Let's consider two prime numbers where each is larger than 2
Say the primes 7 and 11. Adding them gets us 7+11 = 18. This counter example disproves the initial claim since 18 = 9*2 = 6*3 making 18 composite (not prime)
In general, if we let p and q be two primes such that q > p > 2 and q is the next prime after p, then p and q are both odd. If any of them were even then they wouldn't be prime (2 would be a factor)
Adding any two odd numbers together leads to an even number
Proof:
p = 2k+1 where k is some integer
q = 2m+1 where m is some integer
p+q = 2k+1+2m+1 = 2(k+m) + 2 = 2(k+m+1) which is in the form of an even number
That proof above shows us that adding any prime larger than 2 to its next prime up leads to an even number. This further shows us that the claim is false overall. It is only true if you restrict yourself to the primes 2 and 3, which add to 5. Otherwise, the claim is false.
Answer:
12)
11)
10)
9)
8)
7)
6)
5)
4)
3)
2)
1)
Step-by-step explanation:
12)
y - 4 = −(x - 4)
y - 4 = −x + 4
+ 4 + 4
__________
_______________________________________________
11)
y + 2 = 12(x + 2)
y + 2 = 12x + 24
- 2 - 2
____________
_______________________________________________
10)
y - 1 = 5(x - 1)
y - 1 = 5x - 5
+ 1 + 1
_________
_______________________________________________
9)
y - 5 = −2(x + 2)
y - 5 = −2x - 4
+ 5 + 5
___________
_______________________________________________
8)
y - 5 = 2(x + 2)
y - 5 = 2x + 4
+ 5 + 5
__________
_______________________________________________
7)
y + 4 = 12(x - 2)
y + 4 = 12x - 24
- 4 - 4
____________
_______________________________________________
6)
4x - 3y = −6
-4x - 4x
__________
−3y = −4x - 6
___ _____
−3 −3
_______________________________________________
5)
4x - y = 2
-4x - 4x
_______
−y = −4x + 2
_______________________________________________
4)
x - y = 0
______
−y = −x
_______________________________________________
3)
7x - 5y = 35
-7x - 7x
_________
−5y = −7x + 35
___ ______
−5 −5
_______________________________________________
2)
2x - y = 4
-2x - 2x
_______
−y = −2x + 4
_______________________________________________
1)
2x - 3y = 24
-2x - 2x
_________
−3y = −2x + 24
___ _______
−3 −3
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Answer:
Step-by-step explanation:
The second expression 5 (x minus 3) the third 4 x + 3 y minus 15 minus 3 y + x
and there is no more
Answer:
0.07
Step-by-step explanation:
to find the IQR you do Q3-Q1
2.00-1.93