12). Which of the following is the equation of the line that contains the

points (3,-1) and is perpendicular to the line y= 3x+ 3.

12.) The slope of a line perpendicular to an equation is always the negative recipricol of that slope of that equation. So in this case, the slope is -1/3.

You then have the general equation y = -1/3x + b

Plug in the points (3, -1) into the equation to find b.

-1 = -1/3(3) + b

b = 0

32.) y=(x+2)/(x-3), they wanted you to solve for x

(x-3)y=(x+2)

xy-3y = x+2

xy-x = 2+3y

x(y-1) = 2+3y

x = (2+3y)/(y-1)

35.) You have to realize that if you have a sheet that is constrained to 19x23, you have to take the size restriction in mind. The entire area is not useable. Take the 19in side. If you are cutting 3 inch squares, then you will reach 18inches (six square sides), but then that last inch is unusable. The way to solve this problem is to divide each side of the tin by 3 (19/3 and 23/3) and see what the maximum number of squares you can produce, which is 6 full squares off the 19in side and 7 squares off the 23 in side. Then you multiply 6x7 and get 42. Try drawing out the squares on a sheet of paper if you still dont understand this.