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63% (01:14) correct 37% (00:55) wrong based on 83 sessions
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Which of the following points is not on the line \(y = 5x + 3\)?
A. \((\frac{1}{2}, \frac{11}{2})\) B. \((\frac{1}{3}, \frac{14}{3})\) C. \((\sqrt{8}, 3 + 10*\sqrt{2})\) D. \((\sqrt{4}, 13)\) E. \((\sqrt{2}, \frac{31}{3})\)
Which of the following points is not on the line \(y = 5x + 3\)?
A. \((\frac{1}{2}, \frac{11}{2})\) B. \((\frac{1}{3}, \frac{14}{3})\) C. \((\sqrt{8}, 3 + 10*\sqrt{2})\) D. \((\sqrt{4}, 13)\) E. \((\sqrt{2}, \frac{31}{3})\)
For \((\sqrt{2}, \frac{31}{3})\), the left hand side (LHS) becomes \(LHS=y=\frac{31}{3}=\text{rational}\) and \(RHS=5x + 3=5\sqrt{2}+3=\text{irrational}\) and since \(\text{rational} \ne \text{irrational}\), then line \(y=5x+3\) does not pass through point \((\sqrt{2}, \frac{31}{3})\).
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi, I have the following doubts please clarify: 1. In D can't square root of 4 be + or -2? . 2. I did not understand your explanation for E. Square root if 2 is approximately 1.41. so LHS is approximately 10.33. RHS = 5 * 1.41 + 3 which is approximately 10.08. Does this negligible difference be attributed to the reason that it does not lie on the line?
Bunuel, chetan2u, thanks for your explanation. I have question on rational vs irrational point here. 31/3 also turns out to be irrational because 31/3 = 10.333333 which continues. So how 31/3 is rational.
Bunuel, chetan2u, thanks for your explanation. I have question on rational vs irrational point here. 31/3 also turns out to be irrational because 31/3 = 10.333333 which continues. So how 31/3 is rational.
Rational numbers are numbers that can be written in a fraction form. So they can be terminating decimal or can ALSO be non-terminating where the sequence repeats endlessly.. here too 31/3 =10.333333.... But in the right side √2 is non terminating and there is no sequence. Thus it is irrational
chetan2u , thanks this helps. Then can I assume any number in fraction form in given question is rational and any number like root 2 , root 3 for which square root is not integer is irrational number ?
chetan2u , thanks this helps. Then can I assume any number in fraction form in given question is rational and any number like root 2 , root 3 for which square root is not integer is irrational number ?
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63% (01:14) correct 
