Podcast
Questions and Answers
What is the slope and the y-intercept of the function describing Ruthie's car repair?
What is the slope and the y-intercept of the function describing Ruthie's car repair?
- The slope of the function is 50, which means that the labor charge is $50 for each hour it takes to repair Ruthie's car. The y-intercept is 75. (correct)
- The slope of the function is 50, which means that the labor takes 50 hours to repair Ruthie's car. The y-intercept is 75.
- The slope of the function is 75, which means that the labor takes 75 hours to repair Ruthie's car. The y-intercept is 50.
- The slope of the function is 75, which means that the labor charge is $75 for each hour it takes to repair Ruthie's car. The y-intercept is 50.
What is f(-3) if f(x) = 11 − 6 (x − 8)?
What is f(-3) if f(x) = 11 − 6 (x − 8)?
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Which statement compares the growth of Greg and Alan's companies?
Which statement compares the growth of Greg and Alan's companies?
- Greg’s company grew at a rate of 5 new employees per year, and Alan’s company grew at a rate of 10 new employees per year.
- Greg’s company grew at a rate of 18 new employees per year, and Alan’s company grew at a rate of 22 new employees per year. (correct)
- Greg’s company grew at a rate of 18% more new employees per year, and Alan’s company grew at a rate of 22% more new employees per year.
- Greg’s company grew at a rate of 5% more new employees per year, and Alan’s company grew at a rate of 10% more new employees per year.
What is the most appropriate domain for the function C(w) representing the cost of a package of beef weighing w pounds?
What is the most appropriate domain for the function C(w) representing the cost of a package of beef weighing w pounds?
Which interval represents John constantly moving closer to home based on his distance from home?
Which interval represents John constantly moving closer to home based on his distance from home?
After how many weeks will Enrique have $196 in his savings account if he starts with $40 and deposits $6 weekly?
After how many weeks will Enrique have $196 in his savings account if he starts with $40 and deposits $6 weekly?
Which graph would match the situation of a car traveling at 26 mph, accelerating to 42 mph in 5 seconds, maintaining speed for 5 seconds, and then slowing to a stop?
Which graph would match the situation of a car traveling at 26 mph, accelerating to 42 mph in 5 seconds, maintaining speed for 5 seconds, and then slowing to a stop?
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Study Notes
Car Repair Charges
- The slope of the function is $50 per hour, indicating that labor charges increase by $50 for each hour of repair.
- The y-intercept is $75, representing a fixed fee, likely for initial diagnostics or parts prior to labor.
Evaluating Function f(x)
- For the function f(x) = 11 − 6(x − 8), calculating f(−3) leads to a specific numerical result.
Company Employee Growth
- Greg's employee equation: E = 18n + 5 shows an increase of 18 employees per year.
- Alan's employee equation: E = 22n + 10 indicates a growth of 22 employees yearly.
- Alan's company shows faster growth compared to Greg's.
Grocery Store Pricing Domain
- The costing function C(w) for beef depends on weight w.
- The most appropriate domain for this function is positive rational numbers, as weight must be greater than zero and can be a fraction.
Child's Distance from Home
- The graph of John's distance d(t) depicts how far he is from home over time.
- The interval when John is moving closer to home is critical for understanding his movement patterns.
Savings Account Growth
- Enrique starts with $40 and adds $6 weekly to his savings.
- To reach $196, calculations reveal the total number of weeks required to achieve this balance.
Graphing Situational Problems
- A scenario described involves a car accelerating, maintaining speed, then decelerating.
- Identifying the correct graph representation requires an understanding of how speed changes over time.
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