how much water do they hold?
container a : y=16x+104
containor b : y=-2x^2+40x+160
360 ounces
328 ounces
232 ounces
136 ounces
To determine how much water each container holds, you can substitute the given quantities into the respective equations.
Container A: y = 16x + 104
a) If y = 360 ounces:
360 = 16x + 104
16x = 360 - 104
16x = 256
x = 256/16
x = 16
Therefore, container A holds 360 ounces of water at the value of x = 16.
Container B: y = -2x^2 + 40x + 160
b) If y = 360 ounces:
360 = -2x^2 + 40x + 160
2x^2 - 40x + 520 = 0
Divide the equation by 2:
x^2 - 20x + 260 = 0
The above quadratic equation does not have real solutions since the discriminant (b^2 - 4ac) is negative. Therefore, container B cannot hold 360 ounces of water.
b) If y = 328 ounces:
328 = -2x^2 + 40x + 160
2x^2 - 40x + 168 = 0
Divide the equation by 2:
x^2 - 20x + 84 = 0
(x - 14)(x - 6) = 0
Setting each factor equal to zero:
x - 14 = 0 OR x - 6 = 0
x = 14 OR x = 6
Therefore, container B holds 328 ounces of water at the values of x = 14 or x = 6.
232 ounces and 136 ounces are not valid options based on the given equations.