Question

a telephone company offers a monthly cellular phone plan for $30.00. it includes 350 free minutes plus $0.20 per minute for additional minutes. the following function gives the monthly cost for a subscriber, where ( x ) is the number of minutes used. simplify the expression in the second line of the piecewise function. then use point - plotting to graph the function.
c(x) = \begin{cases} 30.00 & \text{if } 0 leq x leq 350 \\ 30.00 + 0.20(x - 350) & \text{if } x > 350 end{cases}
fill in the simplified expression below:
c(x) = \begin{cases} 30.00 & \text{if } 0 leq x leq 350 \\ square & \text{if } x > 350 end{cases}
(use integers or decimals for any numbers in the expression. do not factor.)

Explanation:

Step1: Expand the expression

We start with the expression \( 20.00 + 0.20(x - 350) \). Using the distributive property \( a(b - c)=ab - ac \), we get \( 20.00 + 0.20x - 0.20\times350 \).

Step2: Calculate the constant term

Calculate \( 0.20\times350 = 70.00 \). Then the expression becomes \( 20.00 + 0.20x - 70.00 \).

Step3: Combine like terms

Combine the constant terms \( 20.00 - 70.00=-50.00 \). So the simplified expression is \( 0.20x - 50.00 \).

Answer:

\( 0.20x - 50.00 \)