Mr. Scott likes to pose interesting problems to his Mathematics classes. Today,
he started with the expression 6^2020 + 7^2020. He stated that the expression was
not equivalent to 13^2020 and that he was not interested in the actual sum. His
question to his class and to you is, “What are the final two digits of the sum?

Answers

Answer 1

Answer:

The last two digits of 6²⁰²⁰ + 7²⁰²⁰ is 7, 7

Step-by-step explanation:

The given question is to find the value of the sum of two numbers 6²⁰²⁰ + 7²⁰²⁰, where,  6²⁰²⁰ + 7²⁰²⁰ ≠ 13²⁰²⁰

We have;

The last two digits of the powers of 6 are;

6¹ = 6, last two digits = 06

6² = 36, last two digits = 36

6³ = 216, last two digits = 16

6⁴ = 1,296, last two digits = 96

6⁵ = 7,776, last two digits = 76

6⁶ = 46,456, last two digits = 56

6⁷ = 279,936, last two digits = 36

6⁸ = 1,679,616, last two digits = 16

6⁹ = 10,077,696, last two digits = 96

6¹⁰ = 60,466,176, last two digits = 76

6¹¹ = 362,767,056, last two digits = 56

Therefore, the last two digits repeat itself every 5 times

For 6²⁰²⁰, the last two digits will be for the 2020/5 = 404 complete times, which will be 76

The last two digits of the powers of 7 are;

7¹ = 7, last two digits = 07

7² = 49, last two digits = 49

7³ = 343, last two digits = 43

7⁴ = 2,401, last two digits = 01

7⁵ = 16,807, last two digits = 07

7⁶ = 117,649, last two digits = 49

7⁷ = 823,543, last two digits = 43

7⁸ = 5,764,801, last two digits = 01

Therefore, the last two digits repeat itself every 4 times

For 7²⁰²⁰, the last two digits will be for the 2020/4 = 505 complete times, which will be 01

Therefore, the last two digits of 6²⁰²⁰ + 7²⁰²⁰ is 76 + 01 = 77, which is 7, 7


Related Questions

The graph below shows the distance, y, in miles, of a bird from its nest for a certain amount of time, x, in minutes:

Graph titled Distance Vs Time is shown with Time in minutes along the x axis and Distance from Nest in miles along the y axis. The scale on the x axis shows the numbers 0 to 25 at increments of 5, and the scale on the y axis shows the numbers 1 to 8 at increments of 1. A straight line joins the ordered pairs 0, 3 and 5, 4 and 10, 5 and 15, 6 and 20, 7.

Based on the graph, what is the initial value of the graph and what does it represent? (1 point)

a
3 miles per minute; it represents the speed of the bird

b
0.2 mile per minute; it represents the speed of the bird

c
0.2 mile; it represents the original distance of the bird from its nest

d
3 miles; it represents the original distance of the bird from its nest

Answers

Answer:

(d).

Step-by-step explanation:

The y-intercept (0, 3) is initial value of graph ⇒ (d). 3 miles; it represents the original distance of the bird from its nest

Answer:

0.2 mile; it represents the original distance of the bird from its nest

Step-by-step explanation:

What is the slope of the line that passes through the points (5,-11) and (-9,17)?

Answers

Answer:

-2

Step-by-step explanation:

m=y2-y1

    x2-x1

Answer:

-2=slope

Step-by-step explanation:

17--11=28

-9-5= -14

28/-14= -2

A hungry Emperor penguin was swimming 21 feet below sea level. It swam up 9 feet to eat a fish. What is the position of the penguin now relative to sea level?

Answers

Answer:

Step-by-step explanation:

21 feet below is written as -21

9 feet up is written as +9

So we have -21 + 9 = -12 or 12 feet below sea level

Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width. The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height. Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.

Answers

Answer:

Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width.

The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height.

Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.

3x2 + 15x = 252

Is it possible for the width of the tray to be 7.5 centimeters?

no it is too large

Step-by-step explanation:

An equation is formed when two equal expressions. The equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the width of the rectangular prism die be represented by x.

Given that the length of the tray should be five centimeters longer than its width. Therefore, the length and the width of the prism can be written as,

Width = x

Length = x + 5

Further, it is given that the volume of die is 252 cubic centimeters in order for the dice to roll properly. Also, the height of the prism is 3 centimeters. Therefore, the Volume can be written as,

Volume = Length × Width × Height

252 = (x + 5) × x × 3

252 = 3x(x+5)

252 = 3x² + 15x

3x² + 15x - 252 = 0

Hence, the equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.

