IDNLearn.com is designed to help you find the answers you need quickly and easily. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
Sagot :
To determine which piecewise function correctly represents the charges based on Tracy's cell phone plan, we need to carefully analyze each option given the details provided:
1. Understand the plan:
- Tracy pays a flat rate of \[tex]$29 for the first 250 minutes. - For any additional minutes beyond 250, Tracy is charged \$[/tex]0.35 per minute.
2. Analyze each option:
Option A:
[tex]\[ f(x) = \begin{cases} 29, & x > 250 \\ 29 + 0.35x, & x \leq 250 \end{cases} \][/tex]
- For [tex]\(x > 250\)[/tex], it states the charge remains \[tex]$29, which is incorrect because there should be an additional charge for the extra minutes. - For \(x \leq 250\), it states the charge is \(29 + 0.35x\), which means it incorrectly adds \$[/tex]0.35 per minute for all minutes, even the first 250, which are free.
Option B:
[tex]\[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 0.35(x-250), & x > 250 \end{cases} \][/tex]
- For [tex]\(x \leq 250\)[/tex], it correctly states the charge is a flat \[tex]$29. - For \(x > 250\), it correctly computes the charge as the flat \$[/tex]29 plus \[tex]$0.35 for each additional minute over 250. Option C: \[ f(x) = \begin{cases} 29, & x \leq 250 \\ 35x, & x > 250 \end{cases} \] - For \(x \leq 250\), it correctly states the charge is \$[/tex]29.
- For [tex]\(x > 250\)[/tex], it incorrectly states the charge is \[tex]$35 per minute for all minutes, which doesn't make sense according to the plan. Option D: \[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 35x, & x > 250 \end{cases} \] - For \(x \leq 250\), it correctly states the charge is \$[/tex]29.
- For [tex]\(x > 250\)[/tex], it incorrectly states the charge is \[tex]$29 plus \$[/tex]35 per minute for all minutes, which is an erroneous interpretation of the plan.
After evaluating each option:
- Option A is incorrect because it miscalculates the charges for both [tex]\(x \leq 250\)[/tex] and [tex]\(x > 250\)[/tex].
- Option C is incorrect because it applies an erroneous \[tex]$35 charge for all minutes when \(x > 250\). - Option D is incorrect because it adds an excessive \$[/tex]35 per minute charge on top of the flat \$29.
The correct representation is found in Option B, which accurately models the charges:
[tex]\[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 0.35(x-250), & x > 250 \end{cases} \][/tex]
Thus, Option B is the correct piecewise function representing Tracy's cell phone plan charges.
1. Understand the plan:
- Tracy pays a flat rate of \[tex]$29 for the first 250 minutes. - For any additional minutes beyond 250, Tracy is charged \$[/tex]0.35 per minute.
2. Analyze each option:
Option A:
[tex]\[ f(x) = \begin{cases} 29, & x > 250 \\ 29 + 0.35x, & x \leq 250 \end{cases} \][/tex]
- For [tex]\(x > 250\)[/tex], it states the charge remains \[tex]$29, which is incorrect because there should be an additional charge for the extra minutes. - For \(x \leq 250\), it states the charge is \(29 + 0.35x\), which means it incorrectly adds \$[/tex]0.35 per minute for all minutes, even the first 250, which are free.
Option B:
[tex]\[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 0.35(x-250), & x > 250 \end{cases} \][/tex]
- For [tex]\(x \leq 250\)[/tex], it correctly states the charge is a flat \[tex]$29. - For \(x > 250\), it correctly computes the charge as the flat \$[/tex]29 plus \[tex]$0.35 for each additional minute over 250. Option C: \[ f(x) = \begin{cases} 29, & x \leq 250 \\ 35x, & x > 250 \end{cases} \] - For \(x \leq 250\), it correctly states the charge is \$[/tex]29.
- For [tex]\(x > 250\)[/tex], it incorrectly states the charge is \[tex]$35 per minute for all minutes, which doesn't make sense according to the plan. Option D: \[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 35x, & x > 250 \end{cases} \] - For \(x \leq 250\), it correctly states the charge is \$[/tex]29.
- For [tex]\(x > 250\)[/tex], it incorrectly states the charge is \[tex]$29 plus \$[/tex]35 per minute for all minutes, which is an erroneous interpretation of the plan.
After evaluating each option:
- Option A is incorrect because it miscalculates the charges for both [tex]\(x \leq 250\)[/tex] and [tex]\(x > 250\)[/tex].
- Option C is incorrect because it applies an erroneous \[tex]$35 charge for all minutes when \(x > 250\). - Option D is incorrect because it adds an excessive \$[/tex]35 per minute charge on top of the flat \$29.
The correct representation is found in Option B, which accurately models the charges:
[tex]\[ f(x) = \begin{cases} 29, & x \leq 250 \\ 29 + 0.35(x-250), & x > 250 \end{cases} \][/tex]
Thus, Option B is the correct piecewise function representing Tracy's cell phone plan charges.
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.
