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3 years ago

How many triangles and quadrilaterals altogether can be formed using the vertices of a 7-sided regular polygon?

Mathematics

1 answer:

MAVERICK [17]3 years ago

8 0

Answer: The correct option is

(E) 70.

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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Which graph represents an exponential function?

olga_2 [115]

Answer:

The answer to your question is the third one

Step-by-step explanation:

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3 years ago

How do you do percent of change?

dusya [7]

Answer:

Percentage change equals the change in value divided by the absolute value of the original value, multiplied by 100.

Step-by-step explanation:

First: work out the difference (increase) between the two numbers you are comparing.

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Then: divide the increase by the original number and multiply the answer by 100.

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Hope this helps

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3 years ago

Read 2 more answers

To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. The

kupik [55]

Answer:

The height of the building is 153.664 meter.

Step-by-step explanation:

Consider the provided function.

$s(t) = 4.9t^2 + v_0 t + s_0$

Here t represents the time v₀ represents the initial velocity, s₀ represents the initial height and s(t) represents the height after t seconds.

It is given that the splash is seen 5.6 seconds after the stone is dropped.

That means after 5.6 seconds height s(t) = 0, Also the initial velocity of the stone is 0.

Substitute respective values in the above function.

$0 = 4.9(5.6)^2 +5.6(0)+ s_0$

$0 = 4.9(31.36)+ s_0$

$s_0=-153.664$

As height can't be a negative number so the value of s₀ is 153.664.

Hence, the height of the building is 153.664 meter.

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3 years ago

HELPPP! Which two expressions are equivalent to

ankoles [38]

Answer:

7/3

Step-by-step explanation:

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2 years ago

The championship record in baseball in a particular year was 52 games won and 14 lost. What percent of the games were won?

tester [92]

52 games won......14 lost....for a total of 66 games

games won : 52/66 = 0.7878 = 78.8% <====
games lost : 14/66 = 0.2121 = 21.2%

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3 years ago