Quarter 1 Project - Pythagorean Theorem Investigation 1
It is Monday moming and you and your partner have been selected by the local police force to assist on a case
while the police force is short staffed due to the flu. A janitor at the local art museum arrived to work this
morning only to discover the door was unlocked, valuable artifacts were missing, and the curator is nowhere
to be seen and cannot be reached.
This is the infomation you are given:
The curator is not at the museum or at home, and hasn't been seen or heard from since Friday.
The curator walks to and from work every day (see map), stopping to get coffee every moming at the
Coffee House, and stopping for dinner every night at the Cafe.
Every day, the curator has lunch at the Deli.
The curator's keys are also missing.
1.
1.
How many blocks did he walk from his house, to the coffee shop, and
then to the museum?
2.
If the curator walked directly from home to the coffee shop, then to the 2.
museum, and the police want to search the area enclosed by his path,
what would the area of that triangle be? Remember, each block is 500 feet.

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.