Algebra final exam featuring multiple-choice questions on functions, exponential growth, inequalities, systems of equations, and sequences.

Let’s solve each problem step by step.

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Problem 1: Given the function f(x) = 3x - x², find f(-2)

We plug in x = -2 into the function:

f(-2) = 3*(-2) - (-2)²
= -6 - (4)
= -6 - 4
= -10

✔ So the answer is -10

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Problem 2: Bacteria growth — starts at 180, increases 22% per hour. How many after 4 hours? Use y = ab^x

Here:
- a = initial amount = 180
- b = growth factor = 1 + 0.22 = 1.22
- x = time in hours = 4

So:

y = 180 * (1.22)^4

First calculate 1.22^4:

1.22² = 1.4884
1.22^4 = (1.4884)² ≈ 2.2153

Now multiply:

180 * 2.2153 ≈ 398.75 → rounds to 399

✔ So the answer is 399

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Problem 3: Solve the inequality: -2(x - 3) > 36

Step 1: Distribute the -2:

-2*x + (-2)*(-3) > 36
→ -2x + 6 > 36

Step 2: Subtract 6 from both sides:

-2x > 30

Step 3: Divide by -2 — remember to flip the inequality sign when dividing by negative!

x < -15

✔ So the answer is x < -15

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Problem 4: Solve the system:

3x - y = 17
-x + y = -7

Add the two equations together to eliminate y:

(3x - y) + (-x + y) = 17 + (-7)
→ 2x = 10
→ x = 5

Now plug x = 5 into one of the equations, say the second:

-x + y = -7
→ -5 + y = -7
→ y = -2

✔ So the solution is (5, -2)

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Problem 5: Sequence: 4, 1, -2, -5. What is the 65th term?

This is an arithmetic sequence.

First term a = 4
Common difference d = 1 - 4 = -3

Formula for nth term:
a_n = a + (n - 1)d

So for n = 65:

a_65 = 4 + (65 - 1)(-3)
= 4 + 64*(-3)
= 4 - 192
= -188

✔ So the answer is -188

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Final Answer:
1. B
2. A
3. C
4. B
5. C