Mary states, "If the diagonals of a parallelogramare congruent, then the

Mathematics

1 answer:

slava [35]2 years ago

4 0

Answer:

True

Step-by-step explanation:

A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,

AD ≅ BC (opposite side property)

AB ≅ CD (opposite side property)

<ABC = <BCD = <CDA = <DAC = $90^{0}$ (right angle property)

Thus,

<ABC + <BCD + <CDA + <DAC = $360^{0}$

AC ⊥ BD (diagonals are perpendicular to each other)

AC ≅ BD (congruent property of diagonals)

Therefore, the parallelogram is a rectangle.

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Marina86 [1]

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Step-by-step explanation:

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2 years ago

In an international film festival, a penal of 11 judges is formed to judge the best film. At last two films FA and FB were consi

valentina_108 [34]

Answer:

The answer is "0.4329 ".

Step-by-step explanation:

P( three in favor of FA)

Select 3 out of 6 FA supporters then select 2 out of 5 FB supportive judges

$=\frac{^{6}_{C_{3}}\times ^{5}_{C_{2}}}{^{11}_{C_{5}}}\\\\=\frac{\frac{6!}{3!(6-3)!}\times \frac{5!}{2!(5-2)!}}{\frac{11!}{5!(11-5)!}}\\\\=\frac{\frac{6!}{3! \times 3!}\times \frac{5!}{2! \times 3!}}{\frac{11!}{5! \times 6!}}\\\\=\frac{\frac{6 \times 5 \times 4 \times 3!}{3 \times 2 \times 1\times 3!}\times \frac{5 \times 4 \times 3!}{2 \times 1 \times 3!}}{\frac{11 \times10 \times 9 \times 8 \times 7 \times 6! }{5 \times 4 \times 3 \times 2 \times 1 \times 6!}}\\\\$

$=\frac{ (5 \times 4) \times(5 \times 2)}{(11 \times 3 \times 2 \times 7 )}\\\\=\frac{ 20 \times 10 }{(11 \times 42)}\\\\=\frac{ 200 }{462}\\\\=\frac{100 }{231}\\\\=0.4329$