Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. (If the series is divergent, enter DIVERGENT.)1+1/3+1/9+1/27+...

The approximate surface area of the prism is 537 cm².

A 3-dimensional solid prism's base shape determines how much surface area it has. The total area filled by a prism's faces is known as the prism's surface area. A polyhedron with flat faces is called a prism.

The surface area of the prism formula

So,

[surface area ]=

2×[area of the base]+[perimeter of the base]×height

area of the base=10×8.7/2= 43.5 cm²

the perimeter of the base=10×3= 30 cm

height of the prism=15 cm

[surface area ]=2×[43.5]+[30]×15 = 537 cm²

so the approximate surface area of the prism is 537 cm².

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The value of Three less than eight times a number is at least 15 is x≥6

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or explain the overall situation, this is known as an equation.

Given ,

8x

3 less goes to 8x-3

then there is at least 15 which changes to

8x-3≥15

Then solve for x:

add 3 to the sides--> 3x≥15+3

3x≥18

Divide both of the sides by 3

x≥6

Therefore  the value of three less than eight times a number is at least 15 is x≥6

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The Oregon Trail is a western route that runs 1,000 miles from Illinois to Utah Territory.

In American history, the Oregon Trail, also known as the Oregon-California Trail, was an overland route that connected Independence, Missouri, with Oregon City, which is located close to Portland, Oregon, today, in the Willamette River valley. In the nineteenth century, it was one of two major emigration routes to the American West, the other being the southerly Santa Fe Trail from Independence to Santa Fe (now in New Mexico). A spur of the northerly Oregon route, which was a component of the Oregon Trail, headed to the Great Salt Lake region of what is now northern Utah. Additionally, branches from each main trail provided links to places in California.

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Answer:

I can "Confirm" The answer is not Oregon Trail, I believe the answer is "The Mormon Trail "

Step-by-step explanation:

Or "A"

Have a Joyous Day

The missing number in the boxes using the concept of perfect square are;

1) 4

2) 7 and 2

3) 4

4) 3 and 9

5) 3

A perfect square is defined as a number that is the square of a whole number. For example, 36 is a perfect square being the square of 6. Other perfect squares that are between 0 and 1000 are 1, 4, 9, 16, 25, 3649, 64, e.t.c

1st box: We see it as;

___ * 2 * 2

Using the concept of perfect squares and the pattern given, we can say that the missing number is 4

2nd box: 14 * __ * ___

Using the concept of perfect squares and the pattern given, we can say that the missing numbers are respectively 7 and 2

3rd box: 2 * 8 * ___

Using the concept of perfect squares and the pattern given, we can say that the missing number is 4

4th box: __ * 3 * _____

Using the concept of perfect squares and the pattern given, we can say that the missing numbers are respectively 3 and 9

5th: 3 * ____

Using the concept of perfect squares and the pattern given, we can say that the missing number is 3

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Z test and the X² test (Chi squared) will be used to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2.

Any statistical test for which the test statistic's distribution under the null hypothesis may be roughly represented by a normal distribution is known as a Z-test. Z-tests examine a distribution's mean. To determine if a discovery or relationship is statistically significant or not, hypothesis testing uses a z-test. It specifically checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more can a z-test be applied.

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The total amount of waste these households are expected to produce in 2020 is 117,649 tones.

Define Modelling Exponential Decay

Given,

Total tonnes of waste in 2017 = 125 000 tonnes

The rate of fall each year is = 2%

Now, find the total amount of waste produce in 2020.

There are 3 years from 2017 to 2020.

So, the amount of waste produce is

= 125000 (1 - 2/100) ^ 3

= 125000 (0.98) ^ 3

= 125000 * 0.941192

= 117,649

Hence, the total amount of waste these households are expected to produce in 2020 is 117,649 tones.

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Answer:

The rate of decrement is given as: r = 4%. From the table, the initial population is. P (0) = 7900. So, the population in t years is. P (t) = P (0) * (1 - r)^t. This gives. P (t) = 7900 * (1 - 4%)^t. Evaluate the difference.

Population after 2 years = P (1 + 4/100)2 = 62500 X (104/100)2

= 62500 × 26/25 X 26/25 = 100 × 26 ×26 = 67600.

Hence, the population after two years will be 67,600.

Answer:

A Factor is a number that is multiplied. With another number to get a Product.

Step-by-step explanation:

Example  7 * 5 = 35

7 and 5 are factors of 35 that when multiplied give a product of 35

Answer:

139 degrees

Step-by-step explanation:

you just add both the angles together since they share a vertex

After choosing every proportion, if 24 people have the flu out of 360 people, then 60 people would have the flu out of 900.

