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7.66. In an isosceles trapezoid which has base angles measuring 60 , find the lengths of (a) the lower base and altitude if the upper base has length 12 and the legs have length 16; (b) the upper base and altitude if the lower base has length 45 and the legs have length 28. (7.39) 7.67. In an isosceles right triangle, find the length of each leg if the hypotenuse has length (a) 34; (b) 2a. Find the length of the hypotenuse if each leg has length (c) 34; (d) 15 22. (7.40) 7.68. In a square, find the length of (a) the side if the diagonal has length 40; (b) the diagonal if the side has length 40. (7.40) 7.69. In an isosceles trapezoid which has base angles of measure 45 , find the lengths of (a) the lower base and each leg if the altitude has length 13 and the upper base has length 19; (b) the upper base and each leg if the altitude has length 27 and the lower base has length 65; (c) each leg and the lower base if the upper base has length 25 and the altitude has length 15. (7.40) 7.70. A parallelogram has an angle measuring 45 . Find the distances between its pairs of opposite sides if its sides have lengths 10 and 12. (7.40)



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(c) Up 3 spaces and 7 spaces to the left (d) Down 2 spaces and 8 spaces to the right (e) Up 4 spaces and to the left 1 space

* (asterisk)

18.5. Let trapezoid ABCD be formed by A(1, 3), B(5, 3), C(4, 1), and D(2, 1). Graph trapezoid ABCD and its image under (a) reflection across the y axis P(x, y) A P ( x, y) , (b) reflection across the line y 1, P(x, y) A Ps(x, 2 y), and (c) reflection across the line x 8, P(x, y) A P-(16 x, y). 18.6. Name the reflection that takes ^ABC to (a) ^ArBrCr, (b) ^AsBsCs, and (c) ^A-B-C- as illustrated in Fig. 18-18.

Fig. 18-18

18.7. Name the transformation that (a) Reflects across y (b) Reflects across x (c) Reflects across y (d) Reflects across x 5 2 1

Fig. 18-19





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18.9. Let parallelogram ABCD be defined by A(1, 2), B(4, 2), C(5, 1), and D(2, 1). Graph parallelogram ABCD and its image under (a) a 90 clockwise rotation about the origin, (b) a 180 rotation about the origin, and (c) a 270 clockwise rotation about the origin.

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The income statement may be de ned as a summary of the revenue (in come), expenses, and net income of a business entity for a speci c peri od of time. This may also be called a pro t and loss statement, an oper ating statement, or a statement of operations. Let us review the meanings of the elements entering into the income statement. Revenue. The increase in capital resulting from the delivery of goods or rendering of services by the business. In amount, the revenue is equal to the cash and receivables gained in compensation for the goods delivered or services rendered. Expenses. The decrease in capital caused by the business s revenue-producing operations. In amount, the expense is equal to the value of goods and services used up or consumed in obtaining revenue. Net income. The increase in capital resulting from pro table operation of a business; it is the excess of revenue over expenses for the accounting period. It is important to note that a cash receipt quali es as revenue only if it serves to increase capital. Similarly, a cash payment is an expense only

Name the rotation that takes ^ABC to (a) ^ArBrCr, (b) ^AsBsCs , and (c) ^A-B-C- as illustrated in Fig. 18-20.

Fig. 18-20

18.11. Name the transformation that rotates clockwise about the origin: (a) 40 (b) 50 (c) 80 18.12. For each figure in Fig. 18-21, give the smallest angle by which the figure could be rotated around its center and still look the same.

Fig. 18-21

18.13. Let triangle ABC be defined by A(2, 1), B(3, 2), and C(3, 1). Graph ^ABC and its image under the following combinations of transformations: (a) Reflect across the line y 3 and then move to the right 2 spaces.

(c) Rotate about the origin 270 clockwise and then reflect across the x axis. (d) Reflect across the line x 1 and then move up 2 spaces.

18.14. Name the single transformation that does the same thing as (a) P(x, y) A Pr(x (b) P(x, y) A Pr(5 5, y 3) and then Qr(x, y) A Qs(x 4, y 3, y y) x, y) 6) 1, y 2) 2)

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