Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.
After a brief hiatus, the Algebra 2 Problems of the Day are back. Hopefully, daily.

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January 2019, Part II

All Questions in Part I are worth 2 credits. Partial credit can be earned.


27. Erin and Christa were working on cubing binomials for math homework. Erin believed they could save time with a shortcut. She wrote down the rule below for Christa to follow.

(a + b)³ = a³ + b³
Does Erin’s shortcut always work? Justify your result algebraically.

Answer:
Erin's shortcut does not work.
Substituting non-zero numbers will show this. However, that method will not receive full credit because the question stated "algebraically".

(a + b)³
= (a + b)(a + b)(a + b)
= (a + b)(a² + ab + ab + b²)
= (a + b)(a² + 2ab + b²)
= (a³ + 2a²b + ab² + ba²b + 2ab² + b³)
= (a³ + 3a²b + ab² + 3ab² + b³)
=/= a³ + b³

28. The probability that a resident of a housing community opposes spending money for community improvement on plumbing issues is 0.8. The probability that a resident favors spending money on improving walkways given that the resident opposes spending money on plumbing issues is 0.85. Determine the probability that a randomly selected resident opposes spending money on plumbing issues and favors spending money on walkways.

Answer:
Multiply the probabilities: 0.80 * 0.85 = 0.68

Comments and questions welcome.

More Algebra 2 problems.