answer:Call the number of one dollar bills x and the number of two dollar bills y. We can use the following system of equations to represent the given information: begin{align*} x + y &= 49, 1x + 2y &= 66. end{align*}The first equation represents the total number of dollar bills in the piggy bank, and the second equation represents how much money is in the piggy bank. Solving for x in the first equation gives x = 49 - y. Substituting for x in the second equation yields 49 - y + 2y = 66, or y = 17. But y is the number of two dollar bills, and the question asks for the number of one dollar bills, so solve for x: x = 49 - 17. Thus, there are boxed{32} one dollar bills.

answer:We can rewrite the given equation as y = -frac{1}{2}x - frac{17}4. Since all lines parallel to a given one have the same slope as the given line, our answer is boxed{-frac{1}{2}}.

answer:Using the associative property and simplifying gives begin{align*} (15x^2) cdot (6x) cdot left(frac{1}{(3x)^2}right) &= (15 cdot 6) cdot (x^2 cdot x) cdot left(frac{1}{9x^2}right) &= frac{90x^3}{9x^2} &= 10x^{3-2} = boxed{10x}. end{align*}

answer:Recall that two lines are perpendicular if and only if the product of their slopes is -1. The first equation is already in slope-intercept form, so we can see that its slope is 2. Subtract ax and divide by 6 in the second equation to get it in slope-intercept form as well: y=-frac{a}{6}x+1. The negative reciprocal of 2 is -1/2, so setting -a/6=-1/2 we find that a=boxed{3} is the value for which the two lines are perpendicular.