Since there are 3 H's in H3PO4 and only 1 OH in NaOH that means you need three moles of NaOH for every mole of H3PO4. So Moles NaOH = 3x moles H3PO4 moles NaOH =0.1 moles/liter x L liters (L is our unknown) moles H3PO4 = 0.2 moles/liter x 0.015 liters so (0.1)L = 0.2(3)(0.015)...

You need to use trig identities. There is the double angle cos 2€ and 1/2 angle  identity cos 1/2€. If you can get your fraction to fit into one of these formulas you should be able to solve it from there. For example, if you have cos 1/4@ you could rewrite it as cos 2(1/8)@. The identity tells...

Robert's answer looks good.  If, however, the 3(2-x) is in the denominator, then try this:   f(x) = x^2 / (6-3x)   Use Chain Rule where a = x^2 and b = (6-3x)^-1   f'(x) = ab' + ba' f'(x) = (x^2)(-1)(-3)(6-3x)^-2 + 2x(6-3x)^-1 f'(x) = (3x^2)/(6-3x)^2...

If two lines are parallel they have the same slope.  Since both of these equations are in slope intercept format, y=mx+b, it is easy to see the slope. It is the coefficient of the x, or m. What is the slope of the first line? It is the coefficient of x, which is 1. What is the slope of...

20x-y=5 x=10-5y 20(10-5y)-y=5 200-100y-y=5 200-101y=5 -101y=5-200 -101y=-195 y=195/101=1.93 20x-1.93=5 20x=6.93 x=6.93/20 =0.347

Ok, good job. X is less than -7 is correct. On a number line you have the negative numbers, zero, then the positive numbers to the right. Right? So to plot x<-7 we need an open circle on negative seven. This is because x cannot be equal to negative seven, it has to be less. So x could be -7.0001...

Ok, we know we have x seagulls and 2x ducks because they are in the ratio if 1:2.  We know the total number of birds is 12, therefore x plus 2x or 3x must equal 12. So set 3x = 12. Solving for x, x=4. So in the beginning we must have 4 seagulls and 8 ducks. To get to the end ratio of 19:8 we...