The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.
step 1: –c = ax2 + bx
which best explains or justifies step 1?
a. subtraction property of equality
b. completing the square
c. factoring out the constant
d. zero property of multiplication

Option a is correct

Subtraction property of equality

Step-by-step explanation:

Given the quadratic equation:

         .....[1]

Subtraction property of equality states that you subtract the same number to both sides of an equation.

Subtract c from both sides in [1] we have;

Simplify:

Therefore, the step 1 justifies the subtraction property of equality

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.