) + 6.

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Answer:

3y + 5.

Step-by-step explanation:

There are an infinity of expressions that are equivalent to this one. However, you may get the simplest equivalent by simplifying it. This is how you do it:

[tex]3 ( y + 4 ) - 7\\ \\(3)(y)+(3)(4)-7\\ \\3y+12-7\\ \\3y+5[/tex]

Final answer: 3y + 5.

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Solving equations is a process that requires a lot of rewritting and simplifying, so you might be interested on checking out some examples of this topic here to improve your math simplifying skills!

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The solution of the expression is 2√5x(√2-1).

Multiplication is an arithmetic operation in mathematics that combines two or more numbers to obtain a product. It is denoted by the "×" or "·" symbol, or by placing numbers adjacent to each other with no symbol between them. For example, 2 × 3 = 6, and 4 · 5 = 20.

Multiplication is commutative, meaning that changing the order of the factors does not change the product. For example, 3 × 5 = 5 × 3 = 15. Multiplication is also associative, meaning that changing the grouping of the factors does not change the product. For example, (2 × 3) × 4 = 2 × (3 × 4) = 24.

From the question, we have

√5x ( √8x² - 2√x)

= √5x ( 2√2x - 2√x)

= √5x(√2-1)(2√x)

= 2√5x(√2-1).

The solution of the expression is 2√5x(√2-1).

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The complete question is:

Find the simplified product where x20: √5x (√8x²-2√x)

√10x

2x √40x-2x

O 2x10x-2√5x

O2x10x-2x√√5

DONE

Answer:

The drone is not free. The final price of the drone is $31.08

Answer:

51.06

Step-by-step explanation:

SOH CAH TOA

Sine = opposite/hypoteneuse

Cosine = adjacent/hypoteneuse

Tangent = opposite/adjacent

When looking for angles use the inverse function.

According to image you have the opposite of the angle and the hypotenuse

hypotenuse = 9

opposite = 7

using SOH we can find the angle: sin^-1(7/9) = 51.06

A. (1, 5), B. (4, 6), and C. (2, 4) is ordered pair is a solution to the system of inequalities where y > 2x y >  3

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

To check which ordered pair is a solution to the system of inequalities y > 2x and y > 3, we need to check if each pair satisfies both inequalities.

A. (1, 5)

Plugging in x=1 and y=5 into the inequalities, we get:

5 > 2(1) and 5 > 3

Both inequalities are true, so (1, 5) is a solution.

B. (4, 6)

Plugging in x=4 and y=6 into the inequalities, we get:

6 > 2(4) and 6 > 3

Both inequalities are true, so (4, 6) is a solution.

C. (2, 4)

Plugging in x=2 and y=4 into the inequalities, we get:

4 > 2(2) and 4 > 3

Both inequalities are true, so (2, 4) is a solution.

D. (0, 3)

Plugging in x=0 and y=3 into the inequalities, we get:

3 > 2(0) and 3 > 3

The first inequality is true, but the second inequality is false. Therefore, (0, 3) is not a solution.

Therefore, the solutions are A. (1, 5), B. (4, 6), and C. (2, 4).

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a) the critical number x= N/A ,b) the absolute maximum is -16 at x= 5

c) the absolute maximum is -4 at x= 0.25

what is critical number?

The term "critical number" can have different meanings depending on the context in which it is used. Here are a few possible definitions:

In the given question,

To find the critical numbers of the function, we need to find where the derivative is either zero or undefined. Let's find the derivative of y with respect to x:

y' = 4/x²

The derivative is undefined at x = 0, but this point is not in the given interval, so we don't have to consider it. The derivative is zero when:

4/x² = 0

This equation has no real solutions, so there are no critical numbers in the interval (0.25, 5).

Since the function y = -4/x is decreasing on the interval (0.25, 5), the absolute maximum will occur at the left endpoint x = 0.25, and the absolute minimum will occur at the right endpoint x = 5. Therefore:

a) the critical number x= N/A

b) the absolute maximum is -16 at x= 5

c) the absolute maximum is -4 at x= 0.25

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Therefore, 6:15 is less than 30:80.

