1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
xz_007 [3.2K]
3 years ago
9

Suppose that a and b are integers, a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ) . Find the integer c with 0 ≤ c ≤ 12 such that: c ≡ 9 a

( mod 13 ) c ≡ 11 b ( mod 13 ) c ≡ a + b ( mod 13 ) c ≡ a 2 + b 2 ( mod 13 ) c ≡ a 2 − b 2 ( mod 13 )
Mathematics
1 answer:
g100num [7]3 years ago
3 0

Answer:

A) For c ≡ 9 a ( mod 13 ) ; C is 10

B) For c ≡ 11 b ( mod 13 ) ; C is 8

C) For c ≡ a + b ( mod 13 ); C is 0

D) For c ≡ a² + b² ( mod 13 ); C is 6

E) For c ≡ a² − b² ( mod 13 ) ; C is 0

Step-by-step explanation:

This is a modular arithmetic problem where a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ).

And 0 ≤ c ≤ 12.

A) c ≡ 9 a ( mod 13 )

Substituting the value of a to obtain;

c ≡ 9 x4 ( mod 13 ) = 36 mod 13

To find 36 mod 13 using the Modulo Method, we first divide the Dividend (36) by the Divisor (13).

Second, we multiply the whole part of the Quotient in the previous step by the Divisor (13).

Then finally, we subtract the answer in the second step from the Dividend (36) to get the answer. Here is the math to illustrate how to get 36 mod 13 using Modulo Method:

36 / 13 = 2.769231

2 x 13 = 26

36 - 26 = 10

Thus, the answer to "What is 36 mod 13?" is 10

So C = 10

B) c ≡ 11 b ( mod 13 ) = 11 x 9 ( mod 13 ) = 99 ( mod 13 )

Using the same method as above,

99 ( mod 13 );

99 / 13 = 7.6155

7 x 13 = 91

99 - 91 = 8

So, C = 8

C)c ≡ a + b ( mod 13 ) = 4 + 9 (mod 13) = 13 (mod 13)

Thus;

13 / 13 = 1

1 x 13 = 13

13 - 13 = 0

So, C = 0

D)c ≡ a² + b² ( mod 13 ) = 4² + 9²( mod 13 ) = 16 + 81 ( mod 13 ) = 97 ( mod 13 )

Thus;

97 / 13 = 7.46154

7 x 13 = 91

97 - 91 = 6

So, C = 6

E)c ≡ a² − b² ( mod 13 )= 4² - 9²( mod 13 ) = 16 - 81 ( mod 13 ) = - 65 ( mod 13 )

Thus;

-65 / 13 = - 5

-5 x 13 = - 65

-65 - (-65) = 0

So, C = 0

You might be interested in
Write the equation 2y - 4x = 5 in the form y = mx + b.
notka56 [123]
Yea the answer is Y=2x+ 5/2
4 0
3 years ago
An ice-skating competition lasted three days. Day one had an attendance of 16,390 people. Day two had an attendance of 16,550 pe
lana [24]

Answer:

Day\ 3 = 16237

Day\ 1 = 16390

Day\ 2 = 16550

Step-by-step explanation:

Given

Day\ 1 = 16390

Day\ 2 = 16550

Day\ 3 = 16237

Required

Order from least to greatest

Comparing 16390, 16550 and 16237.

The order of arrangement from least to greatest is:

16327, 16390 and 16550.

So, we have:

Day\ 3 = 16237

Day\ 1 = 16390

Day\ 2 = 16550

6 0
3 years ago
What are the intercepts of the line?
Ann [662]
D is not the answer bc it is a 


8 0
3 years ago
Read 2 more answers
4 tons of bark cost $29,120.00. What is the price per pound?
son4ous [18]
4*2000

29120/8000=$3.64
7 0
3 years ago
Can you help me to create a histogram graph with the following data please?
AlekseyPX

The attached graph represents a histogram that has a range of 55

<h3>How to create the histogram?</h3>

The range is given as:

Range = 55

The range is calculated as:

Range = Maximum - Minimum

So, we have:

Maximum - Minimum = 55

Rewrite as:

Maximum = Minimum + 55

Let the minimum be 10.

So, we have:

Maximum = 10 + 55

Evaluate

Maximum = 65

The following dataset can be used to create the histogram

Score   Frequency

10           2

15            5

45          3

65         1

This is so because it has a range of 55

See attachment for the histogram

Read more about histogram at:

brainly.com/question/14421716

#SPJ1

7 0
1 year ago
Other questions:
  • The sum of the digit of a certain two-digit number is 12. Reversing its digit increases the number by 36.find the number
    11·1 answer
  • The cost of five shirts and three pairs of pants is $229.25. If one pair of pants costs $37.25, what is the cost of one shirt? (
    8·1 answer
  • Find their total volume if x=10 feet, y=12 feet, and z= 7 feet
    7·1 answer
  • 21 is 75%, percent of what number?
    15·2 answers
  • fifty students are trying to raise at least 12,500 for a class trip. they have already raised 1,250. how much should each studen
    6·1 answer
  • URGENT SIMPLE TRIANGLE AND SINES PROBLEM ONLY ASKING FOR A WORD EXPLANATION: PLEASE HELP!!
    8·1 answer
  • What is d=rt for t.
    12·1 answer
  • Math<br> 2+3-6+7X5-34\65
    12·1 answer
  • Can someone help me solve this?!
    12·2 answers
  • Pi/6 is the reference angle for:
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!