3) A Venn diagram is a common way for teachers and students to organize information. Have you ever seen a three-circle V

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3) A Venn diagram is a common way for teachers and students to
organize information. Have you ever seen a three-circle Venn
diagram?



a) Create a Venn diagram by writing equations for three circles.
Your equations do not have to create a perfect replica of this
image, but your circles must overlap in a similar way. It may help
you to visualize your equations if you graph them! What are the
equations to your circles?
b) What are coordinates of the centers of your circles? Assign each
center a name.
c) What is the distance between each pair of centers? Show how you
arrived at your answer.
d) If you choose two of your circle equations and solve them, how
many solutions will you find?
e) Now consider all three circles together. How many solutions
would you find if you were to solve them all as one system? Explain
how you know your answer is correct.
4) To calculate the volume of a chemical produced in a day
a chemical manufacturing company uses the following formula
below:
V(x)=[C1(x)+C2(x)](H(x))
where x represents the number of units produced. This
means two chemicals are added together to make a new chemical and
the resulting chemical is multiplied by the expression for the
holding container with respect to the number of units produced. The
equations for the two chemicals added together with respect to the
number of unit produced are given below:
C1(x)=x/x+1,C2(x)=2/x−3
The equation for the holding container with respect to the number
of unit produced is given below:
H(x)=x3−9x/x
a. What rational expression C(x) do you get when you
combine the two chemicals?
b. What is the simplified equation of V(x)?
c. What would the volume be if 50, 100, or 1000 units are produced
in a day?
d. The company needs a volume of 3000 c3 How many units
would need to be produced in a day?
5) Jaxon and Isaac live in different directions from the
city center. Jaxon lives 10 blocks east and 5 blocks north. Isaac
lives 8 blocks west and 15 blocks south.

a. The city center is the origin. What would the coordinates be for
Jaxon and Isaac? What quadrant would each of them live in?
b. If Jaxon and Isaac wanted to ride bikes to each other’s house,
how far would it be to travel one way?
c. If they decide to meet in the middle and then ride to Jaxon’s
house, how far would it be? What would the coordinate be for the
middle?
d. If the city blocks were overlaid on a coordinate grid, what
would be the slope of the straight line that would connect Jaxon’s
home to Isaac’s home? Would it be horizontal, vertical, or
neither?