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The stockholders, as owners of the business, have the right: 1. to vote (one vote for every share of stock held) 2. to share in pro ts 3. to transfer ownership 4. to share in the distribution of assets in the case of liquidation. The board of directors is elected by the stockholders within the framework of the arti cles of incorporation. The board s duties include the appointing of corporate of cers, determining company policies, and the distribution of pro ts. A share of stock represents a unit of the stockholders interest in the business. The par value of a share is an arbitrary amount estab lished in the corporation s charter and printed on the face of each stock certi cate. It bears no relation to the market value, that is, the current pur chase or selling price. There are several categories of stock shares: 1. Authorized shares are shares of stock that a corporation is permit ted to issue (sell) under its articles of incorporation. 2. Unissued shares are authorized shares that have not yet been of fered for sale. 3. Subscribed shares are shares that a buyer has contracted to pur chase at a speci c price on a certain date. The shares will not be issued until full payment has been received.



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(c) P(x, y) A Pr(y, x) and then Qr(x, y) A Qs(x (d) P(x, y) A Pr( y, x) and then Qr(x, y) A Qs(x, 4 (e) P(x, y) A Pr(x, 3

y) and then Qr(x, y) A Qs(6

18.15. Name the transformation that takes ^ABC to (a) ^ArBrCr, (b) ^AsBsCs , and (c) ^A-B-C- as illustrated in Fig. 18-22.

( ) (parentheses)

Fig. 18-22

18.16. Name the transformation that (a) Reflects across the x axis and then moves everything down 3 spaces (b) Rotates around the origin clockwise 90 and then moves everything to the right 2 spaces (c) Reflects across the line y 2 and then rotates 180 around the origin 2 4





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18.17. Let rectangle ABCD be formed by A( 1, 2), B(1, 2), C(1, 1), and D( 1, 1). Graph this rectangle and also its image under the transformation P(x, y) A Pr(3x, 3y). 18.18. Name the transformation that (a) Scales everything to be twice as large (b) Scales everything by scale factor 8 (c) Dihilates everything by a scale factor of 3

4. Treasury stock represents shares that have been issued and later reacquired by the corporation. 5. Outstanding stock represents shares authorized, issued, and in the hands of stockholders. (Treasury stock is not outstanding, as it belongs to the corporation and not to the stockholders.)

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For most of the years since Euclid wrote the Elements in 325 B.C., people felt that only one sort of geometry was possible. Planes looked like infinitely large, flat sheets of paper, lines went on forever as straight as the mind could imagine, and a grid of parallel lines could be drawn to make a plane look like graph paper. However, the foundations of this geometry were unfortunately vague. As discussed in 1, the concepts of point, line, and plane were not given formal definitions. The individual points, infinite straight lines, and flat planes discussed throughout this book all fit the properties and descriptions of points, lines, and planes, but other objects fit these general descriptions as well. When these basic objects are different, the resulting geometry is different as well. Similarly, as discussed in 2, the entire structure of geometric proof rests upon unproved postulates. These postulates lead to the geometry with which we are familiar. However, why should we believe one set of postulates and not a different set If we start with different postulates, then our theorems will be different as well. Our choices lead to different sorts of geometry, called non-euclidean geometries.

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