Graph the equation on the coordinate plane
y=-1/2x
Select two points on the line to graph the line

In order to run a successful charity event for 6 people, it is important to ensure that everyone has something to enjoy.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


One way to do this is to provide cupcakes to one out of every three people. This will ensure that some people get a special treat while the others still have a chance to get one if they come to the event again. It also allows for a sense of fairness and equality, as everyone has an equal chance of receiving a cupcake. Additionally, it helps to build a sense of community and fellowship among the participants, as they can share the cupcakes and enjoy the experience together. It is also a great way to raise awareness about the charity and its cause, as people can talk about it while enjoying the cupcakes. To make sure that the event runs smoothly, it is important to have plenty of cupcakes on hand and to make sure that everyone is aware of the rules for receiving one.

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Answer50.5

ffffffffffffffff

Answer:

No

Step-by-step explanation:

The y intercept is 7. For it to be proportional it has to go through (0,0).

Answer:

Yes

Step-by-step explanation:

The moment about point O of the resultant force exerted on the tree by the cable at B is approximately 3830.06 N·m.

Since we know the tensions in cables AB and BC, we can find the horizontal and vertical components of the forces exerted by the cables at point B:

The horizontal component of the force exerted by the cable

AB = 630 cos(45) = 444.21 N

Similarly,

The vertical component of the force exerted by the cable  = 444.21 N

The horizontal component of the force exerted by the cable  = 637.55 N

The vertical component of the force exerted by cable  = 367.50 N

Total horizontal force = 444.21 N + 637.55 N = 1081.76 N

Total vertical force = 444.21 N + 367.50 N = 811.71 N

The moment about point O of the resultant force exerted on the tree by the cable at B is given by:

Moment = F * d

Using the Pythagorean theorem, we can find the magnitude of the resultant force,
= 1351.44 N

Perpendicular distance = 4 m * sin(45) = 2.828 m

Therefore, the moment about point O of the resultant force exerted on the tree by the cable at B is,

Moment = F * d = 1351.44 N * 2.828 m = 3830.06 N·m

Therefore, the moment about point O of the resultant force exerted on the tree by the cable at B is approximately 3830.06 N·m.

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The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.

Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).

In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:

a + b + c = 180

Substituting the given values, we get:

(6x-1) + 20 + (x+14) = 180

Simplifying and solving for x, we get:

7x + 33 = 180

7x = 147

x = 21

Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:

angle a = (6x-1) = (6*21-1) = 125 degrees

angle b = 20 degrees

angle c = (x+14) = (21+14) = 35 degrees

Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.

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To construct a 2x2 matrix B such that AB is the zero matrix, we need to find two different nonzero columns for B that will result in the product of AB being the zero matrix. One way to do this is to choose the columns of B such that they are the negatives of the rows of A. This will result in the product of AB being the zero matrix.

Let A = [[a,b],[c,d]]

We can choose the columns of B to be [[-a,-c],[-b,-d]]. This will result in the product of AB being the zero matrix.

So, B = [[-a,-b],[-c,-d]]

AB = [[a,b],[c,d]] * [[-a,-b],[-c,-d]] = [[0,0],[0,0]]

Therefore, the 2x2 matrix B that will result in the product of AB being the zero matrix is B = [[-a,-b],[-c,-d]].

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The congruent angles in the similar figures are as follows:

∠M ≅ ∠R

∠N ≅ ∠S

∠P ≅ ∠T

∠Q ≅ ∠U

Two figures are said to be similar if they are the same shape.  Similar figures have the corresponding sides in proportion to each other.

Similar figures also have the corresponding angles equal to each other.

Therefore, the figures are similar by MNPQ ~ RSTU

Hence,

∠M ≅ ∠R

∠N ≅ ∠S

∠P ≅ ∠T

∠Q ≅ ∠U

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Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The cost of renting from Low Price Rentals can be calculated as follows:

Rental fee + Cost per mile × Distance driven = $49 + $0.16 ×60 = $58.60

The cost of renting from Easy Rental can be calculated as follows:

Rental fee + Cost per mile × Distance driven = $25 + $0.50×  60 = $55.00

Therefore, the correct answer is: Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60. So, option 1 is the correct answer.

Hence, Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60

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Answer: The answer is 6.

Step-by-step explanation:

All of the solutions of the given system of linear inequalities above include the following:

A. (0, 3).

C. (6, 2)

E. (0, -1)

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph of a system of linear inequalities.

In this scenario, we can reasonably infer and logically deduce that the solution to the given system of linear inequalities is the shaded region and it lies in both quadrant I and quadrant IV with the following ordered pairs:

Ordered pair = 0, 3).

Ordered pair = (6, 2)

Ordered pair = (0, -1)

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The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;

If we perform a 180° rotation about the point O the following happens

Ray [tex]\overleftrightarrow{EF}[/tex] maps unto ray [tex]\overleftrightarrow{GH}[/tex]

Ray [tex]\overleftrightarrow{GH}[/tex] maps unto ray [tex]\overleftrightarrow{FE}[/tex]x

[tex]\overleftrightarrow{FG}[/tex] maps unto itself

Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.

The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.

The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;

The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.

Whereby the center of rotation of the line [tex]\overleftrightarrow{EF}[/tex] is equidistant from both the line [tex]\overleftrightarrow{GH}[/tex] which is parallel to the line [tex]\overleftrightarrow{EF}[/tex], the image of the line [tex]\overleftrightarrow{EF}[/tex] maps to the line [tex]\overleftrightarrow{GH}[/tex] following a 180° rotation about the point O, and the rotation of the line [tex]\overleftrightarrow{FG}[/tex] about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;

∠x ≅ 40° (A rotation transformation is a rigid transformation)

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Answer:

It depends. Depends on what? Depends on the type of triangle that this shelf forms. If Sandra wants the shelf to fit perfectly, she needs a shelf with the shape of a right triangle, the only type of triangles that have a 90° angle in one of their corners. Any other type of triangle will fit in some ways, but they won't fot perfectly.

Check the attached images to better understand this explanation.

As you can see on the images, the only type of shelf that fits the room's corner perfectly is a right triangle shaped shelf. Any other triangular shelf will fit in a specific orientation, but it won't fit perfectly.

The average baggage-related revenue per passenger is $29.80, using the variance the standard deviation of the baggage-related revenue is $27.35 and  the airline should expect about $3874 in revenue from baggage fees for a flight of 130 passengers (rounded to the nearest dollar).

a) To find the average baggage-related revenue per passenger, we need to calculate the expected value of the baggage fees. Let X be the random variable that represents the number of checked bags per passenger. Then the expected value of the baggage fees per passenger is:

E[Baggage Fees] = E[20X + 40(max(0, X-1))]

= 20E[X] + 40E[max(0, X-1)]

= 20(0.31 + 0.14(2)) + 40(0.14 + 0.31)

= 29.80

Therefore, the average baggage-related revenue per passenger is $29.80

b) To find the standard deviation of the baggage-related revenue, we can use the formula for the variance:

Var[Baggage Fees] = E[(Baggage Fees - E[Baggage Fees])^2]

= E[(20X + 40(max(0, X-1)) - 29.80)^2]

= E[(20X - 40(max(0, X-1)))^2]

= E[400X^2 - 1600X(max(0, X-1)) + 1600(max(0, X-1))^2]

= 400E[X^2] - 1600E[X(max(0, X-1))] + 1600E[(max(0, X-1))^2]

To calculate these expected values, we can use the fact that:

E[X^2] = Var[X] + (E[X])^2

E[X(max(0, X-1))] = E[X^2] - E[X]

E[(max(0, X-1))^2] = Var[X] + (E[X])^2 - 2E[X] + 1/4

Plugging in the values, we get:

Var[Baggage Fees] = 400(0.31 + 0.14(4)) - 1600(0.31 + 0.14) + 1600(0.31 + 0.14 + 1/4)

= 748

Therefore, the standard deviation of the baggage-related revenue is $27.35 (rounded to the nearest cent).

c) For a flight of 130 passengers, the total revenue from baggage fees can be found by multiplying the average baggage-related revenue per passenger by the number of passengers:

Total revenue = 130($29.80)

= $3874

Therefore, the airline should expect about $3874 in revenue from baggage fees for a flight of 130 passengers (rounded to the nearest dollar).

