a. Find the next term in the sequence:  1/2, -4, 32
b. What is the perimeter of a rectangle that has an area of 400 square
meters and a width of 16 meters?
c. If one gallon of stain covers 350 square feet, what is the least
number of gallons of stain you need to cover the floor of a
rectangular deck that is 25 feet long and 16 feet wide?
d. Write the converse of the conditional statement below:
   "If it is raining, then there are clouds in the sky"
e. Draw and label a figure for the situation described below:
   On line l, ray AB and ray CD have no points in common.
f. What is the area of a rectangle that has a perimeter of 47 mm and a
length of 18.5 mm?
g. Draw and label: Lines l and m in plane ABC intersect at point C

a.

Each term in the sequence is -8 times the previous one. Since

    -8 * 32 = -256

the first four terms are

    1/2, -4, 32, -256.


b.

Knowing that the rectangle has area 400 and width 16, we deduce that its length is

    400 / 16 = 25.

The perimeter is therefore

    2*16 + 2*25 = 32 + 50
                = 82

square feet.


c.

The area of the floor is

    25 * 16 = 400

square feet. This calls for

    400 / 350 = 1 + 1/7

gallons of stain. Assuming that one must buy a full gallon at a time,
we conclude that two gallons of stain are necessary.


d.

To obtain the converse, we reverse the antecedent and the consequent.

    If there are clouds in the sky, then it is raining.


e.

    l -----+-----------+------------------+------+-------------------
           A           B                  C      D


f.

If the perimeter is 47 and the length is 18.5, then twice the height is

    47 - 2*18.5 = 47 - 37
                = 10.

The height is therefore

    10 / 2 = 5

millimeters.


g.

You will find a diagram in PostScript format at the following address.

    http://plg.uwaterloo.ca/~mlaszlo/answers/tt001.ps

Note that lines l and m happen to pass through all the points that
define the plane ABC.


If you find that my answer is incomplete or inaccurate in any way,
please let me know so that I can meet your needs before you assign a
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leapinglizard