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Itzel Brown

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Q: What is 12 t - 6?
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How do you solve the square root of t plus 12 minus t equals 0?

I am going to guess that you mean: Find t when (√(t + 12)) - t = 0. Then, √(t + 12) = t; t + 12 = t²; (squaring both sides) t² - t - 12 = 0; (t - 4)(t + 3) = 0; and t = 4 or -3. We'd best check both results, because we squared both sides at an earlier stage, which introduces an ambiguity and, probably, an extraneous answer: Our original equation is seen to hold, for t = 4: √(4 + 12)) - 4 = √16 - 4 = 4 - 4 = 0. However, it does not hold, for t = -3. √(-3 + 12)) + 3 = √9 + 3 = 3 + 3 = 6 ≠ 0. Thus, the answer is that t = 4.


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How many possible outcomes of tossing a coin and rolling a 6-sided number cube with a tree diagram?

There are 12 possible outcomes: ....................................................... ............................./---- 1 = H + 1 ..... ............................/.......................... .........................../../--- 2 = H + 2 ..... ........................../../......................... ........................./../../-- 3 = H + 3 ..... .............../-- H _/_/_/......................... ............../.........\..\..\-- 4 = H + 4 ...... ............./...........\..\.......................... ............/.............\..\--- 5 = H + 5 ...... .........../...............\........................... ........../.................\---- 6 = H + 6 ...... ........./............................................. .........\............................................. ..........\................./---- 1 = T + 1 ...... ...........\.............../........................... ............\............./../--- 2 = T + 2 ...... .............\.........../../.......................... ..............\........./../../-- 3 = T + 3 ...... ...............\-- T _/_/_/......................... ........................\..\..\-- 4 = T + 4 ...... .........................\..\.......................... ..........................\..\--- 5 = T + 5 ...... ...........................\........................... ............................\---- 6 = T + 6 ...... .......................................................