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Answer:

[tex]4\sqrt2[/tex]

Step-by-step explanation:

1) a=4 and b=8

2) Let geometric mean is g. [tex]g=\sqrt ab[/tex] or you can do [tex]g=\sqrt 4 times8[/tex]

3) g=[tex]4\sqrt2[/tex]

Answer:

angle a: 70°

angle d: 70°

angle dce: 35°

x: 15m

y: 14m

Step-by-step explanation:

all triangles add to 180° so 35 + 75 = 110 and 180-110 = 70

where the two triangles connect and cross, the angles will be the same so it will have the same angle measures as the first triangle which makes the triangles similar

knowing that they are similar triangles will help with figuring out the lengths of the sides.

since they are similar, their sides will be proportional, we just need to figure out the ratio

if we lay the triangles on top of each other, the two 75° angles match up and therefore the sides do too so we can make a fraction 12/18 = 10/x

now we can solve for x

multiply both sides by x

12x/18 = 10

now multiply both sides by 18

12x = 180

divide both sides by 12

x = 15

now we do the same for y

12/18 = y/21

12*21/18 = y

y = 14

hope this helps!

Answer:

0.1

Step-by-step explanation:

10^2=100

0.01^3=0.000001

10^-3=0.001

100 x 0.000001

----------------------    = 0.1

        0.001

For each relation, we would determine whether or not it is a function as follows;

Relation 1 is: B. not a function

Relation 2 is: B. not a function.

Relation 3 is: B. not a function

Relation 4 is: A. a function.

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.

Based on relations 1, 2, and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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The annual yield of the bond is 3.50%.

To calculate Mike's profit, we first need to determine the total cost of his investment, including the back-end load. The back-end load is calculated by multiplying the initial investment by the loading rate:

Back-end load = $14,000 * 5.5% = $770

So the total cost of Mike's investment is:

Total cost = $14,000 + $770 = $14,770

To determine the profit, we need to subtract the total cost from the total amount Mike received when he sold his shares:

Profit = ($21.85 - $20.00) * 14,000 - $770 = $2,730

Therefore, Mike made a profit of $2,730.

Note that the problem statement is exactly the same as the previous question. The answer is $2,730.

The annual rental income that Clara Teague needs to receive to achieve an annual yield of 8% can be calculated as follows:

Annual rental income = Total investment * Yield

where Total investment = $115,800 - $25,000 = $90,800

So the annual rental income that Clara Teague needs to receive is:

Annual rental income = $90,800 * 8% = $7,264

To determine the monthly rent, we divide the annual rental income by 12:

Monthly rent = $7,264 / 12 = $605.33

Therefore, Clara should charge a monthly rent of $605.33 to achieve an annual yield of 8%.

The annual yield of the bond can be calculated as follows:

Annual yield = (Annual interest payment / Bond price) * 100%

The annual interest payment is:

Annual interest payment = Bond face value * Annual interest rate = $25,000 * 3.7% = $925

The bond price is quoted at 105.7% of its face value, so the bond price is:

Bond price = Bond face value * 105.7% = $25,000 * 1.057 = $26,425

So the annual yield is:

Annual yield = ($925 / $26,425) * 100% = 3.50%

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After 2.5 years the price of land and the price of house will be equal.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S.

And, At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000.

Since, The price of land increases at the rate of 20% per annum.

Hence, We get;

A = 80,00,000 (1 + 20/100)ⁿ

And, The price of house depreciates at the rate 20% per annum.

Hence, We get;

A = 2,70,00,000 (1 - 20/100)ⁿ

Let after n years the price of land and the price of house will be equal.

