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
VikaD [51]
3 years ago
5

Discrete Math

Mathematics
1 answer:
andrezito [222]3 years ago
3 0

Answer:

Part c: Contained within the explanation

Part b: gcd(1200,560)=80

Part a: q=-6         r=1

Step-by-step explanation:

I will start with c and work my way up:

Part c:

Proof:

We want to shoe that bL=a+c for some integer L given:

bM=a for some integer M and bK=c for some integer K.

If a=bM and c=bK,

then a+c=bM+bK.

a+c=bM+bK

a+c=b(M+K) by factoring using distributive property

Now we have what we wanted to prove since integers are closed under addition.  M+K is an integer since M and K are integers.

So L=M+K in bL=a+c.

We have shown b|(a+c) given b|a and b|c.

//

Part b:

We are going to use Euclidean's Algorithm.

Start with bigger number and see how much smaller number goes into it:

1200=2(560)+80

560=80(7)

This implies the remainder before the remainder is 0 is the greatest common factor of 1200 and 560. So the greatest common factor of 1200 and 560 is 80.

Part a:

Find q and r such that:

-65=q(11)+r

We want to find q and r such that they satisfy the division algorithm.

r is suppose to be a positive integer less than 11.

So q=-6 gives:

-65=(-6)(11)+r

-65=-66+r

So r=1 since r=-65+66.

So q=-6 while r=1.

You might be interested in
How do you break down 213 in times
gtnhenbr [62]

Answer:2 hundred+1 tens+3 ones

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
If i have 2 apple and get 3 more then lose 2 how many do i have left
nydimaria [60]
You have 2 apples, get 3 more, and then lose 2 of them.

So, you HAVE 2 apples, and if you get 3 more, you can add it to the 2.
2 + 3 = 5

In total at the moment, you have 5 apples. Now, you lose 2 more. We can subtract that from our total number of apples.
5 - 2 = 3

We now know that you are left with 3 apples.
6 0
3 years ago
Read 2 more answers
3х - 3 = -12<br> What is the solution to this equation?
Lapatulllka [165]
3x-3=-12

3x=-9

X=-3


I am in calculus. Algebra is easy
5 0
2 years ago
What would 4(2+x)=18-x equal
matrenka [14]

Answer:

x=2

Step-by-step explanation:

4( 2+x) = 18-x

8 + 4x = 18 - x

4x+x = 18-8

5x= 10

x=2

8 0
3 years ago
X+2y=6 <br> SHOW ALL OF YOUR WORK!
Alika [10]

Answer:

x+2y=6

Subtract 2y from both sides.

x=6−2y

Step-by-step explanation:

x=6-2y

3 0
2 years ago
Read 2 more answers
Other questions:
  • If log50=1.699 then what is log(100)50? with the 100 being the subscript of log
    7·1 answer
  • a rock climber that is 0.74 mile above sea level ascends 0.18 mile and then descends 0.8 mile which represents the location of t
    7·2 answers
  • A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes a) are there in total?
    11·1 answer
  • Help me please:)))<br> (20 points)<br> Will Mark BRAINLIEST !
    6·2 answers
  • Need help on 1 and 2 please
    12·1 answer
  • Which expression entered into a graphing calculator will return the probability
    9·1 answer
  • Line m is perpendicular to lines l and n. Line n is parallel to line p. All four lines are coplanar. Which of the following stat
    6·2 answers
  • –19w + 11 = –17w − 19<br> w=<br> Please help, will mark brainliest to correct answer!
    9·1 answer
  • Joe is 6 feet tall and cast a 3 foot shadow. He is standing next to a building that cast a shadow that is 20 feet long. How tall
    15·2 answers
  • What is the arc length for a central angle of 120° on a circle with radius 5 units?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!