Answer:
Proofs are in the explantion.
Step-by-step explanation:
We are given the following:
1)
for integer
.
1)
for integer
.
a)
Proof:
We want to show
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(a+c)-(b+d)=rn. If we do that we would have shown that
.
kn+mn = (a-b)+(c-d)
(k+m)n = a-b+ c-d
(k+m)n = (a+c)+(-b-d)
(k+m)n = (a+c)-(b+d)
k+m is is just an integer
So we found integer r such that (a+c)-(b+d)=rn.
Therefore,
.
//
b) Proof:
We want to show
.
So we have the two equations:
a-b=kn and c-d=mn and we want to show for some integer r that we have
(ac)-(bd)=tn. If we do that we would have shown that
.
If a-b=kn, then a=b+kn.
If c-d=mn, then c=d+mn.
ac-bd = (b+kn)(d+mn)-bd
= bd+bmn+dkn+kmn^2-bd
= bmn+dkn+kmn^2
= n(bm+dk+kmn)
So the integer t such that (ac)-(bd)=tn is bm+dk+kmn.
Therefore,
.
//
This means 339 calories burned while combining diet with 1 hour of exercise
Step-by-step explanation:
Given the functions as:
f(x)=2x+210
g(x)=2x+125 then
(f+g)(x) = 2x+210 +2x+125 = 4x +335
(f+g)(1) = 4(1)+335
=339
This means 339 calories burned while combining diet with 1 hour of exercise
Learn More
Functions :brainly.com/question/3122826
Keywords : function, calories,exercising, deficit
#LearnwithBrainly
-8 = m/3 + 2
Subtract 2 from both sides
-10 = m/3
Multiply both sides by 3
M = -30
Answer:
it isn't proportional because it doesn't go through the origin.
Step-by-step explanation: