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Melody asked: Do I need to commit this to memory?

Probably best to remember it in terms of polar representation of complex numbers:

etc.  

Hi Dragon,

$$As a fraction 22 out of 120 is $\frac{22}{120}$\\
and if you want to change a fraction to a percentage then you have to multiply by 100.\\
$\frac{22}{120}\times 100=18.33333333...\%$\\
Rounded to 1 decimal place this is 18.3\%$$

Does that make more sense now Dragon?

Oh sorry, I thought you needed more explanation - I didn't read what you said properly. 

Just use the compound interest formula

$$$FV=P(1+i)^n$\\
where n=15\\
i=1.06/100=0.0106\\
P=25000$$

You can take over from here.  

Takahiro I think you may have forgotten one minus sign.  Two of your answers are the same. (The last 2)

Also your answers are approximations.  You would be better off to stick to exact answers.  

I gave you thumbs up though.  Thanks

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NOW I am looking at these answers and I can certainly see that they work BUT to find these for this or a similar question what do I need to know or keep in mind?

$$[\pm(1\pm i)]^2=\pm2i\;\rightarrow \;[\pm2i]^2=-4$$

Do I need to commit this to memory?

I suggest you google it.  You would have had your answer long ago. 

120 ml solution contains 60 grams water.

40 ml solution is one-third of 120 ml, so it would contain one-third the mass of water, namely 20 grams.

If 20 grams is 1 mole, then 16 grams is 16/20 of a mole, or 4/5 of a mole (or 0.8 mol).

Select the Equations part (right-hand side of the input line):

You should check the above by raising each of them to the power 4.

To find the y intercept, let x = 0....so we have

(2/3)y = 3/5

So y = (3/5)*(3/2) = 9/10

So the y intercept is (0, 9/10)

To find the x intercept, let y = 0......so we have

(-3/4)x = 3/5

So x  = (3/5)*(-4/3) = (-4/5)

And the x intercept is (-4/5, 0)

Now...just plot both points on a graph and draw your line through them.....

That's it.....!!!

Why don't you provide us with an example and then we will show you. 

Excellent point Chris. 

Very interesting, Aziz !!!

Of course, as one wag on the site pointed out, (x - x) = 0.......so the rest doesn't really matter......!!!

I am impressed but what do you mean by "you did it without colour"?    

Here's a graph of the solution

The graph of y = 5x + x² is in red

The graph of y = 100 is in blue

The solution is both segments of the "red" graph that lie "above" - but not touching - the "blue" graph

In interval notation, the solution set lies in two intervals...(-∞, -12.81)  and  (7.81, ∞)

The height is (x - 3) and the radius is 4 less  = (x - 7)

So (1/3)*(x - 7) =

One third of the radius of the tank....

No prob, ND......"bearing" is a Trig topic.....however, your answer is useful, too. After all, knowing how far you might have to travel to get back to the starting point might be just as important as knowing the bearing to take to get there !!!!

I'll still give you some points for a good try!!

The first table is the correct one......

Ah I see, I as getting caught up of the "bearing" part.

I thought it meant distance to the starting point, but it really meant the angle.

Dr. Jeremiah has an incredible explanation...quite thorough and something I would probably read when I am more refreshed!

Find a common denominator: Easiest one would be 3 X 7 = 21...this means that you have to multiply -2 by 3 and 1 by 7 -->

-2(3) + 1(7) / 21 -->

-6 + 7 / 21 -->

1 / 21 or 0.0476190476190476.

Oh, you have school tomorrow! I know which part of California you are from now....

Let's let the "what"  = x

So we have

x / (1/4) = 9

So

4x = 9  

So

x = 9/4

We can use the inverse tangent to help us, here.

So we have

tan^-1 (4/6.5) ≈ 31.6°

And the complement to this angle is (90 - 31.6) = 58.4°

So the bearing he needs to take to return to his starting spot is just........

N58.4°E

Here's a graph of the situation:

Good Luck!

The coefficient on x is the number of points Jake scored on each test (probably an average).

Thus, Jake had 85x total points and Mike had 15 less.