Tuesday, May 28, 2019

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.

More Algebra 2 problems.

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.

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