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### **6) \( h(x) = f(x) - g(x) \)**

Given:
- \( f(x) = 3x^2 + 9x - 12 \)
- \( g(x) = 3x^2 - x - 7 \)

Find \( h(x) \) and determine what it's divisible by.

#### Solution:
\( h(x) = f(x) - g(x) \)

\[
h(x) = (3x^2 + 9x - 12) - (3x^2 - x - 7)
\]

Simplifying:

\[
h(x) = 3x^2 + 9x - 12 - 3x^2 + x + 7
\]

\[
h(x) = (9x + x) + (-12 + 7)
\]

\[
h(x) = 10x - 5
\]

Now, \( h(x) = 10x - 5 \), and we can factor this:

\[
h(x) = 5(2x - 1)
\]

Thus, \( h(x) \) is always divisible by **5**.

#### Answer: \( \boxed{5} \)

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### **7) \( X \oplus Y = (X - Y)^2 \)**

We are asked to find \( 3 \oplus (-2) \).

#### Solution:
By the definition given, \( X \oplus Y = (X - Y)^2 \). Substituting the values:

\[
3 \oplus (-2) = (3 - (-2))^2
\]

\[
3 \oplus (-2) = (3 + 2)^2 = 5^2 = 25
\]

#### Answer: \( \boxed{25} \)

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### **8) Sum of 5 consecutive odd integers greater than 20**

We need to find the least possible outcome for the sum of 5 consecutive odd integers where all integers are greater than 20.

#### Solution:
The smallest odd integer greater than 20 is 21. The 5 consecutive odd integers starting from 21 are:

\[
21, 23, 25, 27, 29
\]

Now, let's sum them:

\[
21 + 23 + 25 + 27 + 29 = 125
\]

Thus, the least possible outcome is **125**.

#### Answer: \( \boxed{125} \)

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### **9) Rock band concert attendance**

- Year 1: Attendance is 25,000.
- Year 2: Attendance is 5% lower than the first year.
- Year 3: Attendance rises by 10% from the second year.

We need to calculate the attendance for the third year.

#### Solution:

1. For Year 2, we calculate 5% lower than 25,000:
\[
\text{Year 2 Attendance} = 25,000 \times (1 - 0.05) = 25,000 \times 0.95 = 23,750
\]

2. For Year 3, the attendance increases by 10% from Year 2:
\[
\text{Year 3 Attendance} = 23,750 \times (1 + 0.10) = 23,750 \times 1.10 = 26,125
\]

Thus, the attendance for the third year is **26,125**.

#### Answer: \( \boxed{26,125} \)

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### **10) Solve \( x^2 + 7x = -10 \)**

We need to solve the quadratic equation \( x^2 + 7x + 10 = 0 \).

#### Solution:
The equation can be factored as:

\[
x^2 + 7x + 10 = (x +

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