Question

1. no one equation can represent the piece - wise linear function. instead, the function is described like this: 0 - 8 hours: y = 10x; 8+ hours: y = 80 + 15(x - 8) (the 8+ means \8 or more\). 5) for more than 8 hours worked, the total earnings are y = 80 + 15(x - 8). a person works a long 20 - hour day. how many dollars does the person earn for that long day? o $200 o $260 o $380 6) suppose the company above pays double - time (20 dollars/hour) for above 12 hours. the equations are then: 0 - 8 hours: y = 10x; 8 - 12 hours: y = 80 + 15(x - 8); 12+ hours: y = —— + 20(x - 12) o 80 o 140 o 155

Explanation:

Step1: Identify the correct - pay formula

The formula for earnings when a person works more than 8 hours is \(y = 80+15(x - 8)\). When \(x = 20\) (since the person works a 20 - hour day), we substitute \(x = 20\) into the formula.

Step2: Expand the formula

First, expand \(15(x - 8)=15x-120\). So the formula \(y = 80+15(x - 8)\) becomes \(y = 80+15x-120=15x - 40\).

Step3: Substitute \(x = 20\)

Substitute \(x = 20\) into \(y = 15x - 40\). Then \(y=15\times20 - 40\).

Step4: Calculate the result

\(15\times20=300\), and \(300-40 = 260\).

Answer:

\(260\)