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Divisibility Rules

What is the divisibility rule for 4.

A number is divisible by 4 if the number formed by its last two digits is divisible by 4. This video explains the process through the use of examples.

Assignment 4: Divisible By Three

Assignment 4: divisible by three – Embark on an intriguing journey into the realm of divisibility by three, a mathematical concept that unveils hidden patterns and simplifies calculations across diverse fields. From ancient civilizations to modern-day applications, this exploration promises to captivate your curiosity and enhance your understanding.

Delve into the mathematical foundations of divisibility by three, unraveling the rules and properties that govern this fascinating concept. Discover practical applications in computer science, engineering, and finance, where divisibility by three streamlines problem-solving and enhances efficiency.

Mathematical Properties of Divisibility by Three: Assignment 4: Divisible By Three

In mathematics, divisibility refers to the relationship between two integers. When one integer (the dividend) is evenly divisible by another integer (the divisor), the quotient is a whole number without any remainder.

One of the fundamental properties of divisibility is divisibility by three. A number is divisible by three if the sum of its digits is divisible by three. For example, the number 123 is divisible by three because 1 + 2 + 3 = 6, which is divisible by three.

Mathematical Rule for Divisibility by Three

The mathematical rule for determining if a number is divisible by three is based on the sum of its digits. Specifically, a number is divisible by three if the sum of its digits is divisible by three. This rule can be applied to any integer, regardless of its size or number of digits.

For example, to determine if the number 456 is divisible by three, we add its digits: 4 + 5 + 6 = 15. Since 15 is divisible by three, we can conclude that 456 is also divisible by three.

Applications of Divisibility by Three

Divisibility by three has practical applications in various fields, simplifying calculations and problem-solving.

Computer Science

In computer science, divisibility by three is used for:

• Hashing algorithms: Dividing the hash value by three helps distribute data evenly across buckets, reducing collisions.
• Checksums: Checking if a checksum is divisible by three ensures data integrity during transmission.
• Error detection: In certain error detection codes, divisibility by three helps identify errors in data transmission.

Engineering

In engineering, divisibility by three is used for:

• Load balancing: Dividing a load evenly among three or more components ensures optimal performance.
• Structural design: Checking if the number of bolts or rivets used in a structure is divisible by three ensures proper load distribution.

In finance, divisibility by three is used for:

• Investment diversification: Dividing investments into three or more asset classes helps reduce risk and balance returns.
• Debt repayment: Checking if a loan amount or repayment schedule is divisible by three helps ensure manageable monthly payments.
• Financial analysis: Dividing certain financial ratios by three simplifies interpretation and comparison across different companies.

Methods for Checking Divisibility by Three

Determining if a number is divisible by three is a fundamental skill in mathematics. There are several methods to check divisibility by three, each with its own advantages and applications.

Divisibility Test Based on the Sum of Digits

This test involves adding the individual digits of a number and checking if the result is divisible by three. If the sum is divisible by three, then the original number is also divisible by three.

• Example: Consider the number 123. The sum of its digits is 1 + 2 + 3 = 6, which is divisible by three. Therefore, 123 is divisible by three.

Divisibility Test Based on the Remainder of Division by Three

This test checks if the remainder of a number when divided by three is zero. If the remainder is zero, then the number is divisible by three.

• Example: Divide 27 by 3. The remainder is 0. Therefore, 27 is divisible by three.

Properties of Numbers Divisible by Three

Numbers that are divisible by three share certain unique properties that distinguish them from other numbers. These properties are closely linked to the fundamental rules of divisibility and provide valuable insights into the behavior of numbers.

Sum of Digits

One of the most notable properties of numbers divisible by three is that the sum of their individual digits is always divisible by three. For instance, the number 123 is divisible by three because the sum of its digits (1 + 2 + 3) is 6, which is also divisible by three.

Alternating Sum of Digits, Assignment 4: divisible by three

Another interesting property involves the alternating sum of digits. If we take the sum of the digits in the odd positions and subtract the sum of the digits in the even positions, the resulting value is always divisible by three.

Consider the number 456: the alternating sum of digits is (4 – 5 + 6) = 5, which is divisible by three.

Relationship with Other Divisibility Rules

The divisibility rule for three is closely related to other divisibility rules. For example, a number is divisible by both three and nine if it is divisible by nine. Additionally, a number is divisible by three if it is divisible by both three and six.

• The number 36 is divisible by three because its sum of digits (3 + 6) is 9, which is divisible by three.
• The number 153 is divisible by three because its alternating sum of digits (1 – 5 + 3) is 3, which is divisible by three.
• The number 270 is divisible by both three and nine because its sum of digits (2 + 7 + 0) is 9, which is divisible by both three and nine.

Examples and Non-Examples

In mathematics, divisibility is a fundamental concept that determines whether one number is evenly divisible by another. When a number is divisible by three, it means that it can be divided by three without leaving a remainder. Understanding the properties and methods of divisibility by three is essential for various mathematical operations and applications.

To illustrate the concept of divisibility by three, let’s explore examples and non-examples of numbers that fall into these categories:

Examples of Numbers Divisible by Three

• 9 : 9 ÷ 3 = 3, leaving no remainder
• 12 : 12 ÷ 3 = 4, leaving no remainder
• 18 : 18 ÷ 3 = 6, leaving no remainder
• 21 : 21 ÷ 3 = 7, leaving no remainder
• 24 : 24 ÷ 3 = 8, leaving no remainder

Non-Examples of Numbers Not Divisible by Three

• 5 : 5 ÷ 3 = 1 remainder 2
• 10 : 10 ÷ 3 = 3 remainder 1
• 14 : 14 ÷ 3 = 4 remainder 2
• 17 : 17 ÷ 3 = 5 remainder 2
• 22 : 22 ÷ 3 = 7 remainder 1

The key distinction between divisible and non-divisible numbers is the presence or absence of a remainder when the number is divided by three. If the remainder is zero, the number is divisible by three; if the remainder is not zero, the number is not divisible by three.

Historical and Cultural Significance

The concept of divisibility by three has played a significant role in various ancient civilizations and religious practices throughout history. Its presence can be traced back to ancient Egypt, where the number three was considered sacred and associated with the gods.

In the Pythagorean tradition, numbers divisible by three were believed to possess mystical properties and were considered perfect.

Role in Ancient Civilizations

• In ancient Egypt, the number three was associated with the gods and was considered a sacred number. The pyramids were built with a base length that was divisible by three, and the number of steps on each side was also divisible by three.
• In ancient Greece, the number three was considered to be a perfect number. The Pythagoreans believed that the universe was governed by mathematical principles, and they associated the number three with the three elements of earth, air, and water.
• In ancient China, the number three was considered to be a lucky number. It was often used in religious ceremonies and rituals, and it was believed to bring good fortune.

Role in Religious Practices

• In Christianity, the number three is associated with the Holy Trinity (Father, Son, and Holy Spirit). It is also found in the three wise men who visited Jesus at his birth and the three days he spent in the tomb before his resurrection.
• In Islam, the number three is associated with the three main pillars of faith: belief in Allah, prayer, and fasting. It is also found in the three holiest cities of Islam: Mecca, Medina, and Jerusalem.
• In Hinduism, the number three is associated with the three main gods: Brahma, Vishnu, and Shiva. It is also found in the three main stages of life: childhood, adulthood, and old age.

Interesting Anecdotes and Stories

• In the Bible, the number three is mentioned over 400 times. One famous example is the story of the three wise men who visited Jesus at his birth. The three wise men brought three gifts: gold, frankincense, and myrrh.
• In the popular song “Three Blind Mice,” three blind mice are chased by a farmer’s wife. The song is often sung to children as a nursery rhyme.

What is the divisibility rule for three?

A number is divisible by three if the sum of its digits is divisible by three.

How is divisibility by three used in real-life applications?

Divisibility by three is used in various fields, including computer science (error detection and correction), engineering (load balancing), and finance (check digit verification).

What are some examples of numbers divisible by three?

