hectictar

The farthest apart numbers if you just look at their absolute value:

-20 * a = 200

a = -10

The closest together numbers if you just look at their absolute value.

-40 * b = 160

b = -4

The smallest is -10. The biggest is -4.

\(\frac12 -(\frac38+\frac12-1) \times4 \times 25\)

Parenthesees:

\(\frac12 -(\frac38+\frac{1\times4}{2\times4}-\frac{8}{8}) \times4 \times 25 \\~\\ \frac12 -(\frac38+\frac{4}{8}-\frac{8}{8}) \times4 \times 25 \\~\\ \frac12 -(\frac{3+4-8}{8}) \times4 \times 25 \\~\\ \frac12 -(\frac{-1}{8}) \times4 \times 25 \\~\\ \frac12 + \frac{1}{8} \times4 \times 25\)

Multiplication and Division:

\(\frac12 +\frac{1\times 4 \times 25}{8} \\~\\ \frac12 +\frac{100}{8} \\~\\ \frac12 +\frac{100}{8} \\~\\ \frac 12 + \frac{25}{2}\)

Addition:

\(\frac{25+1}{2} \\~\\ \frac{26}{2} \\~\\ 13\)

I don't know if this is the answer you're looking for, but it works!

9,000,000,000

x * 3 = x + 3

3x = x + 3

Subtract x from both sides.

3x - x = 3

2x = 3

Divide both sides by 2.

x = 3/2

Technically, the two numbers are:

\(\frac{-1+\sqrt{241}}{2} \text{ . . .and. . . } \frac{-1-\sqrt{241}}{2}\)

I found just it by using the quadratic formula on this equation:

x² - x - 60 = 0

There are no integers that add to -1 but multiply to -60.

Does your problem look like this:

x² - x - 60 = 0

Or is there a number in front of the x²  ?

\(\frac{9}{60}=\frac{x}{100}\)

Now just solve for x.

\(\frac{9(100)}{60}=x \\ \frac{900}{60}=x \\15=x\)

So 9 is 15% of 60.

Ok I don't know if you will see this, but I just realized that the answer I gave you was probably wrong because I forgot that some places use " . " as a seperator for thousands, not a decimal. In the rest of this post, I will just put spaces to separate thousands to avoid confusion.

actual area of the lake = 18 000 000 square meters

actual area of the lake = 18 000 000 / 1000² square kilometers

actual area of the lake = 18 000 000 / 1 000 000 square kilometers

actual area of the lake = 18 square kilometers

map area of the lake = 18 / 2² square cm

map area of the lake = 18 / 4 square cm

map area of the lake = 4.5 square cm         <---(That " . " is a decimal)

Hey Guest, I'm really curious how that worked...can you explain how you knew to do that??

I'm not sure I understand exactly what you're asking, but sin, cos, and tan are all different things.

Basically, in this picture:

Where the blue line = 1, the red line = x, the green line = y, the purple angle = a,

and there's a right angle between lines x and y,

sin a = y

cos a = x

tan a = y/x

I think this is basically your question:

\(528=\frac{n!}{3!(n-3)!}\)

And you're trying to solve for n.

I would just try plugging in different values for n until you find the right one.

First I tried 5, that gave me 10.

Next I tried 15, that gave me 455.

Next I tried 16, that gave me 560.

....Well...​ I don't think that n should have a fraction....I don't know, but maybe this helps some anyway.