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$$\left(\frac{1+5}{2},\frac{-2+9}{2}\right)\\\\
=\left(\frac{6}{2},\frac{7}{2}\right)\\\\
=(3,3.5)$$

thanks for the quick fix.

$$3x(2x^3-5x^2+3x+1)$$

$$3x \times 2x^3 - 3x \times 5x^2 + 3x \times 3x + 3x \times 1$$

$$3 \times 2 \times x \times x^3 - 3 \times 5 \times x \times x^2 + 3 \times 3 \times x \times x + 3 \times 1 \times x$$

$$3 \times 2 \times x^1 \times x^3 - 3 \times 5 \times x^1 \times x^2 + 3 \times 3 \times x^1 \times x^1 + 3 \times 1 \times x^1$$

$$6 \times x^{3+1} - 15 \times x^{1+2} + 9 \times x^{1+1} + 3 \times x^1$$

$$6x^4-15x^3+9x^2+3x$$

Reinout 

thank you Alan 

There is nothing about this question that makes sense.

I assume that you mean $$cos^{-1}1.6875$$      There certainly should not be a multiply sign in there.

However is still does not make sense because cos ratios must be between -1 and +1 inclusive.

1.6875 is outsided this restricted region!

EDIT: Sorry, no. You need switch it around (basically tan28 = 360/x)

In the figure below start at A and follow the edges in alphabetical order.  Every edge is visited once and you finish where you started.  Note that there is an even number of edges at every node.

To figure out the number of moles, we just need to divide the amount of grams by the molar mass of gold which is 196.97.

2.7*10^-10 g Au / 196.97 g/mol = 1.37076712*10^-12 mol Au

Then we look at the significant figures. Having started with two, the answer must have two figures. Make sure to round the last digit.

1.4*10^-12 mol Au

Okay, so first, let's turn the grams into moles.

1.3 g C / 12.011 g/mol = 0.1082341187 mol C

Next, we need to multiply it by Avogadro's Number for the number of atoms.

0.1082341187 mol C * 6.022*10^23 mol^-1 = 6.51785863*10^22 atoms C

Now we take significant figures into consideration. We started with two, so we need to end it with two.

6.5*10^22 atoms C

-w² is -(w²) not (-w)² because exponentiation (raising to a power) normally takes priority over the unary minus.

This would mean -w²(w - 15) = w²(-w + 15) = -w³ + 15w

To ensure there is no confusion you could use brackets!

First, we should start by distributing.

8x + 16 = 6x + 18

Then we can start simplifying by moving like terms.

8x - 6x = 18 - 16

2x = 2

Then divide both sides by 2.

x = 1

Now we need to go backwards from atoms to grams. First, let's convert it into moles.

8.5*10^9 atoms Ne / 6.022*10^23 mol^-1 = 1.4114912*10^-14 mol Ne

Next, we multiply it by neon's molar mass, 20.180.

1.4114912*10^-14 mol Ne * 20.180 g/mol = 2.84838924*10^-13 g Ne

Now, all that's left is the significant figures. There were two at the start, so there need to be two in the answer.

2.8*10^-13 g Ne

Since we have the amount of moles, we really only have to multiply it by Avogadro's Number.

1.04 mol S * 6.022x10^23 = 6.26288x10^23 atoms S

And then the significant figures turns it into...

6.26x10^23 atoms S

Since this is a compound, we need to find the molar masses of each element and add them all together.

Fe = 55.845 x 3 = 167.535

P = 30.974 x 2 = 61.948

O = 15.999 x 8 = 127.992

And all of adds together to 357.475, which will be the molar mass for iron (II) phosphate (or Fe3(PO4)2). So now we just divide the mass by the molar mass.

130.17 g / 357.475 g/mol = 0.3641373523 mol Fe3(PO4)2

And then the significant figures come into play again. We have five figures this time.

0.36414 mol Fe3(PO4)2

No!  The question says the angle is between the ladder and the side of the house, not the ground.  The answer given by the questioner is correct.

How rude, how rude!

Still, 2 can play at thine game.

Check the points again dear Sir.

And the Lady still hath her head!

Have thou found the Roman zero amounst Zeus's offerings yet?

Thou waste time here annoying the Queen when thou should be attending thine own most urgent tasks.

Be off with you Sir Headless CPhill!

You are but a knat upon Her Royal steed!!

First, we should simplify by distributing.

3x - 15 = 2x + 6

Next, it's just a matter of moving like terms together.

3x - 2x = 6 + 15

x = 21

I already answered this in a previous question, so I'll just copy paste my response.

It's basically the same thing, we just need to use sodium's molar mass instead of silicon's.

43.7 g / 22.990 g/mol = 1.900826446 mol Na

This time I'll be rounding it again, to 1.901 mol Na. We only need to round at the end, due to significant figures, but it's much easier than typing it all out unless you have a calculator that allows you to input the previous answer such as TI-89.

1.901 mol Na * 6.022x10^23 mol^-1 = 1.1447822x10^24 atoms Na

Because we have three figures in the starting measurement, we also need three figures in the answer. Make sure to round the last digit.

1.14x10^24 atoms Na

It's basically the same thing, we just need to use sodium's molar mass instead of silicon's.

43.7 g / 22.990 g/mol = 1.900826446 mol Na

This time I'll be rounding it again, to 1.901 mol Na. We only need to round at the end, due to significant figures, but it's much easier than typing it all out unless you have a calculator that allows you to input the previous answer such as TI-89.

1.901 mol Na * 6.022x10^23 mol^-1 = 1.1447822x10^24 atoms Na

Because we have three figures in the starting measurement, we also need three figures in the answer. Make sure to round the last digit.

1.14x10^24 atoms Na

How many moles of atoms are there in 43.7g Na?

First, simplify.

9x + 1 = 64

Then we combine the like terms, basically subtracting 1 from each side.

9x = 63

Then divide each side by 9.

x = 7

So technically, we can write the square root of 4/5 as...

sqrt(4) / sqrt(5)

And then simplify it as thus...

2 / sqrt(5)

Now we need to move the square root to the numerator. We can do it like this.

( 2 / sqrt (5) ) * ( sqrt(5) / sqrt (5) )

= 2 * sqrt(5) / 5

If you were asked for the exact answer, then leave it as is. If asked for a rounded answer, then find the square root of 5 using a calculator, and go on from there.

7x[1+(12+33)/9] =

7x[1+(45)/9]=

7x[1+5] =

 7x[6] =

42x