We know very well that if any relation of one quantity is given with the second quantity at any instant of  time and same relation question is asking  at another instant of time, then always use unitary methods.

The unitary method is defined as a technique for solving a problem by first finding the value of a single unit, and then with the help of found value the necessary value can be find by multiplying the single unit value.

Here, In 360 people number of people would have flu=24

∴In 900 people number of people would have flu=(24×900)/360

                                                                                   =21600/360

                                                                                    =60people.

Hence, number of people would have flu is 60.

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The height of the Washington Monument is 553.84 feet.

A proportion is a comparison of two numbers that each represent the parts of a whole.

Given that, while on a visit to DC, you measure that the Washington monument casts a shadow 300 feet long. At the same time, your friend who is 6 feet tall is casting a shadow of 3.25 feet.

Let the height of the Washington Monument be x,

Using proportion,

6/3.25 = x/300

x = 553.84 feet

Hence, The height of the Washington Monument is 553.84 feet.

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The third approximation is x3 = 19.6

The Newton's method allow to approximate the root of a function as:

Newton's method, commonly referred to as the Newton-Raphson method after Isaac Newton and Joseph Raphson, is a root-finding algorithm that generates progressively improved approximations to the roots (or zeroes) of a real-valued function. The most fundamental form begins with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial point x0 for the root of f.

xₙ = xₙ₊₁ + f(xₙ)/f'(xₙ)

For this function, it is:

f(x) = 1/3x³+1/2x²+8

f'(x) = 2/3x²+x

For x1=-3,

f(x1) = 1/3x³+1/2x²+8 = -9 + 4.5 + 8 =3.5

f'(x1) = 2/3x²+x = 3

x2 = x1 + f(x1)/f'(x1) = -1.8

Therefore, x2 = -1.8

Then, the third approximation is x_3 is

x3 = x2 + f(x2)/f'(x2) = -1.8+ (7.72/0.36)

x3 = 19.6

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In any group of 6 people there always at least 3 people who either all know one-another or all are strangers to one-another.

The Pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

The Pigeonhole principle applies because every person is related to every other person in two ways, either they know the person or they do not.

Given that there is a group of 6 people.

Let us say A,B,C,D,E,F.

Suppose that A has at least three friends. If any two of these three are friends with each other, then together with A, they are a group of three mutual friends. If none of these are friends with each other, then they are a group of three mutual strangers to themselves.

On the other hand, A has fewer than three friends among the other five people, then there must be at least three that are strangers to A. If any two of these are strangers, then together with A, they are a group of three strangers. If none of them are strangers to each other, then they are a group of at least three mutual friends.

Hence it is proved that, in any group of 6 people there are always at least 3 people who either all know one-another or all are strangers to one-another.

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The Subgraph Isomorphism Problem is NP and NP-Hard. Therefore, the subgraph isomorphism problem is NP-Complete.

What is  Subgraph Isomorphism?

In theoretical computer science, the subgraph isomorphism drawback could be a procedure task during which 2 graphs G and H ar given as input, and one should confirm whether or not G contains a subgraph that's similarity to H.

Proof:

Certificate: Let G be a subgraph of G2. We also know the mapping between the vertices of G1 and G.

Verification: We have to visualize if G1 is isomorphous to G or not. (i) Checking if the mapping could be a bijection and (ii) confirming if, for each edge (u, v) in G1, there's a foothold (f(u), f(v)) gift in G takes polynomial time.

Therefore, the Subgraph similarity downside has polynomial time verifiability and belongs to the NP category.

The Subgraph similarity drawback belongs to NP-Hard –A drawback L belongs to NP-Hard if each NP drawback is reducible to L in polynomial time. To prove that the Subgraph similarity drawback (S) is NP-Hard, we have a tendency to associate degreed} scale back an already celebrated NP-Hard drawback to S for a selected instance. If this reduction is feasible in polynomial time, then S is additionally associate degree NP-Hard drawback. Thus, allow us to scale back the ingroup call drawback (C) that is NP-Complete (hence, all the issues in NP will be reduced to C in polynomial time) to the Subgraph similarity drawback. If this reduction is feasible in polynomial time, each NP drawback will be reduced to S in polynomial time, thereby proving S to be NP-Hard.

Proof:

Let us prove that the Clique Decision Problem reduces to the Subgraph Isomorphism Problem in polynomial time.