Thus, We get;

80,00,000 (1 + 20/100)ⁿ =  2,70,00,000 (1 - 20/100)ⁿ

8 (120/100)ⁿ = 27 (80/100)ⁿ

8 (6/5)ⁿ = 27 (4/5)ⁿ

Take log both side,

log 8 + n (log 6 - log 5) = log 27 + n (log 4 - log 5)

0.9 + n × 0.8 = 1.4 + n × 0.6

0.9 + 0.8n = 1.4 + 0.6n

0.2n = 0.5

n = 2.5 years

Therefore, After 2.5 years the price of land and the price of house will be equal.

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6 cups of dal may be used to make eight bowls of sambar.

The ratio can be defined as the number that can represent one quantity as a percentage of another. They can be compared only when the two numbers in a ratio have the same unit. Ratios are used to compare two objects.

Given, One bowl of sambar is made the use of 3/four cup dal.

If 1 bowl of sambar is made using 3/4 cup of dal, then the number of bowls of sambar that can be made from 6 cups of dal can be found by dividing 6 cups by 3/4 cup per bowl:

6 cups / (3/4 cup per bowl)

We can simplify by multiplying the numerator and denominator by the reciprocal of 3/4:

6 cups / (3/4 cup per bowl) * (4/3)

Simplifying, we get:

8 bowls

Therefore, 6 cups of dal can be used to make 8 bowls of sambar.

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Therefore , the solution of the given problem of expression comes out to be Sunny earned $12x - 15 this week.

Mathematical operations like addition, multiply, and division are necessary. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and arithmetic calculations like additions, subtractions, multiplication and division, and divisions are all found in a statement of fact. Different sentences and words can be contrasted and compared.

Here,

If Sunny worked for x hours and earns $12 per hour, her earnings before the late delivery charge would be:

$12x$

However, since she was charged $15 for the late delivery on Tuesday, her earnings for the week would be:

$12x - 15$

Therefore, Sunny earned $12x - 15 this week.

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The complete question is "Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did Sunny earn this week?"

Using third-order Newton's interpolating a polynomial the value of f(2) is  (25ln(2))/9.

To estimate the value of f(2) using a third-order Newton's interpolating polynomial with the given data points, we first need to calculate the divided differences. The divided differences are defined as:

f[xi] = f(xi) for i = 1, 2, 3

f[x1,x2] = (f[x2] - f[x1]) / (x2 - x1) = (ln(4) - ln(1)) / (4 - 1) = ln(4) / 3

f[x2,x3] = (f[x3] - f[x2]) / (x3 - x2) = (ln(6) - ln(4)) / (6 - 4) = ln(3) / 2

f[x1,x2,x3] = (f[x2,x3] - f[x1,x2]) / (x3 - x1) = ((ln(3) / 2) - (ln(4) / 3)) / (6 - 1) = -0.018

Using these divided differences, we can write the third-order Newton's interpolating polynomial as:

f(x) = f[x1] + f[x1,x2](x - x1) + f[x1,x2,x3](x - x1)(x - x2) + f[x1,x2,x3,x4](x - x1)(x - x2)(x - x3)

Substituting the values of the data points and the divided differences we calculated, we get:

f(x) = ln(1) + ln(4)/3 (x - 1) - 0.018 (x - 1)(x - 4)

Simplifying this expression, we get:

f(x) = ln(1) + (ln(4)/3)x - (11ln(2)/9) + (ln(2)/9)x^2

To estimate f(2), we plug in x = 2:

f(2) = ln(1) + (ln(4)/3)(2) - (11ln(2)/9) + (ln(2)/9)(2)^2

f(2) = 2ln(2) - (11ln(2)/9) + (ln(2)/9)(4)

f(2) = (25ln(2))/9

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The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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Answer:

8(-2)^3= -64

8(-1)^3= -8

8(0)^3= 0

8(3)^3= 216

Hope this helps! Remember PEMDAS (Please forgive My Dear Aunt Sally)

Answer:

12x^2.

