superhelp101
  • superhelp101
SAT Question:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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superhelp101
  • superhelp101
1 Attachment
superhelp101
  • superhelp101
I feel like the first and the last one could be the answer
GreenCat
  • GreenCat
root w over 2 is an odd INTEGER

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More answers

GreenCat
  • GreenCat
so that means root w is even
GreenCat
  • GreenCat
so w is the square of an even number
acxbox22
  • acxbox22
|dw:1434403835527:dw|
GreenCat
  • GreenCat
|dw:1434403901094:dw| remember x is odd so w is 4 times the square of an odd number
GreenCat
  • GreenCat
divide the answer chices by 4 and see which is the square of an odd number
acxbox22
  • acxbox22
you can just plug all the answer choices and check
GreenCat
  • GreenCat
anything that is not divisible by 4 is wrong cross out 49, 81, and 225
GreenCat
  • GreenCat
Divide by 4: 144/4=36 196/4=49
superhelp101
  • superhelp101
but 7.5 is also odd
GreenCat
  • GreenCat
7.5 is not an integer.
acxbox22
  • acxbox22
no it isn't odd or even is only defined for numbers
superhelp101
  • superhelp101
ohh so \[\sqrt{w}\] has to be even?
acxbox22
  • acxbox22
yea then only it can be divided by 2
superhelp101
  • superhelp101
ohh cool let me work it out
superhelp101
  • superhelp101
144 and 196 could work
superhelp101
  • superhelp101
no it is 196 right?
freckles
  • freckles
\[\frac{\sqrt{w}}{2}=2k+1 \\ \text{ multiply 2 on both sides } \\ \sqrt{w}=2(2k+1) \\ \text{ \square both sides } w=2^2(2k+1)^2\]
freckles
  • freckles
this says w is divisble by 4 and some other odd number square
freckles
  • freckles
is 49,81,225 divisible by 4?
superhelp101
  • superhelp101
no
freckles
  • freckles
so your choices are narrowed down to either 144 or 196 write the prime factorization both of these
superhelp101
  • superhelp101
|dw:1434404702547:dw|
GreenCat
  • GreenCat
According to what I had earlier shown, yes 196 works as you said.
superhelp101
  • superhelp101
|dw:1434404755390:dw|
freckles
  • freckles
\[144=2^4 \cdot 3^2 \\ 196=2^2 \cdot 7^2 \] and \[w=2^2(2k+1)^2\] which fits the w form?
freckles
  • freckles
notice the 2 has a square on it in the w factorization both satisfy the odd^2 part but only one of them satisfy the 2 raised to the second power part
superhelp101
  • superhelp101
oh okayyy
superhelp101
  • superhelp101
thank you all for the help! :)

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