Ratio is a mathematical term that describes the relationship between two or more quantities in terms of how many times one quantity contains another. It is usually expressed in the form of a fraction or a colon. For example, if there are 10 boys and 20 girls in a class, the ratio of boys to girls is 1:2, or 1/2. Ratios can be used to compare and analyze data in various fields, including finance, economics, and statistics.

To compare 3:5 and 30:80, we need to make sure they have the same denominator. We can find the equivalent ratio of 30:80 by dividing both terms by 10, which gives 3:8.

Now we can compare 3:5 and 3:8. The first term is the same in both ratios, so we can compare the second terms.

Since 5 is less than 8, we can say that:

6:15 ____ 30:80

Therefore, 6:15 is less than 30:80.

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The complete question is: The question is not clear. However, based on the given information, the task is to compare the two ratios "6:15" and "30:80" by entering either "K" (which means the first ratio is greater), "=" (which means the two ratios are equal), or "<" (which means the second ratio is greater) in the box.

Answer:

Seven Ones and two hundredths

One hundred thirty

Step-by-step explanation:

5.4 X 1.3= Seven Ones and two hundredths

13 X 10= One hundred thirty

We can conclude by answering the provided question that However, standard there is still some height variance within the cohort. Some pupils may be taller or shorter than the average height by more than 1.4 inches

A statistic that shows the variability or variation of a collection of data is the standard deviation. A high standard deviation indicates that the values are more scattered, whereas a low standard deviation indicates that the values are closer to the set mean. The standard deviation is a measure of how far the statistics are from the norm (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is high, the data is more scattered. The standard deviation represents the typical variability of the data collection. It displays the average departure from the mean of each number.

The standard deviation is a measure of the amount of variation or dispersion in a set of data. It tells us how much the values in a dataset differ from the mean value.

We know that the mean height is 61 inches and the standard deviation is 1.4 inches. To calculate the range of heights within one standard deviation from the mean, we can use the following formula:

range = mean ± (standard deviation)

Substituting the values we have:

range = 61 ± (1.4)

range = (59.6, 62.4)

This means that about 68% of the students in the class have heights between 59.6 inches and 62.4 inches.

The fact that the standard deviation is 1.4 inches tells us that there is some variation in the heights of the students. This means that not all students have the same height. Some students may be taller than the mean height of 61 inches, while others may be shorter.

The range of heights within one standard deviation from the mean (59.6 to 62.4 inches) is relatively narrow, which suggests that most of the students in the class have heights that are relatively close to the mean.

Overall, the variation in height can be seen as a natural part of human diversity, and it is something to be celebrated rather than feared. The standard deviation simply helps us to quantify the amount of variation in the height data.

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Answer: The ratio of their heights is 1/2 .

Let the radius of one cone be 'r'

and its height be 'h'

therefore, its perimeter of circular base will be 2 π r

and its volume will be given as  1 /3 π [tex]r^{2}[/tex] h

Let the radius of second cone be 'R'

and the height be 'H'

therefore its perimeter of circular base will be given as 2 π R

and its volume will be given as  1 /3 π [tex]R^{2}[/tex] H

ratio of their perimeters = 3 : 4

                         →         [tex]\frac{2 \pi r}{2 \pi R}[/tex]  =  [tex]\frac{3}{4}[/tex]

                          →         [tex]\frac{r}{R}[/tex]  =  [tex]\frac{3}{4}[/tex]

and ratio of their volume = 9 : 32

                          →      [tex]\frac{\frac{1}{3} \pi r^{2} h}{\frac{1}{3} \pi R^{2} H}[/tex]  =    [tex]\frac{9}{32}[/tex]

                          →      [tex](\frac{r}{R} )^{2}[/tex] * [tex]\frac{h}{H}[/tex] =  [tex]\frac{9}{32}[/tex]

now put the value of  [tex]\frac{r}{R}[/tex]  in the above equation we get

                          →        [tex](\frac{3}{4}) ^{2}[/tex]  *  [tex]\frac{h}{H}[/tex]  =  [tex]\frac{9}{32}[/tex]

solving it we will get

                    →        [tex]\frac{h}{H}[/tex] = [tex]\frac{1}{2}[/tex]  

therefore the ratio of their heights will be    [tex]\frac{1}{2}[/tex] .

