Evaluate the following expressions. Please show your solution. 

1. x = (3 * 9 * (3 + (9 * 3 / (3)))) 

2.  z = p * r % q + w / x – y  
where: p = 5, r =100, q = 8, w = 4, x = 3, y = 5

3.  y = a * x * x + b * x + c   
where: a = 52, x = 2, b = 5, c =4

Let's solve each expression step by step:

### 1. \( x = 3 \times 9 \times \left(3 + \left(9 \times 3 \div 3\right)\right) \)

First, we solve the expression inside the innermost parentheses:

\[
9 \times 3 \div 3 = 27 \div 3 = 9
\]

Now the expression becomes:

\[
x = 3 \times 9 \times \left(3 + 9\right)
\]

Next, simplify the parentheses:

\[
3 + 9 = 12
\]

Now substitute that back into the equation:

\[
x = 3 \times 9 \times 12
\]

Finally, calculate:

\[
x = 3 \times 9 = 27
\]

\[
x = 27 \times 12 = 324
\]

So, \( x = 324 \).

### 2. \( z = p \times r \% q + \frac{w}{x} - y \)

Given values: \( p = 5 \), \( r = 100 \), \( q = 8 \), \( w = 4 \), \( x = 3 \), \( y = 5 \)

First, solve \( p \times r \% q \) (modulus operation):

\[
p \times r = 5 \times 100 = 500
\]
\[
500 \% 8 = 500 \div 8 = 62 \text{ remainder } 4 \quad \Rightarrow \quad 500 \% 8 = 4
\]

Now, calculate \( \frac{w}{x} \):

\[
\frac{w}{x} = \frac{4}{3} = 1.3333
\]

Now substitute these values into the equation:

\[
z = 4 + 1.3333 - 5
\]

Finally, calculate:

\[
z = 5.3333 - 5 = 0.3333
\]

So, \( z \approx 0.3333 \).

### 3. \( y = a \times x \times x +

Evaluate the following expressions. Please show your solution.

1. x = (3 * 9 * (3 + (9 * 3 / (3))))

2. z = p * r % q + w / x – y
where: p = 5, r =100, q = 8, w = 4, x = 3, y = 5

3. y = a * x * x + b * x + c
where: a = 52, x = 2, b = 5, c = 4

Learn how to evaluate expressions like x = 3 * 9 * (3 + (9 * 3 / 3)), z = p * r % q + w / x - y, and y = a * x^2 + b * x + c. This step-by-step solution covers key concepts such as arithmetic operations, modulus, and quadratic expressions. Suitable for students in Grades 7-9.

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