Let the input to the set call drawback be (G, k). The output is true if the graph G contains a set of size k (a set of size k may be a subgraph of G). Let G1 be a whole graph of k vertices and G2 be G, where G1, G2 ar inputs to the Subgraph isomorphy drawback. we have a tendency to observe that k n, then a set of size k can't be a subgraph of G. The time taken to form G1 is O(k2) = O(n2) [since k]as the range of edges in a very complete graph of size k = kC2 = k*(k-1)/2. G contains a pack of size k, if and as long as G1 could be a subgraph of G2 (since G1 itself could be a subgraph of G2 and each graph is similarity to itself, the results of the Subgraph similarity downside is true. Thus, G1 is similarity to a subgraph of G2). Hence, if the pack call downside is true, the Subgraph similarity downside is true and the other way around. Therefore, the pack call downside will be reduced to the Subgraph similarity downside in polynomial time for a specific instance.

Thus, the Subgraph Isomorphism Problem is an NP-Hard Problem

hence,

The Subgraph Isomorphism Problem is NP and NP-Hard. Therefore, the subgraph isomorphism problem is NP-Complete.

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In hypothesis testing, the critical value is option (d) a number that establishes the boundary of the rejection region

The hypothesis testing is defined as the process of collecting the data and using that as inference draw the calculation about the population parameter.

The reject region of the hypothesis testing is defined as the  set of values for the test statistic for which the null hypothesis is rejected.

Therefore, the critical value is  a number that establishes the boundary of the rejection region of the graph

Hence, in hypothesis testing, the critical value is option (d)  a number that establishes the boundary of the rejection region

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the role of auditor is in management skill.

What is accounting?

Accounting, conjointly referred to as business, is that the activity, processing, and communication monetary|of monetary|of economic} and non financial data concerning economic entities like businesses and companies.

Main body:

The role of the auditor or reviewer is to relinquish knowledgeable and freelance on these monetary statements. The review or audit of associate association’s monetary report will guarantee larger responsible to the members and supply associate assurance that every one funds received by the organisation are properly accounted for.

therefore the role of auditor is in management skill.

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One kilogram of mushrooms costs $2.90, whereas one kilogram of turnips costs $1.10.

An expression that describes the relationship between two or more numbers and variables is called an equation.

Dependent and independent variables are the two different categories. A dependent variable depends on another variable, whereas an independent variable does not depend on other variables.

Let x stand in for the price per kilogram of mushrooms, and y for the price per kilogram of turnips.

2 kg of mushrooms and 2.5 kg of turnips are priced at £8.55.

2x + 2.5y = 8.55  ________(1)

3 kg of mushrooms and 4 kg of turnips are priced at £13.10.

3x + 4y = 13.10   ________(2)

From both equations:

x = 2.9, y = 1.1

A kg of mushrooms costs $2.90, whereas a kg of turnips costs $1.10.

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If we consider the function y=2x+1 then the inverse of the function comes to be  y=(x−1)/2.

Each element in the range of an original function f is mapped to its corresponding element in the domain by the inverse function f ⁻¹.

Finding inverse of a function

It is typical to consider the x values as the domain and the y values as the range when considering an equation. The domain and range of f are reversed by the inverse function, f ⁻¹, as was previously mentioned. Flip the x and the y, then solve for y to determine the inverse of a written function.

Find the inverse.

                    y=2x+1

1. Switch the x and y.

                    x=2y+1

2. Then solve the equation for the y value.

                      x−1=2y

                      y=(x−1)/2

The graph of the inverse function is the mirror image to y=x axis

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Procedure for regrouping to find sum is as follows as mentioned.

Regrouping is accomplished by forming groups of tens during operations such as subtraction and addition. Regrouping is the process of rearranging numbers into groups based on place value to make operations easier.

This is known as regrouping because you are rearranging numbers into place value to complete the process.

Assume we want to add 18 and 12, which equals 30.

1. It is best to visualise your problem as a grid when regrouping with addition.

              1 2

         +   1 8

2.In this situation, the first addition would be to add 2 and 8, which equals 10. However, there is no place to write 10 on the bottom row. In this case, regrouping is required. To accomplish this, we take the 0 from the 10 and place it in the bottom row, followed by the 1 above our ten's column. Below is an updated grid:          

     1

     12

   +1 8

        0       

3.We must now add up the tens column. In this case, we have three one-digit numbers to add together. This brings us to the correct solution answer, which is 30.

1

1 2

1 8

3 0

Hence, the regrouping is the simplest way to do addition.

