If you didn’t complete your quiz corrections in class today, here is the format I would like you to use as you complete them tonight:

# Systems of Equations: Story Problem Edition (last night)

These are all considered “classic” story problems. Please create equations and solve 3 of the problems below:

1. During the spring and summer, you do a spring yard cleanup for households and you also paint houses. You earn $8 an hour doing cleanups and $12 an hour painting. Last spring and summer, you worked a total of 400 hours and earned $3800. How many hours did you spend doing yard cleanups? How many hours did you spend painting?

2. A total of $45,000 is invested into two funds paying %5.5 and 6.5% annual interest. The combined annual interest is $2725. How much of the $45,000 is invested in each type of fund?

3. Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3,312.50. How many of each kind of ticket were sold?

4. Two swimming teams are competing in a 400 meter relay. Each leg of the relay is 100 meters. During the last leg of the race, the swimmer in lane 1 has a 1.2 second head start on the swimmer in lane 2 as shown. After how many seconds into the leg will the swimmer in lane 2 catch up to the swimmer in lane 1.

5. In your chemistry lab, you have a bottle of 1% hydrochloric acid solution and a bottle of 5% hydrochloric acid solution. You need 100 milliliters of a 3% hydrochloric acid solution for an experiment. How many milliliters of each solution do you need to mix together?

6. A rectangle has a perimeter of 14 feet, and twice its length l is equal to 1 less than 4 times its width w. Find the length and width of the rectangle

# Systems of Equations and Story Problems

Please pick 3 of the problems below.

- Create equations to represent the situation.
- Explain in words how the equation fits each part of the problem.
- Solve the system of equations.

1. A total of $12,000 is invested in two funds paying 9% and 11% simple interest. If the yearly interest is $1,180, how much of the $12,000 is invested at 9% and how much is invested at 11%?

2. Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3,312.50. How many of each kind of ticket were sold?

3. Larry wants 50 pounds of tea that ha can sell for $5.14 per pound. If he has tea that costs $7.80 per pound and tea that costs $4.30 per pound, how much of each should he use?

4. Kerry’s motorboat takes 3 hours to make a downstream trip with a 3-mph current. The return trip against the same current takes 5 hours. Find the speed of the boat in still water.

5. The Hare knows he can run faster than the Tortoise, so he gave the Tortoise a 2 mile head start. The Hare usually runs about 6 miles per hour while the Tortoise can hold a sustained 3 miles per hour all day long.” Find and explain the meaning of the solution to this linear system.

6. There are 2 times as many quarters as dimes in Eric’s pocket. He has $1.20 in coins totally. How many coins of each type does Eric have?

**Challenge Problem (Optional): ** In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have? (Try solving this problem without guess and check.)

# Test our bandwidth

Put a post here RIGHT NOW!

# Applications of Piecewise Functions 12/3

Today we wrapped up our initial study of transformations, and moved into real world applications of piecewise functions.

Please come to class tomorrow with your ONE parking function complete.

# Piecewise Functions & Transformations

A few of observations from class today:

- y = x – 2 does not create a horizontal line where y is always -2.
- When creating inequalities for piecewise functions, be sure that you don’t have overlapping x-values.
- Always use proper notation for piecewise functions. Start with f(x). Then draw the brace, then an expression. The domain goes last. A comma separates the function and the domain.

Please complete the Problem Set tonight for homework. If you get stuck on problem 4, post a question on the blog, or come to class with a written question tomorrow.

# Transformations and Piecewise Functions (12/1)

Today in class we made a VERY IMPORTANT DOCUMENT summarizing what we’ve learned about transformations of functions.

Please complete the exercises and examples on page 132 and 133 tonight for homework.

# Horizontal Stretch/Shrink 11/24

Today in class we really worked towards formalizing the differences between horizontal (stretch/shrink) and vertical (stretch/shrink). Please be sure to keep those things straight as you complete the PROBLEM SET for homework on Monday.

# Horizontal Transformations 11/21

Today in class we (finally) got to start our study of Horizontal Stretch/Shrink.

Please come to class on Monday with Examples 1 and 2 complete. Be sure to carefully look at which x-values have the same y-values!

# Four More Interesting Transformations 11/20

Today in class we focused on Horizontal Transformations of functions.

Pleases complete the Problem Set tonight for homework.