LOTS OF POINTS!

A juggler throws a ball from an initial height of 4 feet with an initial vertical velocity of 30 feet per second. The height h (in feet) of the ball can be modeled by h 5 216t2 1 vt 1 s where t is the time (in seconds) the ball has been in the air, v is the initial vertical velocity (in feet per second), and s is the initial height.

23. Write an equation that gives the height (in feet) of the ball as a function of the time (in seconds) since it left the juggler’s hand.

24. If the juggler misses the ball, after how many seconds does it hit the ground?

(x + 4y) (3x + 2z)

Step-by-step explanation:

First, write your problem as a mathematical expression:

3x^2 + 12xy + 2xz + 8yz

Factor out the greatest common factor from each group:

(3x^2 + 12xy) + 2xz + 8yz

3x (x + 4y) + 2z (x + 4y)

Factor the polynomial by factoring out the greatest common factor (GCF), x + 47

(x + 4y) (3x + 2z)

Step-by-step explanation:

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.