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The general solution of equation y''+4y=sec(2z) is

y = c₁cos2z + c₂sin2z + [tex]\frac{cos2z}{4}[/tex] ln(cos2z) + [tex]\frac{z sin2z}{2}[/tex].

Given differential equation is,

y'' + 4y = sec(2z)

Characteristic equation of this equation is

(D²+4)=0

⇒ D² = -4

    D =  ±2i

Therefore the roots are imaginary.

D₁=2i ⇒ y₁ = e⁰cos2z = cos2z

D₂=-2I⇒ y₂ = e⁰sin2z = sin2z

yn= c₁cos2z + c₂sin2z

Noe to solve yp, first we need to solve Wronskian

y₁= cos2z ,   y₂=sin2z

y₁'= -2sin2z , y₂'=2cos2z

⇒ W = [tex]\left[\begin{array}{ccc}y1&y2\\y1'&y2'\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}cos2z&sin2z\\-2sin2z&2cos2z\\\end{array}\right][/tex]

                              = (cos2z)(2cos2z)-(-2sin2z)(sin2z)

                              = 2cos²2z + 2sin²2z

                              =2 (cos²2z + sin²2z)

                              = 2 ≠ 0

yp = - y₁[tex]\int\ {\frac{y2 g(z)}{W} } \, dz[/tex] + y₂[tex]\int\ {\frac{y1 g(z)}{W} } \, dz[/tex]

    = -(cos2z)[tex]\int\ {\frac{(sin2z)(sec2z)}{2} } \, dz[/tex] + (sin2z)[tex]\int\ {\frac{(cos2z)(sec2z)}{2} } \, dz[/tex]

    = - (cos2z)[tex]\int\ {\frac{sin2z/cos2z}{2} } \, dz[/tex] + (sin2z)[tex]\int\ {\frac{cos2z/cos2z}{2} } \, dz[/tex]

    = - [tex]\frac{cos2z}{2}[/tex][tex]\int\ {tan2z} \, dz[/tex] + [tex]\frac{sin2z}{2}[/tex][tex]\int\ \,dz[/tex]

    =  - [tex]\frac{cos2z}{2}[/tex](-[tex]\frac{1}{2}[/tex] ln (cos2z)) + [tex]\frac{sin2z}{2}[/tex] (z)

    =  [tex]\frac{cos2z}{4}[/tex]ln(cos2z) + [tex]\frac{zsin2z}{2}[/tex]

Now the general equation will become

y = yn + yp

y = c₁cos2z + c₂sin2z +[tex]\frac{cos2z}{4}[/tex]ln(cos2z) + [tex]\frac{zsin2z}{2}[/tex]    .

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The research is important for the students because it helps them to have a detailed analysis of everything. When you have a proper in-depth analysis of any topic, the result comes out to be fruitful and also the knowledge is enhanced.

The research is important for the students because it helps them to have a detailed analysis of everything. When you have a proper in-depth analysis of any topic, the result comes out to be fruitful and also the knowledge is enhanced.

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The general term of each sequence that are given are [tex]a_{n} = n+2 / 2[/tex] ; nEN for the each infinite sequence suggested below, give its generating function in closed form, i.e., not as an infinite sum.

The infinite sequence that are generally number's that doesn't have any ending and are called as the infinite sequence and other that have finite sequence which have final numbers.

Here given infinite sequence are :

[tex]a1 =1 , a2= 0 , a3= 0 , a4 = 1.\\closed form of infinite sequence is an = 1 and 0 otherwise.\\sequence that s given is 3,2,4,1,1,1 and\\ a1 = 3 , a2 2 , a3= 4, a4= 1.\\an = 3, n =1, a2 = 2, a3 = 4, \\no n= 1, n=2, n=3 1 otherwise\\Given sequence is 1,3,6,10 ,15 \\then an = n+2 /2.[/tex]

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It is difficult to determine the exact volume of a cherry tree without cutting it down, but researchers can use other variables, such as height and diameter, to predict the tree's volume. In a study of black cherry trees

The measurement of how much space an item or substance occupies is called volume. The Allegheny National Forest is occupied by the tree's trunk and branches. Typically, the volume of an object or substance is stated in cubic units, such as cubic feet or cubic metres. The volume variables were looked at in order to comprehend them. Given that it is difficult to quantify without cutting the tree down, the volume of the tree was calculated given its height and diameter. This knowledge may be useful in estimating the potential while looking for them.

Typically, the volume of an object or substance is expressed in cubic units, such as cubic feet or cubic metres. It is determined by multiplying an object's length, breadth, and height.

