1. Write (x^2) + 3x – 1 in the form ((x + a)^2) + b

Step-by-step explanation:

(x^2) + 3x – 1 = x² + 2×(3/2)x - 1

                      = [(x + 3/2)² - (3/2)²] - 1

                      = (x + 3/2)² - 9/4 - 1

                      =  (x + 3/2)² - (9/4 + 4/4)

                     = (x + 3/2)² - 13/4

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.

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step-by-step explanation: