anonymous
  • anonymous
MEDAL AND FAN!
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Two sets of equatic expressions are shown below in various forms: Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25 Line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25 Which line contains three equivalent expressions? A. Line 1 only B. Line 2 only C. Both Line 1 and Line 2 D. Neither Line 1 nor Line 2
anonymous
  • anonymous
I think it is either A or C
anonymous
  • anonymous
Line 1: x² + 3x + 2, (x + 1)(x + 2), (x + 1.5)² − 0.25 Line 2: x² + 5x + 6, (x + 2)(x + 3), (x + 2.5)² + 6.25 If two expressions are equivalent, then no matter what number we substitute into them, they will always simplify to the same numbers. So let's check by substituting a value, say, x=0 in each: Line 1: 0² + 3(0) + 2, (0 + 1)(0 + 2), (0 + 1.5)² − 0.25 Line 1: 2, 2, 2.25 − 0.25 Line 1: 2, 2, 2 Line 2: 0² + 5(0) + 6, (0 + 2)(0 + 3), (0 + 2.5)² + 6.25 Line 2: 6, 6, 6.25 + 6.25 Line 2: 6, 6, 12.50 Looks like the answer is Line 1 only. We have eliminated Line 2. But we can't be sure about Line 1. That's because it might have just been an accident that we got the same. So let's substitute x=1 in each: Line 1: 1² + 3(1) + 2, (1 + 1)(1 + 2), (1 + 1.5)² − 0.25 Line 1: 1+3+2, 2·3, (2.5)² − 0.25 Line 1: 6, 6, 6.25 - 0.25 Line 1: 6, 6, 6 Yes it's probably Line 1 only. For it's not likely that we'd have run into two accidents. Try x = 2 Line 1: 2² + 3(2) + 2, (2 + 1)(2 + 2), (2 + 1.5)² − 0.25 Line 1: 4+6+2, 3·4, (3.5)² − 0.25 Line 1: 12, 12, 12,25 - 0.25 Line 1: 12, 12, 12 No doubt about it. It's Line 1 only.

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anonymous
  • anonymous
Oh wow thank you!
anonymous
  • anonymous
yep I think this is the answer, if not you can have your medal back
anonymous
  • anonymous
It was correct! :)
anonymous
  • anonymous
:)

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