12, 18, 21, 27, 30, 33, 36, 39, 42, 45

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What the title says :3 (I’m still active) - Dm me if you got an error and need help with it * Raging2Raven * for replit - posts will be made as soon as I solve the practice - help is encouraged, up to you - Replit is used to prevent Reddit from mangling the code - this subreddit is made to give you an “idea” on how to finish the practice

Assignment 4: divisible by three

Sorry for the delayed posting, I like just got dumped last night soooo yeah

Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.​

To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;

3·4ⁿ is divisible by 3 and 51 is divisible by 3

Where we have;

[tex]S_{(n)}[/tex] =  3·4ⁿ + 51

[tex]S_{(n+1)}[/tex] = 3·4ⁿ⁺¹ + 51

[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ

[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ

∴ [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9

Given that we have for S₀ =  3×4⁰ + 51 = 63 = 9×7

∴ S₀ is divisible by 9

Since  [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9, we have;

[tex]S_{(0+1)}[/tex] - [tex]S_{(0)}[/tex] =  [tex]S_{(1)}[/tex] - [tex]S_{(0)}[/tex] is divisible by 9

Therefore [tex]S_{(1)}[/tex] is divisible by 9 and [tex]S_{(n)}[/tex]  is divisible by 9 for all positive integers n

Step-by-step explanation:

Related Questions

Each unit on the coordinate grid represents 1 yard. The rectangular pool and triangular hot tub shown are both in need of covers. How much total material is needed to cover both? square yards

29 square yards

see attachment for the graph

Vertices of rectangular pool are A(3,2),B(7,8),C (4,10), and D (0,4).

AB=[tex]\sqrt{(7-3)^{2}+(8-2)^{2}}= \sqrt{16+36}=\sqrt{52}[/tex] yard=CD

BC= [tex]\sqrt{(7-4)^{2}+(8-10)^{2}}=\sqrt{9+4}=\sqrt{13}[/tex]yard=DA

In order to find the area of rectangular pool =Length × Breadth

                                        =√52 ×√13=13×2=26 sq. yard

Vertices of triangle given are: P(5,2),Q(7,2) and R(7,5).

PQ= 2 units, QR= 3 units

Area of right triangle PQR=1/2 ×PQ×PR

                                           =1/2×2×3= 3 sq. yards

Next is to find total material needed to cover( that includes bot rectangular pool and triangular hot tub)

       = Area of rectangle + Area of right triangle

       =26+3=29 square yards

I just did my homework

Two fair dice are rolled 3 times and the sums of the numbers that come up is recorded. Find the probability of these events. A) the sum 10 on each of the three rolls? B) the sum is 10 exactly twice in three rolls?

A) P(10 on three rolls) = 1/1728 = 0.0005787

B) P(10 in two of three rolls) = 11/1728 = 0.0063657

Each die has 6 possible values, so a pair of dice have a total of 6*6=36 outcomes.

To find a sum of 10, the cases are:

(4,6), (5,5) and (6,4).

So to have a sum of 10 we have 3 cases among the 36 possible, therefore the probability is:

P(10) = 3/36 = 1/12

If we want the sum of 10 in each of the three rolls, the probability is:

P(10 on three rolls) = P(10)^3 = (1/12)^3 = 1/1728 = 0.0005787

If the sum is 10 in two of three rolls, in one roll we need the probability of the sum not being 10:

P(not 10) = 1 - P(10) = 1 - (1/12) = 11/12

So we have:

P(10 in two of three rolls) = P(10)^2 * P(not 10) = (1/12)^2 * (11/12)

P(10 in two of three rolls) = 11/1728 = 0.0063657

ASAP! I do not accept nonsense answers, but BRAINLIEST will be given to the person who gets it correct with full solutions.

The range refers to the possible y-values.  You can assume that values on the right column are the y-values if it is not specifically expressed.  The right column is the output, or y, column.

Since you have a table, you have to state each number.  Put the numbers in numerical order.  This gives you an answer of

{46, 49, 52, 53, 58, 63, 64, 67}

I need help!!! Use the rational zero theorem, which of the following could not be a rational zero of: 6x^5+ax^3=bx+12? 1/2 -3/4 -2

Answer: x = -3/4 can not be a rational zero of the polynomial.

We have the polynomial:

6x^5 + ax^3 -bx -12 = 0.

The theorem says that:

If P(x) is a polynomial with integer coefficients, and p/q is a zero of P(x) then p is a factor of the constant term (in this case the constant term is -12) and q is a factor of the leading coefficient (in this case the leading coefficient is 6.).

The factors of -12  (different than itself) are (independent of the sign).

1, 2, 3, 4 and 6.

So p can be: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6.

The factors of 6 are:

1, 2 and 3, so q can be 1, -1, 2, -2, 3, -3.

Then the option that can not be a zero of the polynomial is

because the number in the denominator must be a factor of the leading coefficient, and 4 is not a factor of six.

help i will give brainliest

[tex]\dfrac{|AC|}{\sin B}=\dfrac{|AB|}{\sin C}\\\\\dfrac{9}{\sin38^o}=\dfrac{11}{\sin C}\\\\\dfrac{\sin38^o}9=\dfrac{\sin C}{11}\\\\\sin C=\frac{11}9\sin38^o =\frac{11}9\cdot0,6157=0,7525(2)\\\\\sin C\approx0,7525\quad\iff\quad |\angle C|\approx48^o48'\\\\|\angle A|=180^o-|\angle B|-|\angle C|\\\\|\angle A|=180^o-38^o-48^o48'\\\\|\angle A|=93^o12'\approx93^o[/tex]

Which is the graph of f(x)=2(3) to the x power?

Use a graphing calc.

PLEASE HELP ASAP WITH MATH

t = tennis balls

g = golf balls

Multiply the first equation by -2

-2(70 = 5t+3g)

-140 = -10t -6g

Multiply the second equation by 5

5(85 = 2t+5g)

425 = 10t + 25g

Add these new equation together to eliminate t

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

Divide by 19

85 = 2t +5(15)

85 = 2t + 75

Let the cost of a can of tennis balls be $x and that of a sleeve of golf balls be $y.

5x + 3y = 70

2x + 5y = 85

(5x + 3y) x 2 = 70 x 2

10x + 6y = 140

(2x + 5y) x 5 = 85 x 5

10x + 25y = 425

10x + 25y -10x - 6y = 425 - 140

2x + 75 = 85

Therefore the cost of a sleeve of golf balls is $15 and that of a can of tennis balls is $5.

Water flows through a pipe at a rate of 10 fluid ounces per day. Express this rate of flow in pints per month.

Answer: 18.75 pints per month

A polynomial is factored using algebra tiles. An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 15 tiles are in the Product spot in 3 columns with 5 rows: 1 is labeled + x squared, 2 are labeled + x, the 4 tiles below + x squared are labeled negative x, and the 8 tiles below the + x tiles are labeled negative. Which polynomial was factored? x2 – 2x – 8 x2 + 2x – 8 x2 – 2x – 4 x2 + 2x – 4

x² - 2x - 8

Algebra tiles are tiles used to represent variables or numbers and are rectangular or square shaped.

1 is labeled + x squared, this gives x²

2 are labeled + x, this gives +x × 2 = +2x

4 tiles below + x squared are labeled negative x, this gives - x × 4 = - 4x

8 tiles below the + x tiles are labeled negative, this gives -1 × 8 = -8

Therefore to get the polynomial that was factored, we add all the terms. This gives :

+x² + (+ 2x) + (-4x) + (-8) = x² + 2x - 4x - 8 = x² - 2x - 8

The answer is A, and if edge is being weird the answer is x^2-2x-8, Have fun dreamers!

Which metric unit would be best to measure the volume of water in a swimming pool?​

your answer is

it would be best to use litres

this is because a litre is 1000 millilitres and a swimming pool is a large amount of water.

hope this helps

pls put brainliest

Enter values to complete the table below.

Answer:  The answers are in the steps

x         y        value of y/x

-3        -3            1

1           1             1

3           3             1

6x + 7y + x-8y = 7x - y Write down three other expressions that are equal to 7x - y​

It's pretty easy! You can manipulate the numbers to match the equation.

