If 4 divides a^2-3b^2, then at least one of the integers a and b is even.

Step-by-step explanation:

The proof can be done by contradiction. Suppose both a, and b weren't even. So that a, and b are both odd. This means they both look like

(for some integers k and l)

So, let's compute what would be in this case:

which notice wouldn't be divisible by 4. This shows then that since is divisible by 4, at least one of the integers a and b is even.

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt