The two containers hold 328 ounces at the they hold same amount of water.
Step-by-step explanation:
The equations below model the ounces of water, y, in each container after x minutes.
[tex]y = 16x + 104[/tex]
[tex]y = -2x^{2} +40x+160[/tex]
At the time after the start when the containers hold the same amount of water, the two equations must be equal.
⇒ [tex]16 x + 104 = -2x^{2} + 40 x + 160[/tex]
The first step is to divide everything by 2 to make it simplified.
⇒ [tex]8 x + 52 = - x^2 +20 x + 80[/tex]
Now put everything on the left .
[tex]x^2 + 8 x - 20 x + 52 - 80 = 0[/tex]
Add the like terms together to further reduce the equation
[tex]x^2 - 12 x - 28 = 0[/tex]
Factorizing the equation to find the roots of the equation.
Here, b = -12 and c = -28
where,
Take x = 14 and substitute in any of the given two equations,
⇒ [tex]y = 16(14) + 104[/tex]
⇒ [tex]y =224+104[/tex]
⇒ 328 ounces
∴ The two containers hold 328 ounces at the they hold same amount of water.
Answer:
Containers A and B hold the same amount of water, 328 ounces. Hence, if you are on the same connexus assignment, your answer should be option B.
Hope this helps! ;D
