Algebra 2 - Quadratic Equations- What are the length and width of Jasmine's rectangle?

Jasmine drew a rectangle which is 143 square mm. Ethan drew a rectangle inside of Jasmine's which is 35 square mm. Ethan's rectangle has a three mm border between his and Jasmine's rectangle. What are the length and width of Jasmine's rectangle?


A13 mm by 11 mm


B12 mm by 11 mm


C15 mm by 15 mm


D13 mm by 12 mm


E13 mm by 13 mm


F14 mm by 15 mm





Noah is trying to qualify for a race. A driver needs to complete 8 laps of a seven-mile track at an average speed of 105.66 mph to qualify. Noah has already completed the first three laps. His average speed so far is ninety-two mph. What must his average speed be for the rest of the race to qualify?


A Approximately 146 mph


B Approximately 96 mph


C Approximately 116 mph


D Approximately 136 mph


E Approximately 106 mph


F Approximately 126 mph

Algebra 2 - Quadratic Equations- What are the length and width of Jasmine's rectangle?
Let jw and jl be the length and width of Jasmine's rectangle, and ew and el be the length and width of Ethan's rectangle


We know:


jw * jl = 143





Solve for jw


jw = 143 / jl





We also know


ew * el = 35


ew = jw - 6


el = jl - 6





Plug in ew and el


ew * el = 35


(jw - 6) * (jl - 6) = 35


jw jl - 6 jl - 6 jw + 36 = 35


jw jl - 6 jl - 6 jw = 35 - 36


jw jl - 6 jl - 6 jw = -1





Now plug in jw from the top, and solve for jl


(143 / jl) jl - 6 jl - 6 (143 / jl) = -1


143 - 6 jl - (858 / jl) = -1


143 + 1 = 6 jl + (858 / jl)


144 = (6 jl^2 + 858) / jl


144 jl = 6 jl^2 + 858


6 jl^2 + 858 - 144 jl = 0


jl^2 - 24 jl + 143 = 0


jl^2 - 24 jl + 143 = 0


(jl - 13)(jl - 11) = 0





Two answers


jl - 13 = 0


jl = 13


And


jl - 11 = 0


jl = 11





So the dimentions of Jasmine's rectangle is 13 by 11, whci makes A the correct answer








Total distance = 8 * 7 = 56 miles


The time to qualify = 56 / 105.66 = 0.53 hours





Noah had already done 3 * 7 = 21 miles


And it has taken him 21 / 92 = 0.2283 hours





Distance remaining = 56 - 21 = 35 miles


Time remaining = 0.53 - 0.2283 = 0.3017 hours





To go 35 miles in 0.3017 hours, you have to go


35 / 0.3017 = 116 mph





So the correct answer is C





I hope this helped





Kia