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.
The constant of proportionality is k = y/x.....k = 40/200 = 1/5
y = mx + b
slope(m) = 1/5
(200,40)...x = 200 and y = 40
now we sub...we r looking for b, the y int
40 = 1/5(200) + b
40 = 40 + b
40 - 40 = b
0 = b
so ur equation is : y = 1/5x
if pop star earned 800
800 = 1/5x
800 * 5 = x
4000 = x
It would be C) 5y = -4x -15
6000 - 3672 = 2328
Just use a calculator my friend :)
45. These word problems often seem to be two equations in two unknowns, here <em>h</em> for hits and <em>m</em> for misses.
"After 30 tries" translates into
+5 for a hit, -10 for a miss, John lost 90 translates to
We have
Answer: 14
Check: 5(14)-10(16)=-90, good
46. We have to make the odd assumption the grocer sells for his cost, but let's not beat up the question too hard.
Again, two unknowns, <em>b</em> kilograms of Brazil nuts and <em>c</em> kilograms of cashews.
<em>... sold 12 kg of the mixture ...</em>
<em>... cashews $8/kg and Brazil nuts $10/kg and the results is $8.50/kg ...</em>
This one's a bit more involved to translate because we have to recognize the total price is the 8.50 per kg times 12 kg.
The solving is pretty much just like the last one; we eliminate the unknown we're not asked for.
Answer: 9
Check: (9(8)+10(3))/12=102/12 = 8.50 good
