Question

MEDAL AND FAN!

Answer 1

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

Answer 2

I think it is either A or C

Answer 3

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.

Answer 4

Oh wow thank you!

Answer 5

yep I think this is the answer, if not you can have your medal back

Answer 6

It was correct! :)

Answer 7

:)