Answer:
y = 1/2x + 4
Step-by-step explanation:
Lines that are parallel have the same gradient....in which its 1/2
Equation of the line that is parallel to y = 1/2x + 5 and passes through (-4,2)
(y - 2) = 1/2(x + 4)
2(y - 2) = x + 4
; 2y - 4 = x + 4
Equation of the line,
y = 1/2x + 4
Answer:
<h2>The last costumers got 2.25 kilograms of chocolate candies.</h2>
Step-by-step explanation:
The question is
<em>
There is 11.73 kg of chocolate candies in the grocery store. The first customer bought 48 dag of candies. A second customer bought 4/5 of the remaining quantity. The last three customers bought the same amount of candy. How much chocolate did the last customers get?</em>
<em />
Givens
- The total amount of chocolate candies is 11.73 kilograms.
- First costumer bought 48 dag of candies. (1 kg equals 100 dags)
- Second costumer bougth 4/5 of the remaining.
- Another three costumers bought the same amount of candy.
Let's transform 48 dag to kilograms.

Therefore, the first costumer bought 0.48 kilograms of candies.
The remaining amount is: 
Now, we need to multiply the remaining amount of candies with 4/5

Therefore, the second costumer bought 9 kilograms of chocolate candies.
At last, we need to find the new remaining part of candies, which is

Therefore, the last costumers got 2.25 kilograms of chocolate candies.
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.
Answer:
-2x+5<3
-2x<5-3
-2x<2
-2x>2
Divide de both sides by -2
x>-1