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the absence of a clear agreement, the law provides that all partners share equally, regardless of the differences in time devoted or capital con tributed. Below are outlined the principal methods for pro t and loss distribu tion: Fixed or Capital Basis Pro ts and losses are generally divided equally in a xed ratio or in a ra tio based on the amounts of capital contributed by the partners. Interest Basis Under this method, each partner is paid interest on his or her capital in vestment, and the remaining net income is divided in a xed ratio or on some other basis. Thus, a partner s share depends on his or her capital in vestment. Salary Basis The partners may agree to give recognition to contributions in the form of services, while the remaining net income may be divided equally or in a xed ratio. Salary-Plus-Interest Basis Here, services rendered to the business and capital contribution jointly determine the income division. Each partner gets a salary, and, at the same time, interest on capital. If any balance remains, it is divided in an agreed ratio.



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7.17 Applying principle 2 In similar triangles ABC and A B C (Fig. 7-15), find x and y if /A > /A and /B > /B .

Fig. 7-15

x Since /A > /A and /B > /B , x and y correspond to 32 and 26, respectively. Hence, 32 y 15 so y 191. from which x 24; also 2 26 20 15 , 20

7.18 Applying principle 3 In each part of Fig. 7-16, two pairs of congruent angles can be used to prove the indicated triangles similar. Determine the congruent angles and state the reason they are congruent.

Fig. 7-16





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(a) /CBD > /BDA and /BCA > /CAD, since alternate interior angles of parallel lines are congruent (BC i AD). Also, /BEC and /AED are congruent vertical angles. (b) /A > /C and /B > /D, since angles inscribed in the same arc are congruent. Also, /AED and /CEB are congruent vertical angles. (c) /ABC > /AED, since each is a supplement of /DEC. /ACB > /ADE, since each is a supplement of /BDE. Also, /A > /A.

7.19 Applying principle 6 In each part of Fig. 7-17, determine the angles that can be used to prove the indicated triangles similar.

When the partnership lacks a clear agreement es tablishing the division of net income or loss, the law provides that all partners share equally, regardless of the differences in time devoted or capital con tributed.

Fig. 7-17

(a) /ACB and /ADC are right angles. /A > /A. (b) /AEC and /BDC are right angles. /B > /ACE, since angles in a triangle opposite congruent sides are congruent. (c) /ACB is a right angle, since it is inscribed in a semicircle. Hence, /AED > /ACB. /D > /B, since angles inscribed in the same arc are congruent.

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7.20 Applying principle 4 In each part of Fig. 7-18, determine the pair of congruent angles and the proportion needed to prove the indicated triangles similar.

Fig. 7-18

(a) /AEB > /DEC; 3 9 4 12 (b) /A > /A; 6 12 9 18 (c) /BAC > /ACD; 20 16 25 20

Namespaces are a source of great confusion for XML students and many practitioners. The namespace concept is based on each element having a given set of attributes, with each attribute containing a name and value. There is no problem for element names that have no ambiguity or if there is no chance that an element may be used in a di erent context or meaning. In HTML, the title tags mark up the section of text to appear in the browser title bar. There is no confusion here. However, what if you are combining two documents that both use the title element in di erent contexts, and neither of them relates to the HTML title element Assume, for example, you are discussing books on genealogy, all of which have a (book) title, and the books are about family history, including royal families, which also have a title as part of the name element. How do you separate the book title from the royal title from the Web page title You could rely on case sensitivity, but this is a poor x. Instead, you use a namespace to de ne which title element is intended and how it is constructed. De ning a namespace requires a bit more XML. The namespace syntax used in XML 1.0 is as follows: <royalty:title xmlns:royalty="http://www.royalty.com/xml"/> <genealogy:title xmlns:genealogy="http://www.genealogy.com/xml"/> This allows you to declare where the namespace and declaration for each use of title reside, via the URI of each namespace referenced. To use the namespace, you can write the tag as <royalty:title> or <genealogy:title>, and the

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