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1. The length of the arc is 2π

2. The value of x is 22.95°

3. The measure of side m is (4√3)x

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

1. The length of an arc = tetha/360 × 2πr

= π/3 × 1/360 × 2 × π × 6

= 2π

the length of the arc is 2π

2. Sin60 = y/23

√3/2 = y/23

23√3 = 2y

y = 11.5√3

sin x = 11.5√3/51

sinx = 0.39

x = sin^-1(0.39)

x= 22.95°

3. the measure of mis calculated from

cos 30 = 6x/m

√3/2 = 6x/m

12x = √3m

m = 12x/√3

= 12x√3/3

= 4x√3.

= (4√3)x.

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The area of one segment formed by a 6" square inscribed in a circle cxan be expressed as 5.13 square inches.

Two unique points on a line define the boundaries of a line segment. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

We can form a triangle from this and from trigonometry, let the hypotenus = diameter

C= √6^2 + 6^2 = 6√ 2

diameter = 6√ 2,

radius = 3√ 2

A rea of the segment can be calculated as

r^2/2 [π θ/180 -sin θ)

( 3√ 2)^2 [90π/180 - sinθ)

=9( π/2 - 1)

=5.13 square inches

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Answer:

x=9

Step-by-step explanation:

The angles that measure 13x and 7x make a line. A line is 180°. 13+7 is 20 and 20 x 9 is 180.

Therefore x is 9

Using Laws of Indices, the given expression can be simplified as: 4

Some of the laws of Indices are:

1) Multiplying indices: This states that when multiplying indices with the same base, add the powers.

2) Dividing indices: This states that when dividing indices that have the same base, subtract the powers.

3) Brackets with indices: This states that when there is a power outside the bracket multiply the powers.

4) Power of 0: This states that any non-zero value raised to the power of 0 is equal to 1.

5) Negative and fractional indices: This states that when the index is negative, put it over 1 and flip (write its reciprocal) to make it positive.

When the index is a fraction, the denominator is the root of the number or letter, then raise the answer to the power of the numerator.

We are given the expression:

[tex]16^{\frac{1}{2} }[/tex]

Using law of fractional indices, we have:

[tex]16^{\frac{1}{2} } = \sqrt{16}[/tex]

= 4

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Answer:

7x + 9

Step-by-step explanation:

f(x) = x + 1

g(x) = 7x + 8

therefore, (fog)(x) = f(g(x))

f(g(x)) = (7x + 8) + 1

= 7x + 9

The sum of the probabilities of choosing each weekday is:

0.12 + 0.07 + 0.05 + 0.28 + 0.15 + p(Friday) + p(Weekend) = 1

where p(Friday) is the probability of choosing Friday and p(Weekend) is the probability of choosing one of the weekend days (Saturday or Sunday).

We know that the probability of choosing one of the weekdays is:

p(Weekdays) = 0.12 + 0.07 + 0.05 + 0.28 = 0.52

So, the probability of not choosing one of the weekdays is:

p(Not Weekdays) = 1 - p(Weekdays) = 1 - 0.52 = 0.48

Therefore, the probability that it will not choose one of the weekdays is 0.48.

Answer:

B

Step-by-step explanation:

8.05 by -16.8 = -135.24

all you had to do is multiply 8.05 by -16.8

The product is -135.24

Answer:

To find the constant of proportionality, you need to have two variables that are directly proportional to each other. This means that as one variable increases, the other variable increases in proportion to it.

Once you have identified two variables that are directly proportional, you can find the constant of proportionality by dividing one variable by the other.

For example, if you have two variables, x and y, and you know that they are directly proportional, you can write the equation:

y = kx

where k is the constant of proportionality.

To find the value of k, you can pick any set of values for x and y that satisfy the equation and solve for k. For example, if x = 2 and y = 4, you can write:

4 = k(2)

Solving for k, you get:

k = 4/2 = 2

So the constant of proportionality in this case is 2. This means that y is always twice as large as x, no matter what values of x and y you choose, as long as they are proportional.