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5o% of almost 1500 highway deaths in Pennsylvania each year are attributed to aggressive driving.

Aggressive driving is defined as any behind-the-wheel exertion that, without regard for safety, puts another person( or people) and/ or property in peril.

Aggressive driving can vary from potentially dangerous conduct to serious assault.

From the data attained the percentage of the nearly 1500 highway deaths in Pennsylvania each year attributed to aggressive driving will be 50%

5o% of almost 1500 highway deaths in Pennsylvania each year are attributed to aggressive driving.

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The maximum movement from point of equilibrium for the spring mass would be 140 m above the point of equilibrium and 140 m below the point of equilibrium for a total of 280 m.

A) To find the spring constant k, we use Hooke's law which states that

F = kx __(1)

where, F is the force in Newtons applies to extend a string by a distance 'x' in meters.

Hence, in the question, F = 10kg x 9.8 m/sec^2 = 98 Newtons(N)

and x = 9.8 cm = 0.098 m.

Substituting these values in (1)

98 = k(0.098)

=> k = 1000.

Hence, The spring constant is k = 1000

B) We use the spring constant k = 1000 calculated in part(A) above to give us our general equation of motion here which is :

Force = -ky___(2)

where y = y(t) is the displacement of the object from its rest state measured positively in the downward direction when force is applied to  it.

From Newton's law,

Force = Mass × Acceleration

where, Mass = 10kg and Acceleration = y"(t) = [tex]\frac{d^2y}{dt^2}[/tex].

Further, from the question

we know that at time t = 0, y(0) = 140cos(8(0)) = 140 ,

y'(0)= -8(140)sin(8(0))= 0.

Using all this information we get the following initial - value problem from(2)

10y" = - 1000y __(3)

y(0) = 140 __(4)

y'(0) = 0 __(5)

In (3) above we seek solutions of the form [tex]y = e^p^t[/tex] where p ∈ R and substitute in (3) to get

[tex]e^p^t (p^2 + 100) = 0[/tex]

=> p = ±10i where i = [tex]\sqrt{-1}[/tex]

y(t) = Acos(10t) + Bsin(10t)   (6)

where A, B are constants to be determined by initial conditions (4) and (5).

Using (4) in (6) leads to

140 = Acos (10(0)) +Bsin(10(0))

=> 140 = A

So, this get us to

y(t) = 140 cos(10t) + B sin(10t)    (7)

Now using (5) in (7)

0 = -1400 sin(10(0)) + 10 Bsin (10(0))

=> 0 = 10B

=> B = 0

Hence, Our solution is y = 140cos(10t)

The maximum movement from point of equilibrium for the spring mass would be 140 m above the point of equilibrium and 140 m below the point of equilibrium for a total of 280 m.

This is the incomplete question:

Complete question is:

A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0 , the resulting mass-spring system is disturbed from its rest state by the force. F(t) = 140cos(8t).  The force F(t) is expressed in newtons and is positive in the downward direction, and time is measured in seconds.

Determine the spring constant k.

Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y , y', y" , t)

Solve the initial value problem for y(t).

Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval . if there is no such maximum, enter none. maximum excursion.

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Number of hours that Beth will take to catch up the Angie is 4.5 hours

The speed of Angie = 45 miles per hour

We know,

Speed = Distance / Time

Distance = Speed × Time

Substitute the values in the equation

In one hour the distance she traveled = 45 × 1

Multiply the numbers

= 45 miles

Beth leaves one hour later driving the same route

The speed of Beth = 55 miles per hour

The relative speed = 55 - 45

= 10 miles per hour

Then the time taken to catch up = 45/10

Divide the numbers

= 4.5 hours

Hence, the Beth will take 4.5 hours to catchup Angie

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The measures of the two complementary angles are 28 and 62 degrees

Complementary angles:

In math, the sum of two angles is equal to 90 degrees, they are called complementary angles.

Given,

Here the two angles are complementary if the sum of their measures is 90.

And we need to find the measures of two complementary angles if one angle is more than 6 times the other angle.

Let us consider A is the measure of the smaller angle and B is the measure of the larger angle.

Here we know that they are complementary 

=> A + B = 90

Here we also know that,

=> 2A + 6 = B

Now, we have to replace B in the first equation with the second equation, then we get,

=> A + 2A + 6 = 90

Now, solve for A:

=> 3A + 6 = 90

=> 3A = 84

Therefore, the value of A is 28

Then the value of B is,

=> 2(28) + 6 = 62

Therefore, the two angles that complementary are: 28 and 62 degrees

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