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-135+8x=-x+45 add 135 to both sides of the equations, add +x to both sides.

9x=180  divide both sides by 9

x=20

There are 28 ways to chose the first, 27 ways to chose the second, 26 ways for the third, and 25 ways for the last.

$${\mathtt{28}}{\mathtt{\,\times\,}}{\mathtt{27}}{\mathtt{\,\times\,}}{\mathtt{26}}{\mathtt{\,\times\,}}{\mathtt{25}} = {\mathtt{491\,400}}$$

 $${\sqrt{{\frac{{\mathtt{4}}}{{\mathtt{6}}}}}}$$ 

1.  Change the $${\sqrt{}}$$ so that the numerator and dominator are $${\sqrt{}}$$s by themselves:  $${\frac{{\sqrt{{\mathtt{4}}}}}{{\sqrt{{\mathtt{6}}}}}}$$   

2.  Take the $${\sqrt{}}$$s of the numerator and the dominator and simplify them as much as you can: $${\frac{{\mathtt{2}}}{{\sqrt{{\mathtt{6}}}}}}$$

3.  Since $${\sqrt{{\mathtt{6}}}}$$ cannot be simplified any further and you cannot have a $${\sqrt{}}$$ in in the dominator, the $${\sqrt{}}$$ needs to come out of the dominator.  The easiest way to do that is to multiply the numerator and dominator by $${\sqrt{{\mathtt{6}}}}$$:  

$${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6}}}}}{{\mathtt{6}}}}$$

4.  Simplify the the fraction.  

     a.  Break the fraction up:  $${\frac{{\mathtt{2}}}{{\mathtt{6}}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6}}}}$$

      b.  Reduce the fraction $${\frac{{\mathtt{2}}}{{\mathtt{6}}}}$$ and leave $${\sqrt{{\mathtt{6}}}}$$ alone:  $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6}}}}$$

       c.  Multiply the fraction $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$ and $${\sqrt{{\mathtt{6}}}}$$:  $${\frac{{\sqrt{{\mathtt{6}}}}}{{\mathtt{3}}}}$$

$${\sqrt{{\frac{{\mathtt{4}}}{{\mathtt{6}}}}}}$$  in is simplied form is $${\frac{{\sqrt{{\mathtt{6}}}}}{{\mathtt{3}}}}$$

If you take $${\sqrt{{\mathtt{6}}}}$$ and divide it by $${\mathtt{3}}$$, you get a decimal number that goes on forever:  0.816496580927726...

That would be $${\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{4}} = {\mathtt{320}}$$

1.428571^_ 

$${\frac{{\mathtt{130}}}{{\mathtt{91}}}} = {\frac{{\mathtt{10}}}{{\mathtt{7}}}} = {\mathtt{1.428\: \!571\: \!428\: \!571\: \!428\: \!6}}$$

or converting 10/7 unto a proper fraction, 1 and 3/7.

Consider that

$${\frac{{\mathtt{0.9}}}{{\mathtt{10}}}} = {\frac{{\mathtt{9}}}{{\mathtt{100}}}} = {\mathtt{0.09}}$$

and that

$${\frac{{\mathtt{0.99}}}{{\mathtt{100}}}} = {\frac{{\mathtt{99}}}{{\mathtt{10\,000}}}} = {\mathtt{0.009\: \!9}}$$

What other information are you given?

$${\frac{{\mathtt{15}}}{{\mathtt{60}}}} = {\frac{{\mathtt{1}}}{{\mathtt{4}}}} = {\mathtt{0.25}}$$

$${\mathtt{0.25}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{25}}$$%

Any number divided by itself is 1. So when you divide 1/2 cm sq by 1/2 cm sq, you get 1 or 1/1, or 100%.

Did you mean something else?

If you mean:

$$4\frac{19}{15}$$

Recall that the fraction is larger than 1. In mixed number form it is $$1\frac {4}{15}$$

which when added to 4 totals $$5\frac{4}{15}$$

Should be zero.

Divide and multiply before you add and subtract.

50x1=50

60x0=0

Left to right, 0+50-60-0+10=60-60 = 0

So x is greater than or equal to five and less than 8.

0.9999...  does equal 1

If you don't believe the algebraic explanation, try this:

   --  if 0.9999... doesn't equal 1, then there must be some number between 0.9999... and 1, but what could it        be?  There is no number between 0.9999... and 1, so they must be the same number.

Unless you meant $$7\frac {1}{2}$$

then it is 7.5%

which is 0.075 as a decimal.

log₁₀(20) + 2  =  x

--->     log₁₀(20)  =  x - 2

--->     10^{x - 2}  =  20

or:       10^x ÷ 10²  =  20

--->     10^x  =  20 · 10²

--->     10^x  =  2000

cos(x)  =  -1/2     --->     x  =  cos^-1(x)     --->     x  =  -1/2     --->   x  =  120°   or   x  =  240°.

72 ÷ n  =  12     --->   72  =  12·n   --->   n  =  6.

72·n  =  72·6  =  432

There are 360° in a circle, both the circle itself and the central angles. A central angles has the same number of degrees as the arc that it intercepts.

In 1/2 of a circle there are (1/2) x 360°  =   180°.

In 1/3 of a circle there are (1/3) x 360°  =   120°.

In 1/6 of a circle there are (1/6) x 360°  =   60°.

1 mile = 5280 ft....so...

230 / 5280  =

23 / 528  = .04356 mile

$${\frac{{\mathtt{6\,000}}{\mathtt{\,\times\,}}{\mathtt{576}}}{{\mathtt{3\,456}}}} = {\mathtt{1\,000}}$$

It depends upon what you are evaluating......

Sin  = opp / hyp

but.......

Csc = hyp / opp

Approximately 0.8164965809277.