All Answers 358460 Answers

First, sove the equation for y:

x - y  =  2

   -y  =  -x + 2

     y  =  x - 2

Then, replace 'y' with 'f(x)':

  f(x)  =  x - 2

7/20  =  0.35

In scientific notation, moving the decimal point after the first non-zero digit, the answer is 3.5 x 10^-1.

(It's a negative exponent because you move the decimal point to the right; it's a -1, because you move the decimal point one place to the right.)

I believe that the function should be:  f(x) = 150 + 25x

Graph the function and find the x-value that makes the y-value equal to 500.

The function is continuous because you can put in whatever number of x that you want. However, the situation that it reflects is discrete because fractions such as 3 356/1098725 don't make sense. Your answer makes sense only if you use discrete values (whole numbers) for x; so the situation is discrete.

Could you explain a little how you did that anon please?

Linear equations are equation that, when graphed, produce a straight line.

Their equations can look like:

   x = a  --->  examples:  x = -12  or  x = 0  or  x = 2  (these are vertical lines)

   y = b  --->  examples:  y = 5  or  y = 0  or  y = -2.5 (these are horizontal lines)

   y = mx + b  --->  examples:  y = 2x - 7  or  y = -5x + 9  or  y = -x + ½  (these are diagonal lines)

Yeh, substituting. Before I knew enough to be able to do this sort of thing as close to properly as I do, I used to just play around with substitution as it was the only way I could work out how to do it with common sense alone. Sometimes it could take a while. For years I developed my own common sense coping strategies for maths as I didn't know the correct methods. I very much doubt I came up with anything new but I did come up with them myself, they were never very quick though. You may see that I do some things a little bit unconventionally.

3x²+36=24x    Subtract 24x from both sides;

3x²-24x+36=0    Not sure if I needed to put the "-24x" in this position but it normally sits here as B in the formula so thought it best? Then I factorised;

3(x²-8x+12)=0    Then I divided both sides by 3 which seemed correct for the left hand side but seemed like a bit of a cheat for the right hand side as $${\frac{{\mathtt{0}}}{{\mathtt{3}}}}$$ stays as 0, but it seems to work;

x²-8x+12=0   Then I factorised again;

(x-6)(x-2)=0   So x=6 or x=2

I have expanded the brackets and substituted the numbers and all seems to check ok. This really does help to make sense of factorising, it gives it a purpose.

I'm still never satisfied though to come up with an answer of it could be this or it could be that, I've always been used to there only really being one correct answer in maths, different ways of getting there but only one correct answer.

8x + 28 < 5x + 28

First, get all the variables to one side by subtracting 5x from both sides:

3x + 28 < 28

Now, get rid of the number of the side that has the variable term by subtracting 28 from both sides:

3x < 0                       (Subtracting 28 from 28 gives you 0; it doesn't make the number completely disappear!)

Divide by 3:

x < 0

Well, the answer is simple. All you need to do is type that in the calculator and you should get 1355318534.

1/36

$${\mathtt{6\,000}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.075\: \!3}}}{{\mathtt{365}}}}\right)}^{{\mathtt{3\,650}}} = {\mathtt{12\,739.173\: \!930\: \!774\: \!144}}$$

$${\mathtt{99}}{\mathtt{\,\times\,}}{\mathtt{999\,999}} = {\mathtt{98\,999\,901}}$$

Thank you Heureka and thankyou anons for voicing your concerns.   

If you want to learn effectively you MUST speak up.    

This is always a source of confusion.   

Firstly

$$\\-4^2=-1*4^2=-1*16=-16\\
$Where as $\\
(-4)^2=-4*-4=+16\\\\
$Now why is this so?$\\
consider\\
50-3^2=50-9=41\\
$ See how the minus sign DID NOT belong to the 3$\\
$If it did belong to the 3 then this would be how it had to be done$\\\\
50+(-3)^2=50+9=59 = 50+3^2\\\\$$

Now I do not think that anyone would think    $$50+3^2$$     should equal   $$50-3^2$$

so the minus sign cannot belong to the 3       

(1/3)9^3

3^3

9^2

27

Thanks Geno - I never would have thought to do that !   

No I do not :)

But here is the graph  

http://www.wolframalpha.com/input/?i=%28237%2F22%29%5Ex+%2B+45x%5E2+%3D+%281%2F3%29%5Ex+%2B+400x

Heureka has answered.  Thanks Heureka.

I'm still confused.  Nothing new there I suppose    

THANKS ALAN.

Yep should have used formula 2.   It'd be the same answer you'd just get there quicker.     

It must be my day to eat humble pie.  LOL    

The answer is 276

You are right to criticize and I am sorry I confused you.

YES, YOURS IS THE CORRECT ANSWER,  SORRY     

Hi Tenacious,

That is good :)

So you know how to substitute to check if  2 and -9 are correct ?

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Would you like another?

$$3x^2+36=24x$$

It is the same except you need to factor out the common factor before you factor the rest of the trinomial.

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Also, how do you put the hyperlinks in?   I do not know how to do that.   

Thanks  

9x-15 😃 ....

thanks alot, it's correct aswell!

AB²  =  61 - 60cos(120)

--->  AB²  =  61 - (-30)

--->  AB²  =  61 + 30

--->  AB²  =  91

--->AB  =  √91

This problem is too large for most calclators, so use logs:

x = 2⁴⁰⁰⁰   --->   log(x) = log(2⁴⁰⁰⁰)

With logs, exponents come out as multipliers:   --->   log(x) = 4000·log(2)

Simplifying   --->   log(x)  =   1204.11998

Rewriting in exponential form:  x  =  10^1204.11998  =  10^{1204 + 0.11998}  =  10¹²⁰⁴·10^0.11998

--->   10¹²⁰⁴·l1.318  =  1.318 x 10¹²⁰⁴

Graphing, I got zeros at:  3.7941193, 0, and -7.91666

Does anyone have another way?