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Thank you, AzizHusain.

Hi Aziz,

I know the foil method is widely taught but I am not so keen on it because it cannot be extended to other problems.  eg (x+y+z)(4-x+2y)

I'd prefer to look at it like this

(X+10) (x-1)=x(x-1)+10(x-1) etc

Of course your method is perfectly valid as well.

2 = x - 3

Add 3 to both sides:

5 = x

x = 5.

1.5 + 1.5 = 3.

Suppose we had 1.54 + 1.53. Our front-end estimation would be 1.5 + 1.5 = 3.

2.5 - 1.5 = 1.

Suppose we had 2.52 - 1.53. Our front-end estimation would be 2.5 - 1.5 = 1.

Really, how?

I don't think so Takahiro,

I think Dragon is supposed to ROUND to 2 significant figures - not just truncate!

Foil: First, Outside, Inside, Last

First: x*x = x^2.

Outside: x*-1 = -x.

Inside: 10*x = 10x.

Last: 10*-1 = -10.

Add all the terms: x^2 - x + 10x - 10.

Combine "like" terms: x^2 + 9x - 10.

Thank you, AzizHusain!

8.69 --> 8.6

3.78 --> 3.7

6.32 --> 6.3

8.6 + 3.7 + 6.3 = $18.60 [Front-end estimation].

Exact cost: 8.69+3.78+6.32 = $18.79.

Our estimate is -$0.19 lower.

do it on the site calc - on the home page.

you could enter it like this (this is just one way to enter it, there are others)

(1.9891x10^30)/(1.9008x10^27)

Note:

1) 4 - 3.57 = 0.43

2) 7 - 7.3 = -0.3

3) 5 - 5.14 = -0.14

0.43 - 0.3 - 0.14 = -0.01

We basically estimated and ended up being 0.01 short...the exact answer is 16.01.

Can you help me with the short response?

Thank you, AzizHusain!

3.57 --> ~4.

7.30 --> ~7.

5.14 --> ~5.

4+7+5 = C, ~16 inches of rain.

Mmm interesting

x-7sqrt(x)+10=0

Let y=sqrt(x) then we have

y^2-7y+10=0

(y-2)(y-5)=0

y=2 or 5

$$\\\sqrt x = 2 \;or\; 5\\
x=4 \;or \;25\\\\
check\; x=4\\
4-7*2+10=0 \;true\\
check x=25\\
25-35+10=0 \;true\\\\
So\; x=4\; or\; x=25$$

A = 1/2bh

Multiply both sides by 2:

2A = bh

Divide by b:

2A/b = h.

That if you need 2¢. Is it reliable?

Cab you solve my next post please?

$$\begin{array}{rll}
3(4+3a)&=&21a\\
3(4+3a)/3&=&21/3a\\
4+3a&=&7a\\
4+3a-3a&=&7a-3a\\
4&=&4a\\
a&=&1\\
\end{array}$$

Which bit is confusing Dragon?

Do you mean the fraction button?

look here

I am sort of confused. 

-6(-4p-5)-2

=-6*-4p--6*5-2

=-6*-4p+6*5-2

=24p+30-2

=24p+28

It is already in scientific notation.  It has just one number in front of the point and it is followed by an invisible x10^0

Hi Dragon,

6.49 is $6

8.53 is $9

6+9 is 15 which makes it seem like you MIGHT have enough money.  BUT the fact is you do not have enough money.

this is because on the $9 you have overestimated by 47c and on the $6 you have underestimated by 49c . On balance this is an underestimate of 49-47=2c (I mean the exact answer would be $15.02

The addition is too close.  The ESTIMATED cost  would have to be Less than the amount of money that you have.

----------------------

As an aside I would push everything up rather than rounding if I wanted a quick idea if I had enough money. ie $7+$9 = $16 umm maybe not enough money.

Is this the sort of answer that you wanted Dragon?

This is my best answer.

$${\mathtt{11.833\: \!333\: \!333\: \!333\: \!333\: \!3}}$$