For example,

x + 8y + 6x - 9y = 7x - y

5x + 2x - 2y + y = 7x - y

10x + 7y - 3x - 8y = 7x - y

The other equivalent expressions that are equal to 7x - y​ could be; x + 8y + 6x - 9y = 7x - y, 5x + 2x - 2y + y = 7x - y and 10x + 7y - 3x - 8y = 7x - y

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication , and division . The Numbers constants, variables , operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol ; that can also be used to indicate the logical syntax's order of operations and other features.

We have been given the expression as;

6x + 7y + x-8y = 7x - y

When someone asks to solve an equation, then it usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

The other equivalent expressions that are equal to 7x - y​ could be;

To know more about an expression follow;

brainly.com/question/19876186

The solutions to 2x2 + 8x + 4 = 0 are x = -87,32. Choose the simplified form of these solutions. ​

the answer is "C"

i just took the test

A skateboard ramp has a slope of 5/6. What is the measure of the angle the ramp forms with the ground to the nearest degree

We know slope is rise over run. That would mean our right triangle would have a horizontal leg of 6 and a vertical leg of 5. From there we use tan∅ to help solve ∅:

∅ = tan⁻¹(5/6)

∅ = 39.8056

Kevin cuts lawns during the summer months. He charges $10 plus $5 per hour. The algebraic model is C = 5h + 10, where C represents the total cost and h represents the hours worked. Use pencil and paper to create a table of values for hours worked from 1 to 5, incrementing h by 1 in each row.

1 hour   : 15 dollars

2 hours: 20 dollars

3 hours: 25 dollars

4 hours: 30 dollars

5 hours: 35 dollars

Substitute the hour number in for h and solve. for example, if you were trying to find 5 hours, you would produce the equation c = 5(5) + 10. once you solve that you get c = 25 + 10 which is also c = 35.

The first law of thermodynamics states that ΔE= Q− W. Is this also a statement of the principle of conservation of energy? No, the heat that is added to the system is only used to do work. No, the change in internal energy is the energy lost in the system. Yes, the heat added and the change in internal energy of the gas equal the work done by the piston. Yes, the heat that flows into the system is used to change the internal energy of the gas and becomes work done by the piston.

Yes, the heat that flows into the system is used to change the internal energy of the gas and becomes work done by the piston.

I took the K12 test :)

Approximately how many seconds would it take for the Mississippi River( 16,790 cubic meters per second) to fill the volume of the Gulf of Mexico(2,434,000,000,000,000)? Choice A : 1 *10^9 Choice B : 1* 10^10 Choice C : 1 * 10^11

Take the gulf of mexico and divide by the rate to get the number of seconds

2,434,000,000,000,000 / 16790

Change each to scientific notation

2 * 10 ^15/ 1.6 *10^ 4

2 * 10^15 / 2 * 10^4

Dividing the numbers 2/2 =1

Dividing the exponents means subtracting the powers = 10 ^(15-4) = 10 ^1

hi can you help me i can’t move forward if i skip this question.

. Mr. Wayne has a 3-year contract for his cell phone service. He pays $124.65 each month to cover everyone in his family. How much will the cell phone service cost over the 3-year period? Explain your answer​

The cell phone cost is $124.65 per month. With 12 months in a year, we multiply $124.65 x 12 to get the answer $1,507.80. Since one year equals $1,507.80, we multiply this answer by 3 for 3 years to get $4,523.40. Thus three years of service with $124.65 a month would equal $4,523.40.

find the midpoint of the line segment that has endpoints at (10,8) (-3,-10)

Hey there! :)

Use the midpoint formula to solve this problem:

[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Plug in the coordinates given:

[tex](\frac{10-3}{2}, \frac{8-10}{2})[/tex]

[tex](\frac{7}{2}, \frac{-2}{2})[/tex]

Therefore, the coordinates of the mid-point are:

Is [tex]\frac{\pi }{2}[/tex] irrational or rational, include explanation

It would be irrational.

A rational number is any number that can be expressed as a fraction of two integers provided that the denominator is not zero.

