1. Sketch a swimming pool design that uses all of these elements: one circle, one rectangle, and one triangle. You may want to use graph paper for this activity to aid you in your creation.

Sketch a pool in the shape of an unknown gure containing two rectangles. Make the area of the
unknown gure 32 units squared. After you have nished drawing the unknown gure, list the
dimensions of each side AND the areas of each “individual” rectangle.

3. Construct two dierent unknown gures that have the same area.

4. Suppose you have a tray that is 10 inches squared in area. Choose objects to ll the tray
(e. g. muns, cookies, etc.). Then, establish both a quantity of objects AND the overall density of
the objects on the tray.

5. Construct an unknown gure that will have a density of 1 person per square unit if 10 people are
placed within the bounds of the unknown gure.

The ratio of rock songs to dance songs on jonathan’s mp3 player is 5: 6. the total number of rock and dance songs jonathan has is between 101 120. how many rock songs does he have?

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).