True or False?? File attached! (Please show how you know if its true/false)

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True or False?? File attached! (Please show how you know if its true/false)

Mathematics
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1 Attachment
1st is true
i dont think the first is true amistre it should be 9/x^3

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rsvitale i think youre right about number one
you might be right :) without () around it count it as seperate right..
66. false 67. true by distributive property. (-1/6)*(x^2+3x) 68. false you're only multiplying the top by 5 it should be 5x^2/6 69. false you need to divide the first term by 3y as well 70. false 71.false same reasoning as 70. I can explain these if you want. 72.true x^2-8x+16=(x-4)^2. then take the square root. 73.true ln(e^2)=2ln(e) 74.false e^(l+s)=(e^l)*(e^s)
wow lol ok lets start with 67...why did you multiply by -1/6?
70 and 71: assume sqrt(x+y)=sqrt(x)+sqrt(y) square both sides x+y=x+2sqrt(x)*sqrt(y)+y this is not true unless x,y, or both are 0 so the equality cannot be true
dividing by -6 is the same as multiplying by (-1/6)
dividing by anything is the same as multiplying by its inverse.
ok gotcha
inverse as in 1/something, not the technical definition of inverse
do the other ones make sense?
ok and well im still going down the list trying to see if i get it. are you sure 73 is true? b/isnt 2lne not the same thing as just 2 by itself?
2lne=2. the equality is ln(e^2)=2 ln(e^2)=2ln(e)=2. ln(e)=1
e to what power=e? e^1=e
oh ok for some reason i thought lne^2=1
no ln(e^2) means e to what power is e^2. so it is 2.
ok so if i said e^27 it would be 27 correct?
ln(e^27)=27 correct
ok and i dont get the last one
(e^l)^(s)=e^(l*s) not e^(l+s)
do you want me to explain why?
but i thought when you multiply exponents you add them like (x^5)(x^3)=x^8
yeah that is right. But you are multiplying e^l by itself s times. (e^l)^s=(e^l)*(e^l)*(e^l)*....*(e^l) <---- s times =e^(l+l+l+l....+l <---s times)= e^(l*s)
oohhh ok i get it!! well thanks so much for your help!!
you're welcome :)

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