Sure, let's complete the number machine for the given equation [tex]\( z = 5w - 3 \)[/tex].
To understand this more clearly, let's break down the steps:
1. Identify the input variable: The input for our number machine is [tex]\( w \)[/tex].
2. Apply the multiplication: The first operation that we need to perform on our input [tex]\( w \)[/tex] is to multiply it by 5. For instance, if [tex]\( w = 2 \)[/tex], the result after this step would be [tex]\( 5 \times 2 = 10 \)[/tex].
3. Apply the subtraction: The next step is to subtract 3 from the result we obtained in the previous step. Continuing with our example where the result was 10, subtracting 3 gives us [tex]\( 10 - 3 = 7 \)[/tex].
4. Output the result: The final result after these operations is our output [tex]\( z \)[/tex].
Let’s summarize the number machine process:
- Input: [tex]\( w \)[/tex] (this is our starting number)
- Step 1: Multiply the input by 5
- Step 2: Subtract 3 from the result of Step 1
- Output: The result after performing the above operations, which we call [tex]\( z \)[/tex]
So, mathematically, the number machine works as follows:
1. Start with [tex]\( w \)[/tex]
2. Compute [tex]\( 5 \times w \)[/tex]
3. Subtract 3 from the product (i.e., [tex]\( 5w \)[/tex])
4. The resulting value is [tex]\( z \)[/tex], where [tex]\( z = 5w - 3 \)[/tex]
Therefore, if you give it an input [tex]\( w \)[/tex], it will output [tex]\( z \)[/tex] calculated as per the formula [tex]\( z = 5w - 3 \)[/tex].
