Choose three non-collinear points on the coordinate plane, making sure none of your points is the origin. on a sheet of paper, graph the three points and draw line segments to connect the points and make a triangle. label the vertices of the triangle a, b, and c. now describe the new coordinates of points a, b, and c after the following transformations:
translation of point a around the origin
90° rotation around point b
reflection of the triangle across the x-axis
the three points are a(3,3), b(7,7), and c(3,5)

if you're trying to figure out how much each ounce cost it would be 0.20

cents each ounce

n=1.75+1.75

step-by-step explanation:

3.5/2=1.75

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.