Choose the property of real numbers that justifies the equation. Look at the picture below!

1) 4·(n + 9) = 4·n + 4·9; Distributive Property

2) (6·7)·m = 6·(7·n); Associative Property of Multiplication

3) b · 1 = b; Multiplicative Identity Property

4) a + (-a) = 0; Additive Inverse Property

Step-by-step explanation:

1) The given equation and the properties that justifies the equation are;

4·(n + 9) = 4·n + 4·9

The above equation can be written as follows;

4 × (n + 9) = 4 × n + 4 × 9

Therefore, the common factor, 4 is distributed across the to the two terms inside the parenthesis, which gives the property as distributive property

2) (6·7)·m = 6·(7·n)

The above equation gives the association of the product of the  first two terms on the left multiplied by the third term being equal to the product of the first term and the association of the product of the last two terms on the right of the term on the right hand side of the equation

Therefore, we have associative property of multiplication

3) b · 1 = b

The value of the product of any variable and 1 is the value of the variable

Therefore, we have the multiplicative identity property

4) a + (-a) = 0

The sum of a variable (or number) and the negative (or opposite) of the variable (or number) is 0

Therefore, we have the additive inverse property

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.