Answer:
The prove is as given below
Step-by-step explanation:
Suppose there are only finitely many primes of the form 4k + 3, say {p1, . . . , pk}. Let P denote their product.
Suppose k is even. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
ThenP + 2 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 2 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠2. This is a contradiction.
Suppose k is odd. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
Then P + 4 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 4 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠4. This is a contradiction.
So this indicates that there are infinite prime numbers of the form 4k+3.
Which of the following relations is a function? A.{ (-2, 4), (-1, 3), (5, 2), (1, 4) } B.{ (1, 7), (1, 8), (2, 7), (3, 8) } C.{
siniylev [52]
From the pairs of x,y, if the set has two "x" of the same value, that is, "x" repeats, or an x-repeat, then is NOT a function
so, the group that doesn't have any x-repeats, is a function, now let's check
Solve simultaneously:
<span>15x-8y=52 and
6x+14y=38
</span>
Let's solve this system thru elimination by addition/subtraction:
Let's get rid of the x terms.
To do this, mult. the first eqn. by -6 and the second by 15. (This is not the only way in which we can do this!!) We get
-90x + 48y = -312
90x +210y = 570
--------------------------
Add all 3 columns together. We end up with:
258y = 258, so y = 1. You can find x by subst. 1 for y in either of the given equations.
If you'd like more help, please be specific about what you want.
So, 30 is the perimeter. We are told the table is twice as long as it is wide.
So, we have think of 2 numbers, one being twice as big than the other. So, it is a rectangle The two number represents the length and the width. To find the perimeter we add all the lengths and the widths. Since the pool table is a rectangle we have two lengths and two widths.
So,
the tow numbers be 10 and 5. 5 is half of 10 and, when multiplied by 2 it is 10. So just to make sure the numbers 5 and 10 work out lets do a calculation.
So,
10+5+10+5 = 30feet. This proves that the sides are these two numbers.
X + 2 > 3x - 8
subtract x from both sides
2 > 2x - 8
add 8 to both sides
10 > 2x
divide both sides by 2
5 > x
ANSWER: 5 > x
Hope this helps! :)
