Let 
be the short, medium and long side, respectively. If we translate all the information into formulas, we get the following system:
Using the second equation, we can express the middle side in terms of the small one, and reduce the system to two equations in two unknowns:
And thus
But then again, using the first equation, the third becomes
So, the longest side is 12. Since the small is half the long, we have 
. Finally, the medium is three more of the small, so we have 
Step-by-step explanation:
d(t) = -16t² + 96t + 112
A) The quarter's initial height is at t = 0.
d(0) = -16(0)² + 96(0) + 112
d(0) = 112
The quarter is tossed from a height of 112 feet.
B) The maximum height is at the vertex of the parabola, which is at x = -b/(2a).
t = -(96) / (2 × -16)
t = 3
The quarter reaches its maximum height after 3 seconds.
C) d(3) = -16(3)² + 96(3) + 112
d(3) = 256
The quarter reaches a maximum height of 256 feet.
D) When the quarter lands in the water, d(t) = 0.
0 = -16t² + 96t + 112
0 = t² − 6t − 7
0 = (t + 1) (t − 7)
t = -1 or 7
Since t can't be negative, t = 7. So the quarter lands in the water after 7 seconds.
(1/3)^4 = 1^4/ 3^4 = 1/81
Answer: 1/81
Answer:
A= 28
Step-by-step explanation:
To find the area of a parallelogram, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.
Answer:
2 game, $12
Step-by-step explanation:
Given data
Showplace Lanes charges
$4.50 per game as well as
$3 for shoe rental
Let the number of games be x
let the total charge for x games be y
y= 4.5x+3-----------1
Westgate Bowling charges
$4 per game and $4 for
shoe rental
Let the number of games be x
let the total charge for x games be y
y= 4x+4-----------2
Equate 1 and 2
4.5x+3= 4x+4
collect like terms
4.5x-4x= 4-3
0.5x= 1
divide both sides by 0.5
x= 1/0.5
x= 2 games
put x= 2 in equation 1 or 2
y= 4x+4-----------2
y= 4*2+4
y= 8+4
y= $12