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2,11,20 find the t15

Answers

Answer:

128

Step-by-step explanation:

There is a common difference between consecutive terms, that is

11 - 2 = 20 - 11 = 9

This indicates the sequence is arithmetic with n th term

[tex]t_{n}[/tex] = t₁ + (n - 1)d

where t₁ is the first term and d the common difference

Here t₁ = 2 and d = 9 , thus

t₁₅ = 2 + (14 × 9) = 2 + 126 = 128

what does 28-8 represent?

Answers

Step-by-step explanation:

subtraction if that wut u askim

Parallel lines e and f are cut by transversal b. Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 10) degrees. At the intersection of lines b and f, the bottom left angle is (3 x minus 15) degrees. What is the value of x? 1 5 25 37

Answers

Answer:

The Answer would be C

Step-by-step explanation:

Answer: It is C. 25

Step-by-step explanation:

on edge 2020

can someone please help me

Answers

Answer:

a. h(t) = 5t + 10

b. 70

c. h(5) = 35 means that in 5 seconds, it will be 35 feet above ground.

Step-by-step explanation:

a. Since the elevator is already 10 feet of the ground, u have to add that in the equation. And since it's 5 feet per second, 5 will be a multiplier so:

h(t) = 5t + 10

b. We have the equation already and in the equation it said that "t" represents the seconds so just replace 1 with 12:

h(12) = 5(12) + 10

h(12) = 60 + 10

h(12) = 70

c. Refer to b that we just did if u will, "t" represents seconds so h(t) becoming h(5) means 5 seconds. So h(5) = 35 means that in 5 seconds, it will be 35 feet above ground.

3. Three of the following statements are true.
Which one is NOT true?
1-12] > 1
10> -4
120 >1-101
61-3

Answers

Answer:

The correct answer is A or option 1

HELP IM ON GRADPOINT I AM ON A QUIZ IF I CAN ALSO GET THE REST OF THE ANSWERS I WILL MARK BRAINLYEST

Answers

Answer:

top is independent, bottom is dependent

Step-by-step explanation:

top has only 1 answer, bottom has infinite answers

Relationship B has a greater rate than Relationship A. This graph represents Relationship A. Which equations could represent Relationship B? Select each correct answer.

Answers

Answer:

The answer is A. Sorry, i dont have enough time to support my answer. I am rushing sdjeuesjcvjs

What is the greatest common factor of 9 and 12? 3 9 36 108

Answers

Answer:

The GCF would be 3

Step-by-step explanation:

You’re welcome :)

Answer:

1. A

Step-by-step explanation:

It will take 20 points to make the playoffs, the Hockey Team coach told the players. "We get 2 points for a win and 1 point for a tie." Let be the number of wins and be the number of ties. Write an equation to describe the values of and that will let them make the playoffs.​

Answers

Answer:

[tex]2x+y\geq 20[/tex]

Step-by-step explanation:

Given that total points required to make the playoffs = 20 points

As there is 2 points for a win,

so points earned for x win = 2x

Similarly, as there is 1 point for a tie.

so points earned for y ties = 1[tex]\times[/tex] y= y

Total points earned for x win and y ties = 2x+y

As the team makes the playoff so the total points of the team must be equal to or greater than 20 points (i.e the minimum points to make the playoff), so

[tex]2x+y\geq 20[/tex]

Hence, the required equation is [tex]2x+y\geq 20[/tex].

The area of the triangle is 22.4cm^2.
Calculate the length, b, of the longest side of the triangle.

Please help, I will mark first correct answer brainliest.

Answers

Answer:

The longest side length b is approximately 13.172 cm

Step-by-step explanation:

The given parameters are;

The area of the triangle = 22.4 cm²

The given angles of the triangle = ∠97°

The given side of the triangle = 3.7 cm

The formula for the area of a triangle, A = 1/2 × a × b × sin(C)

Where;

a, and b are the side legs forming the angle C

Therefore,  we have;

A = 22.4 = 1/2 × 3.7 × a × sin(97°)

a =  22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199

a ≈ 12.199 cm

Therefore, by cosine rule, we have;

b² = a² + c² - 2 × a × c × Cos(B)

Substituting the values, gives;

b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)

b² ≈ 173.507

∴ b ≈ √173.507 ≈ 13.172

b ≈ 13.172 cm

Find the slope of the following graph and Identify the type of
Slope:

Answers

Answer:

undefined

Step-by-step explanation:

Horizontal lines have no slope. The line on the graph is vertical, so we can't really tell what slope it is. But there isn't any run and only rise, therefore the slope is "undefined."

Find the point that is a solution for y=6x+8

Answers

Answer:

(-8/6, 0) is the answer

first is the absicca and the second is the ordinate

Evaluate -9x-2 when x =-4

Answers

Answer:

34

Step-by-step explanation:

So -9x is 36,36-2=34

Answer:

34

Step-by-step explanation:

-9(-4)-2

36-2

34

Which angles are vertical angles?

Answers

I think NOQ POL.................................

In triangle ABC, the measure of angle A is 48° and the measure of angle C is 24°. What type of triangle is triangle ABC?

Answers

Answer:108 degrees

Step-by-step explanation:

Answer:

Scalene triangle

Step-by-step explanation:

24+48= 72

180-72=108

All three angles are different meaning that the triangle must be a scalene triangle.

What is the value of x in the figure below? In this diagram, ABD ~ CAD. А с B 13 D3 A. 16 B. 208 C. 39 D. 48 E. 13/16 F. 139​

Answers

F. Square root of 39

Step-by-step explanation:

Value of [tex]\boldsymbol{x}[/tex] is [tex]\boldsymbol{\sqrt{39}}[/tex] units.

Option F. is correct.

Define similar triangles.

Two triangles are said to be similar if their sides are proportional and their corresponding angles are equal.

[tex]\bigtriangleup ABD \sim \bigtriangleup CAD[/tex]

[tex]\boldsymbol{\frac{AD}{CD}=\frac{BD}{AD} }[/tex]

  [tex]\frac{x}{13}=\frac{3}{x}[/tex]

  [tex]x^2=39[/tex]

   [tex]x=\sqrt{39}[/tex] units.

Value of [tex]\boldsymbol{x}[/tex] is [tex]\boldsymbol{\sqrt{39}}[/tex] units.

Option F. is correct.

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Does this graph represent a function? Why or why not?
10
10
A. No, because it is not a straight line.
B. Yes, because it passes the horizontal line test.
c. Yes because it passes the vertical line test
D. No, because it fails the vertical line test.

Answers

Answer:

No because it does no pass the vertical line test

Step-by-step explanation:

How do you solve n=17

Answers

Answer:

uhm chile anyways

Step-by-step explanation:

i just want points lol

help me plz asap now I just need answer question in pic

Answers

I was just about to ask this question

Step-by-step explanation:

Im on this question rn, i need help to :(

Answer:  just guess :)

Step-by-step explanation:

Evaluate 1/6t+1/12 when t=1/2

Answers

Answer:

1/6

Step-by-step explanation:

You're welcome :)

(Urgent please help!!!) Maria earned $5,250; $4,800; $3,990 and $5,120 from her home business during the last four months. What was her average monthly income during this period?

Answers

5250 + 4800 + 3990 + 5120
19160 / 4 = $4,790 average monthly income

Help!!! Worth 12 points !!!! I’ll mark brainliest!!!❤️

Answers

Answer:

good handwritting the first is 87

Step-by-step explanation:

somebody please help me what is 15 / 3 ×7/20​

Answers

Answer:

1.75

Step-by-step explanation:

By Order of Operations, You read it left to right since Multiplication and Division are of the same importance. You would start with 15/3, which is 5.

Then your equation would be:  5*7/20.

Again, you would just read it left to right, 5*7=35

Then divide by 20, which is 1.75.

For each triangle, check all that apply.
PHOTO ABOVE
⚠️TEST

Answers

Answer:

Step-by-step explanation:

Triangle A - Equilateral triangle because all the angles are equal which means all the sides will be equal.

Triangle B - Isosceles Triangle because 2 sides are equal (we know this because 2 of the angles are equal)

Triangle C - Equilateral triangle because all the sides are equal.

Triangle D - Scalene triangle because all the sides have different lengths.

Seth has game and education apps on his tablet. He noticed that he has 5 game apps for every 2 education apps. Which of the following is another way to write this ratio?

2:3
2:5
3:2
5:2
Question 4(Multiple Choice Worth 3 poi

Answers

Answer:

it would be 5:2

Step-by-step explanation:

none of these are equivalent to the ratio and 2:5 would be 2 to 5

Answer:

5:2

Step-by-step explanation:

Lisa loaned John $5000 at an interest rate of 6%. He repaid her $5750 to cover the principal and interest. How long did he borrow the money?

Answers

Answer:

time in years = 2.5 years

Step-by-step explanation:

time = interest / (principal amount x rate)

time = 750 / 5000 x 0.06

time = 750 / 300

time = 2.5 years

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