Exam 15: Further Topics in Algebra and Change

Ordinarily, it takes Brother 20 minutes to go from home to school, and it takes Sister 16 minutes to go from home to school. Each child walks at a steady rate. Today, Brother left home at 8:00 AM and got a three-minute head start on Sister, who left at 8:03 AM. A) Draw a graph to show the percent of the distance to school that Sister has covered versus the time. Label the graph S. B) On the coordinate system above, draw a second graph to show the percent of the distance to school that Brother has covered. Label the graph B. C) According to your graphs, will Sister catch up with Brother? If so, how do you know, and when does she catch up? If not, how do you know? D) What is the slope of Brother's graph, and what does that slope mean in this situation?

You like to go to the neighborhood salad smorgasbord for a meal. The smorgasbord has a fixed charge for the salad makings but charges separately for drinks. When you had 2 sodas, you paid $11.45. When you had 4 sodas, you paid $13.95. A) Write an equation that would enable you to tell the cost c (in dollars) for the salad makings and sodas d. B) What does the slope of the equation tell you about this situation? C) What is the cost for the salad alone?

Use the addition/subtraction method to find a common solution to the given equations, if there is one, or state that there is no common solution. $\left\{ \begin{array} { l } x + 3 y = 11 \\3 x = 33 - 9 y\end{array} \right.$

Wile E. was at the top of a cliff when he spotted Road Runner at the bottom of the cliff. Wile E. jumped off the cliff, using an umbrella as a parachute to get a steady speed. After 2 minutes, Wile E. was 960 feet from the bottom of the cliff, and after 5 minutes, he was 480 feet from the bottom. A) What was Wile E.'s speed going down? B) What was the height of the cliff, top to bottom? C) When did Wile E. reach the bottom of the cliff?

A new "over" distance is set at 100 feet. Rabbit takes 5 $\frac { 1 } { 2 }$ seconds to go over and comes back at 40 feet/second. What should Turtle's speed be so that the animals tie? Write enough so that your thinking is clear.

Ordinarily, it takes Brother 20 minutes to go from home to school, and it takes Sister 16 minutes to go from home to school. Today, Brother got a two-minute head start on Sister. A) Draw a graph to show the percent of the distance to school that Sister has covered versus the time that Sister travels. Label the graph S. B) On the coordinate system above, draw a second graph B to show the percent of the distance to school that Brother has covered, using Sister's travel-time scale as the clock. One point, taking into account Brother's head start, is shown. (Be sure to notice that the horizontal axis scale is for Sister's travel time.) C) According to your graphs, will Sister catch up with Brother? If so, how do you know, and when does she catch up? If not, how do you know?

Write an equation for the line that has slope ${}^ {-} \frac { 2 } { 5 }$ and passes through the point (4, $\frac { 7 } { 5 }$ ). Simplify to the $y = m x + b$ form.

What does it mean to say, "the combination of functions is not commutative"?

Write an equation for the line that has slope ${}^ {-}5$ and passes through the point (20, 10). Simplify to the $y = m x + b$ form.

Write an equation for the line that passes through the points (1, 8) and (7, 44). Simplify to the $y = m x + b$ form.

Give an example of a function that does NOT involve numbers exclusively.

What is the HIGHEST power of x that could be involved in the polynomial function rule for these data? Tell how you know. x F(x) 0 0 1 3 2 20 3 87 4 264 5 635

Find a function rule for the following data. x y 5 28 1 4 3 12 4 19 2 7

A) Someone buys a few candy bars at 55¢ each and several others on sale at 35¢ each. Is the average price for the candy bars 45¢? Explain. B) A store sells two sizes of soft drinks: a large for $1.10 and a small for $0.90. Friday, the store sold 236 soft drinks. The manager reasons, "The $1.10 and $0.90 give an average of $1. So, we must have taken in $236 from soft drinks on Friday." Is the manager correct/incorrect? Explain in some detail.

Write an equation for the line that passes through the points (10, 5) and (3, ${}^ {-} 9$ ). Simplify to the $y = m x + b$ form.

Write an equation for the line that passes through the points (4, ${}^ {-} 3$ ) and ( ${}^ {-} 2$ , ${}^ {-} 2$ ). Simplify to the $y = m x + b$ form.

Tell whether each is correct and explain why or why not. A) Fund-raiser: "We got two donations of $5000 and two of $1000 each! That's an average of $3000 per donation!" B) Quality-control trainee: "One shipment had 1% of the items defective, and another shipment had 5% defective. That's an average of 3% defective."

Find a function rule for the following data. x g(x) 8 26 10 32 12 38 14 44 16 50

Write an equation for the line that passes through the points (1, 9) and (4, 0). Simplify to the $y = m x + b$ form.

Solve the following problem with two different approaches. Label them A and B. Write enough to make it clear that your approaches are different. Dylan and Eddie like to race each other. But Dylan is faster than Eddie. Dylan can run 50 yards/second, and Eddie can run only 40 yards/second. So Dylan gives Eddie a head start of 2 seconds. How far will the boys have to run when Dylan catches Eddie?