π is an irrational number because its approxiamation is [tex]\frac{22}{7}[/tex] is not the exact value of π. Additionally, we know that the quotient of irrational numbers can be rational or irrational. Here is the case where we have [tex]\frac{\pi }{2}[/tex], an irrational number divided by a rational number giving a quotient that is irrational.

Answer: irrational

Apart from multiplying by 0 or dividing by pi, nothing can make pi rational. pi/2 is the same thing as 1/2pi, which is irrational, because it cannot be simplified into a repeating or terminating decimal

cot(45-A)=tan2A+ sec2A​

See picture.

WILL GIVE BRAINLIEST. PLEASE HELP. In order to inscribe a circle in a triangle, the circle's center must be placed at the incenter of the triangle. True or false?

In order to inscribe a circle in a triangle, the circle's center must be placed at the in center of the triangle, is true. the in center also is a point where the bisectors of the angles meet.

Yuri measures the height of the water in an aquarium in one metric unit. He then moves the decimal point three units to the left. Which pair of measurements might he be converting? Use the metric table to help answer the question.

Answer:the answer A( kiloliters to liters)

Millimeter to Meter

Explain how to determine the solutions to a quadratic equation, graphically.

In a nutshell, you have to graph the parabola. Where the parabola intersects the x-axis is the solutions to the quadratic equation.

On Friday, Mica has $22.50 in her bank account. Mica goes to the market to get groceries for the week and ends up spending more than planned. When Mica checks her account, she now has a balance of $-48.15. How much money did Mica spend at the market?

Answer: $70.65

From the question, we are informed that Mica has $22.50 in her bank account and then she goes to the market to get groceries for the week and ends up spending more than planned. She later checks her account and found out that she now has a balance of $-48.15.

To get the amount of money that Mica spent at the market, we subtract her balance from the opening balance she had in her bank account. This will be:

= $22.50 - (-$48.15)

= $22.50 + $48.15

Mics spent $70.65 at the market.

Work out the mean for the data set below: 3, 5, 4, 3, 5, 6 Give your answer as a fraction

To find the mean of a data set, you must add all the given numbers and then divide the numbers by how many numbers there are.

3+5+4+3+5+6=26/6=4.3333...

When we convert the answer from a decimal to a fraction, we get 13/3.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

A pack of cards is numbered 1 to 24. A card is chosen at random. Find the probability that the number on the card is divisible by 2 or 3

It's simple. So the only cards which are divisible by 2 or 3 are: 2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24. The formula of probability is P= m/n. Where m-Number of ways it can happen and n- Total number of outcomes.

Our answer is P= 16/24=2/3=66,66%

1 11 Kenzie monitors her investment on a technology stock. She uses the expression 2013e2+, where t is the time in years, to estimate the future value of the stock. What is the meaning of 2013 in this context? A. beginning year B. invested amount C. future value D. annual growth rate

The term 2013 in this context refers to the amount invested.

Mathematically, in finance, we can express the amount to be recouped on an investment, having a particular rate of return over a couple of years using the general formula;

V = P(1+r)^t

Such as in the case of amount obtained in a compound interest formula

Where P is the present value or principal or amount invested

V is the future value

r is the rate of investment

with t being the time taken

John is standing at the point (-4,-8) and his friend Victor is standing at the point (-4,12). Find the distance between them. A. 20 units B. -20 units C. 28 units D. -28 units

sol ution ,

Let the points be A and B

A ( - 4 , - 8 ) - - - > ( X1, y1 )

B ( - 4 , 1 2 ) - - - - > ( x2 , y2 )

[tex]ab = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \: \: \: = \sqrt{ {( - 4 - ( - 4)}^{2} + 12 - ( - 8) ^{2} } \\ \: \: \: \: = \sqrt{ {( - 4 + 4)}^{2} + {(12 + 8)}^{2} } \\ = \: \: \: \: \sqrt{ {(0)}^{2} + {(20)}^{2} } \\ \: \: \: \: = \sqrt{0 + 400} \\ \: \: \: = \sqrt{400} \\ \: \: = \sqrt{ {(20)}^{2} } \\ \: \: = 20 \: units[/tex]

Hope this helps . .

Good luck on your assignment . . .