Step-by-step explanation:

let y = 4x^3

If y is increased by a small amount Δy then x is increased by a small amount Δx, so we write:

y + Δy = 4(x + Δx)^3

y + Δy = 4(x^3 + 3x^2 Δx + 3x(Δx)^2 + (Δx)^3)

y + Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3

Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3 - y

    = 4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2 - 4x^3

Δy/Δx = (4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2- 4x^3 ) / Δx  

          = (12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2) / Δx

          = 12x^2 + 12x(Δx)^2 + 4Δx

Now as Δx approaches zero, the limit  ( that is the derivative) of f(x)

= 12x^2

- as we can neglect the last 2 terms.

The second part can be solved by the same process.

The area of the shaded region is 104 m².

What is a Triangle ?

The intersection of the two sides of a triangle's three sides, which are known as the vertex, is a sort of polygon. Between two sides, an angle forms. This is among geometry's crucial components.

We know that Area of a triangle = 1/2 × base × height

The area of Big triangle = 1/2 × 30 × 13

                                        = 15 × 13

                                       = 195 m²

Area of Small triangle = 1/2 × 14 × 13

                                    = 91 m²

So, Area of the shaded region

        =  Area of big triangle - Area of small triangle

        = 195 - 91

        =  104 m²

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Answer:

the capital value of the property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year is approximately $166,667.

Step-by-step explanation:

The capital value (present sale value) CV of property that can be rented on a perpetual basis for R dollars annually is given by the formula:

CV = ∫₀^∞ R e^(-it) dt

where i is the prevailing continuous interest rate.

To show that CV = R/i, we can evaluate the integral:

CV = ∫₀^∞ R e^(-it) dt

We can use the formula for the exponential integral, which is:

∫ e^(ax) dx = (1/a) e^(ax) + C

Using this formula, we can integrate the exponential function in the integral and obtain:

CV = [ (-R/i) e^(-it) ] from t = 0 to t = infinity

Since e^(-infinity) = 0, we have:

CV = [ (-R/i) e^(0) ] - [ (-R/i) e^(-i*0) ]

Simplifying this, we get:

CV = [ (-R/i) ] - [ (-R/i) ] = R/i

So we have shown that CV = R/i, as required.

Now, to find the capital value of property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year, we can use the formula CV = R/i with R = $10,000 and i = 0.06:

CV = $10,000 / 0.06 ≈ $166,667 (rounded to the nearest whole number)

Therefore, the capital value of the property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year is approximately $166,667.

The values of the coordinates x and y is P ( 6 , 3 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( x , y )

Let the second point be Q ( 0 , 0 )

Now , the slope of the line is m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = y / x

m₁ = 1/2

So , y/x = 1/2

And , x = 2y

Now , the third point is R ( 7 , 5 )

m₂ = ( 5 - y ) / ( 7 - x )

m₂ = 2

On simplifying , we get

( 5 - y ) / ( 7 - x ) = 2

Multiply by ( 7 - x ) , we get

5 - y = 14 - 2x

Adding 2x and subtracting 5 on both sides , we get

2x - y = 9

Substitute the value of x from m₁ , we get

2 ( 2y ) - y = 0

3y = 9

Divide by 3 on both sides , we get

y = 3

And , the value of x = 6

Hence , the coordinate of the point P is P ( 6 , 3 )

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All frumpable numbers are odd Suppose n is an even integer so n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of \dfrac{a}{b} where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

We are given that;

A integer n is frupable if n2 2n is odd

Now,

Suppose n is an even integer, so n = 2k for some integer k. Then:

n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

Since k and k+1 are consecutive integers, one of them is even and the other is odd. Therefore, their product is even. This means that 4k(k+1) is even, and therefore, n^2 + 2n is even.

Since n^2 + 2n is even, it cannot be frumpable by definition. Therefore, if n is frumpable, n must be odd.

We have shown that if n is even, then n^2 + 2n is even and therefore, n cannot be frumpable.

Therefore, by the given numbers all frumpable numbers will be odd and n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

Learn more about numbers here;

https://brainly.com/question/3151755

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