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I think your answer 'any integer ending with zero' is probably indeed the only answer which doesn't have any counterexamples. You don't need to explain the logic of it...I'm so tired of this problem haha...Anyways, thank you for taking the time to help me with this.

JedithiousDec 2, 2013

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Oh dear, yes. Sorry, this nasty little problem is making my brain fuzzy. And one that does actually work is 55 obviously.

JedithiousDec 2, 2013

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Definitely comfortable with algebra. Comfortable with all of Grade 11 and some of 12.

JedithiousDec 2, 2013

+118727

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105?
10 doesn't go into 105

MelodyDec 2, 2013

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105, but I just realized that 5 actually doesn't work because the number 25 contradicts it. (25 is not divisible by 2.)

JedithiousDec 2, 2013

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Also Jedithious could you tell me your age or give me an idea of what level you are at.
I want to pitch my answers at an appropriate level.
Are you comfortable with algebra?
Melody

MelodyDec 2, 2013

+118727

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Can you give me an example of where you think the 5 will work?

MelodyDec 2, 2013

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Seems like your answer 'when the last digit is 5' always works, though.

I definitely understand that any integer with the last digit is 0 will work...But any logic as to the process of which you deduced it would be much appreciated.

JedithiousDec 2, 2013

+118727

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I deleted all the previous stuff.

I believe it will only work when the last digit is 0.
Do you want to see some logic behind it?

MelodyDec 2, 2013

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"Which integers have the following property? If the final digit is deleted, the integer is divisible by the new number?

Any integer with a 0 on the end would work.

MelodyDec 2, 2013

+118727

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Identify the solution(s) of the system of equations, if any -3x-4y=2 8y=-6x-4

These are both lines
If you try to solve them simulltaneously you will get no answer.

If you rearrange them to get the gradients you will find that they both have a gradient of 3/4
This means that they are parallel. They will never bump into each other.

When you solve 2 equations simultaneously you are finding where they are both true at the same time. This is also where they will cross over when they are graphed.
These two curves (which just happen to be lines) will never meet therefore they have no simultaneous solution.

MelodyDec 2, 2013

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Hello Melody, likewise.

Thanks for the answer to that and my palindrome problem; I found it on an interesting site full of all the types of strange math questions which I don't know the precise procedure for solving and therefore am usually frustrated by. I would like to post all such questions I find until my ability to organize the seemingly-only-do-able-through-brute-force-aka-trial-and-error problems into clear methodical procedures is such that I will no longer dread, but rather look forward to those problems my math books usually catch me off guard with. Well, there's a lot of 'em. Better get posting .

Jedithious

JedithiousDec 2, 2013

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GuestDec 2, 2013

+118727

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this was another more succinct answer.

http://gyazo.com/0f99cac55518414ad8b93eb7d5c9b5c4

MelodyDec 2, 2013

+118727

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How about 10:16
there are of course and infinite number of answers

MelodyDec 2, 2013

+118727

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Okay, I have consulted an expert and this is my feedback.

I am going to experiment with a specific example.
g(x) = 1/x
from g(x) x cannot be 0

f(x) = 3/(x+2)
from f(x) x cannot be -2 (THIS IS NOT RELEVANT)

f(g(x))= 3/ (1/x +2)
x can't be 0
1/x can't be -2 therefore x can't be -1/2

So, x is not defined at -1/2 or 0 (but it is defined at -2)

So the restrictions are from g(x) and from f(g(x)) but not from f(x)

MelodyDec 2, 2013

Dec 1, 2013

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How do I step by step solve this?: 5x-2(x+1)=2-(x-5)

B rackets
E exponents
D ivision l division and multiplication you l
M ultiplication l do in the order they appear in l
A ddition l addition and subtraction you l
S ubtraction l do in the order they appear l

GuestDec 1, 2013

+118727

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5x-2(x+1)=2-(x-5)

hint - this is a different question
3-(x-5)
=3+ -1(x-5)
=3+ -1*x + -1*-5
=3 + -x ++5
=3-x+5
=3+5-x
=8-x

-(x+8) = -x-8
-(-2+5) = +2-5
etc

MelodyDec 1, 2013

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sqrt 75 = sqrt (25*3) = sqrt 25 * sqrt3

and you can finish it.

MelodyDec 1, 2013

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Answer by 77E9VW

8(x-7)=-3 =>

8x - 56 = -3 =>

56 - 3 = 8x

56 = 8x

x = 56/8

x=6.625

77E9VW has made a little mistake. Can you find it?

MelodyDec 1, 2013

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how to find a domain of a combined function? example f(g(x)) do we have to consider the domain of both f and g?

I think so

I am going to experiment with a specific example.
g(x) = 1/x
from g(x) x cannot be 0

f(x) = 3/(x+2)
from f(x) x cannot be -2

f(g(x))= 3/ (1/x +2)
x can't be 0
1/x can't be -2 therefore x can't be -1/2
I don't think that x can be -2 either.

But what if i simplify first,
f(g(x))= 3/ (1/x +2)
f(g(x))= 3/ {(1+2x)/x}
f(g(x))= 3 * x/(1+2x)
now x can't be -1/2 (x=-2 or 0 would work here)

anyway, I think x cannot be -2, -1/2 or 0
I will get back to you on this one.

MelodyDec 1, 2013

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113.98 x 1.09 = 124.2382

GuestDec 1, 2013

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help please 3a squared +4ab

=3a*3a +4ab

=9a squares +4ab

MelodyDec 1, 2013

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f the density of a substance is equal to 2.5 g/mL and its mass is equal to 19 g, what is the volume of the substance?

Use the units to help you
ml/g * g cancels down to ml (the g cancel out)

2.5g/ml is equivalent to 1ml/2.5g

therefore
1ml/2.5g * 19g will give you the answer (in ml)

MelodyDec 1, 2013

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8(x-7)=-3 =>

8x - 56 = -3 =>

56 - 3 = 8x

56 = 8x

x = 56/8

x=6.625

GuestDec 1, 2013

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