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.
Answer:
360 cm cubed
Step-by-step explanation:
Use the volume formula.
V=whl
V=12 x 6 x 5
V=360
Use the formula of the present value of annuity ordinary which is
Pv=pmt [(1-(1+r)^(-n))÷r]
Pv present value 50760
PMT annual Social Secrity benefit ?
R average annual salary0.42
N time 35 years
We need to solve for pmt
PMT=Pv÷[(1-(1+r)^(-n))÷r]
PMT=50,760÷((1−(1+0.42)^(−35))÷(0.42))
=21,319.20
X=4 and x=6
I suppose this is the correct answer.
Answer:
Yes it is.
Step-by-step explanation:
No matter how you rearrange the addition expressions on either side, it will always equate to be the same answer. This is because of the commutative property of addition, which states that a+b=b+a. That is the case in this problem, soooooo yeah.
