Algebra II Honors
Review
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Date:____________________ Per:______
Solve the following system of equations. (7 points each)
1. 2x – 3y = 11
2.
2x + 2y = 6
4x + 2y = 10
1. (4, –1)
2. (1, 3)
x + 3y = 10
3. (4, –3)
3. x + 4y = –8
4.
3x + 2y = 6
5. 10x – 9y = 15
6.
5x – 4y = 10
3x – 5y = 6
2x – 4y = 4
4. (2, 0)
3x – 2y = –31
5. (6, 5)
5x + 6y = 23
Use the zero products property to find solutions for x in the following
polynomial equations. (15 points each)
7. x3 + 3x2 – 18x = 0
8.
x3 + x2 = 20x
9. The number of bacteria in a colony is growing exponentially. At 2 pm there
were 100 bacteria in a petri dish. At 4 pm there were 4000.
Part 1:(14 points) Write an exponential function to model the population y, of
bacteria x hours after 2 pm.
y = abx
so at the start (x = 0) we have 100 bacteria or 100 = ab0 or 100 = a
y = 100bx after 2 hours (4pm or x = 2) we have 4000.
So 4000 = 100b2
40 = b2 or b = 6.32
So y = 100(6.32)x
Part B:(14 points) How many bacteria were there at 7 pm.
y = 100(6.32)x
x = 7pm – 2pm = 5 hours
y = 100(6.32)5 = 100(10082.898)= 1,008,289.8
6. (–5, 8)
7. { –6, 0, 3}
8. { –5, 0, 4}
9. Pt1: y = 100(6.332)x
Pt B: ~1,008,290