Phineas is the lead research scientist in a lab and responsible for ordering supplies and equipment. The lab is out of petri dis
hes, so Phineas orders 185 of them. The lab uses 12 petri dishes each day.Explain how you would write a two-variable linear equation for this situation.
Since the walkway has length and width, it is rectangular in shape. For a rectangle, the two lengths and two widths are equal. The area is expressed as length, L × Width,W.
The front walkway from the street to Pam's house has an area of 250ft^2. It means that
LW = 250
Its length is two less than four times its width. It means
L = 4W - 2
Substituting L = 4W - 2 into LW = 250, it becomes
W(4W - 2) = 250
4W^2 - 2W- 250 = 0
Using the general formula for quadratic equations,
W = [- b ± √b^2 - 4ac]/2a
a = 4
b = -2
c = - 250
W= [- - 2 ±√-2^2 -4(4 × -250)]/2×4
= (2 ± √4 + 4000)/8
= (2 ±63.277)/8
W= (2 + 63.277)/8 or W = (2 - 63.277)/8
W = 8.16 or W = - 7.91
Since the width cannot be negative, width = 8.16 ft