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Alecsey
12 days ago
6

Ron finds 9 books at a bookstore that he would like to buy, but he can afford only 5 of them. In how many ways can he make his s

election? How many ways can he make his selection if he decides that one of the books is a must?
a. 3024; 1680
b. 7560; 840
c. 120; 1680
d. 126; 70
Mathematics
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Line RS intersects triangle BCD at two points and is parallel to segment DC. Triangle B C D is cut by line R S. Line R S goes th
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Answer:

The correct statements are;

1) ΔBCD is similar to ΔBSR

2) BR/RD = BS/SC

3) (BR)(SC) = (RD)(BS)

Step-by-step explanation:

1) Since RS is parallel to DC, we conclude that;

∠BDC = ∠BRS (Angles formed on the same side of the transversal)

Furthermore;

∠BCD = ∠BSR (Angles formed on the same side of the transversal)

∠CBD = ∠CBD (Reflexive property)

Thus;

ΔBCD ~ ΔBSR by the Angle-Angle-Angle (AAA) similarity criterion.

2) Given that  ΔBCD ~ ΔBSR, we obtain;

BC/BS = BD/BR → (BS + SC)/BS = (BR + RD)/BR = 1 + SC/BS = RD/BR + 1

1 + SC/BS = 1 + RD/BR thus, SC/BS = 1 + BR/RD - 1

SC/BS = RD/BR

By inverting both sides we find;

BR/RD = BS/SC

3) From BR/RD = BS/SC, we apply cross multiplication;

BR/RD = BS/SC leads to;

BR × SC = RD × BS → (BR)(SC) = (RD)(BS).

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