Achemistry student mixes two solutions to study the properties of the resulting mixture. the temperature of the new solution is given by the function t = 24t − 2t2 + 5, where t is the temperature in degrees celsius and t is the time elapsed in seconds after the solutions are mixed. what is the time interval that the temperature of the solution will be at least 69°c? [2, 6] [3, 8] [5, 8] [4, 8]

  [4, 8]

Step-by-step explanation:

You want to find t such that ...

  T ≥ 69

  24t − 2t^2 + 5 ≥ 69

  t^2 -12t +32 ≤ 0 . . . . . subtract the left side, divide by 2

  (t -4)(t -8) ≤ 0 . . . . . . . factor

The factors will have different signs, so their product will be negative, for values of t between 4 and 8. Of course, the equality holds at t=4 and t=8, so the solution interval is ...

  t ∈ [4, 8]

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

c is the correct answer

step-by-step explanation: