What is the length of segment DC?

Mathematics

1 answer:

erik [133]3 years ago

5 0

Since BD is the bisector of angle B, the segments to its left are proportional to those to its right. The proportion can be written at least 4 ways, but it is convenient to write it with x in a numerator.

x/(15 cm) = (5.6 cm)/(7 cm)
Multiplying by 15 cm, we get
x = (15 cm)×(5.6/7) = 12 cm

The appropriate choice is
D. 12 cm

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<u>Answer</u>:

3003 number of 5-member chess teams can be chosen from 15 interested players.

<u>Step-by-step explanation:</u>

Given:

Number of the interested players = 15

To Find:

Number of 5-member chess teams that can be chosen = ?

Solution:

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula $nCr = \frac{n!}{r!(n - r)!}$

where

n represents the total number of items,

r represents the number of items being chosen at a time.

Now we have n = 15 and r = 5

Substituting the values,

$15C_5 = \frac{15!}{5!(15- 5)!}$

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$15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{5 \times 4 \times 3 \times 2 \times 1(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)}$