Problem of the Week Day 2: Week of 7/15/13 - 7/19/13

Today is day two of July’s problem of the week! For the medium and hard problems, today is when you will start to use variables. For the easy problem, plug in the variables from yesterday for today.

Easy:

Using the answers from yesterday, solve the following problems for f, g, and h. Remember to use the order of operations.

f = 2(a) + a ÷ 10 - 2

g = m² + (m - 2)(m - 7)

h = p² ÷ 18 - (p ÷ 30)³

f = ____

g = ____

h = ____

Medium:

The graphs of the four lines from yesterday should form a quadrilateral on your graph paper. Ignore the rest of the lines, and just analyze each segment forming the quadrilateral.

First, find the length of the each of the four segments, and use their names (ex: f₁) for the variables equal to them. So, f₁ = the length of the segment that was originally the graph of f₁.

f₁ = ____

f₂ = ____

f₃ = ____

f₄ = ____

Then, find the perimeter of this quadrilateral. Call this perimeter f.

f = ____

Hard:

First, plot points P and Q on the graph’s x-intercepts and point R on the graph’s positive y-intercept. Then, find all six measurements within triangle PQR. Use d to denote the measure of angle P, f to denote the measure of angle Q, g to denote the measure of angle R, s to denote the measure of segment PQ, t to denote the measure of segment PR, and v to denote the measure of segment QR. Round all angle measures to the nearest degree.

d = ____

f = ____

g = ____

s = ____

t = ____

v = ____