2 years ago

What are the coefficients of 60a+30c

Mathematics

1 answer:

Gekata [30.6K]2 years ago

6 0

I think the answer is 60 and 30 but I'm on break so I'm not thinking rn

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Step-by-step explanation: We are given to find the number of triangles and quadrilaterals altogether that can be formed using the vertices of a 7-sided regular polygon.

To form a triangle, we need any 3 vertices of the 7-sided regular polygon. So, the number of triangles that can be formed is

$n_t=^7C_3=\dfrac{7!}{3!(7-3)!}=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}=35.$

Also, to form a quadrilateral, we need any 4 vertices of the 7-sided regular polygon. So, the number of quadrilateral that can be formed is

$n_q=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.$

Therefore, the total number of triangles and quadrilaterals is

$n=n_t+n_q=35+35=70.$

Thus, option (E) is CORRECT.

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