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Home » 0.25x + 30 - 0.10x = 45 - Veritas Home Health

0.25x + 30 - 0.10x = 45 - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Factor out $ y $:

📌 y(y^2 - 5y + 6) = 0 \Rightarrow y(y - 2)(y - 3) = 0

📌 So the solutions for $ y $ are $ y = 0, 2, 3 $. Since $ x = y^2 $, the corresponding $ x $-values are:

📌 $ y = 0 \Rightarrow x = 0 $

📌 $ y = 2 \Rightarrow x = 4 $

📌 $ y = 3 \Rightarrow x = 9 $

📌 All roots are non-negative. The sum of the roots is $ 0 + 4 + 9 = 13 $.

📌 Question: An industrial designer is modeling the cross-section of a sustainable packaging shape defined by the region enclosed by the graph of $ |x + y| + |x - y| \leq 8 $. Find the area of this region.

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