Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic progression is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given 
= 12 and 
= 22, then
a₁ + 5d = 12 → (1)
a₁ + 7d = 22 → (2)
Subtract (1) from (2) term by term to eliminate a₁
2d = 10 ( divide both sides by 2 )
d = 5
Substitute d = 5 into (1) to find a₁
a₁ + 5(5) = 12
a₁ + 25 = 12 ( subtract 25 from both sides )
a₁ = - 13
Thus
= - 13 + 5 = - 8
= - 13 + 5(n - 1) = - 13 + 5n - 5 = 5n - 18 ← n th term
Answer:
<h2>
i) Angle AOC is 95° </h2>
Reason:- Angle AOC is equal to Angle DOB since they are Vertically Opposite Angles.
<h2>
ii) Angle BOC is 85°</h2>
Reason:- Angle AOC + Angle BOC - 180° (they lie in a straight line so they are a linear pair. Sum of the angles will be 180°)
Angle AOC is 95°, So:-
95° + Angle BOC = 180°
Angle BOC= 180° - 95°
<h3><u>
Angle BOC = 85°</u></h3>
<u></u>
<h2>
iii) Angle DOE is 17°</h2>
Reason:- Angle AOE+ Angle DOE+ Angle DOB = 180° (they lie in a straight line so they're a linear pair. Sum of the angles will be 180°)
So,
68° + Angle DOE+ 95° = 180°
163° + Angle DOE = 180°
Angle DOE= 180° - 163°
<h3><u>
Angle DOE is 17°</u></h3>
23.4375 or 24.0 is the bacteria count after 6 hours.
