Solve if possible, the following quadratic equations by factorising or by using the quadratic formula. Calculation the answer with full explanation.

Write 230,000,000,000 in scientific notation.

b) Evaluate: 30 - 12÷3×2 =

c) Evaluate: -18 + 4(6 ÷ 2)2

d) Evaluate: |4 - 8(3 - 12)| - |5 - 11| =

e) Evaluate: 11 + sqrt(-4 + 6×4÷3)

Let's break down and solve each of the problems step by step.

### 1. **Write 230,000,000,000 in scientific notation:**

Scientific notation expresses numbers as a product of a coefficient and a power of 10. To write 230,000,000,000 in scientific notation:

- Move the decimal point 11 places to the left (as there are 11 digits after the first one).
  
Thus, \( 230,000,000,000 = 2.3 \times 10^{11} \).

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### 2. **Evaluate: \( 30 - \frac{12}{3} \times 2 \)**

We follow the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)):

1. First, solve the division: \( \frac{12}{3} = 4 \)
2. Then, solve the multiplication: \( 4 \times 2 = 8 \)
3. Finally, subtract: \( 30 - 8 = 22 \)

Thus, the value is \( \boxed{22} \).

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### 3. **Evaluate: \( -18 + 4\left( \frac{6}{2} \right)^2 \)**

Following the order of operations:

1. Start with the division inside the parentheses: \( \frac{6}{2} = 3 \)
2. Next, square this result: \( 3^2 = 9 \)
3. Then, multiply by 4: \( 4 \times 9 = 36 \)
4. Finally, add to \(-18\): \( -18 + 36 = 18 \)

Thus, the value is \( \boxed{18} \).

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### 4. **Evaluate: \( |4 - 8(3 - 12)| - |5 - 11| \)**

We will calculate each part separately, handling absolute values and operations step by step:

1. Inside the first absolute value, start with the parentheses: \( 3 - 12 = -9 \)
2. Multiply by 8: \( 8 \times (-9) = -72 \)
3. Then subtract: \( 4 - (-72) = 4 + 72 = 76 \)
4. Now take the absolute value: \( |76| = 76 \)

For the second part:
1. Subtract: \( 5 - 11 = -6 \)
2. Take the absolute value: \( |-6| = 6 \)

Finally, subtract the results:
- \( 76 - 6 = 70 \)

Thus, the value is \( \boxed{70} \).

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### 5. **Evaluate: \( 11 + \sqrt{-4 + \frac{6 \times 4}{3}} \)**

Step-by-step:

1. Start with the multiplication in the denominator: \( 6 \times 4 = 24 \)
2. Now divide: \( \frac{24}{3} = 8 \)
3. Next, subtract: \( -4 + 8 = 4 \)
4. Take the square root: \( \sqrt{4} = 2 \)
5. Finally, add to 11: \( 11 + 2 = 13 \)

Thus, the value is \( \boxed{13} \).

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### Summary of Answers:
1. \( 230,000,000,000 \) in scientific notation is \( \boxed{2.3 \times 10^{11}} \).
2. \( 30 - \frac{12}{3} \times 2 = \boxed{22} \).
3. \( -18 + 4\left( \frac{6}{2} \right)^2 = \boxed{18} \).
4. \( |4 - 8(3 - 12)| - |5 - 11| = \boxed{70} \).
5. \( 11 + \sqrt{-4 + \frac{6 \times 4}{3}} = \boxed{13} \).

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Would you like a deeper explanation of any step, or have additional questions?

Here are 5 related questions for practice:
1. Write 5,400,000 in scientific notation.
2. Simplify: \( 45 - \frac{15}{5} \times 3 \).
3. Evaluate: \( 12 + 5\left(\frac{8}{4}\right)^2 \).
4. Solve: \( |7 - 9(5 - 10)| - |2 - 8| \).
5. Solve: \( 10 + \sqrt{16 - \frac{8 \times 3}{6}} \).

**Tip**: Always follow the order of operations to simplify complex expressions effectively.

Solve if possible, the following quadratic equations by factorising or by using the quadratic formula. Calculate the answer with full explanation. Write 230,000,000,000 in scientific notation. b) Evaluate: 30 - 12÷3×2 = c) Evaluate: -18 + 4(6 ÷ 2)2 d) Evaluate: |4 - 8(3 - 12)| - |5 - 11| = e) Evaluate: 11 + sqrt(-4 + 6×4÷3)

Learn how to write 230,000,000,000 in scientific notation, solve arithmetic expressions using the order of operations, and evaluate expressions with square roots and absolute values. This step-by-step solution is perfect for Grades 6-9 students looking to strengthen their math skills.

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