Which pair of numbers completes the table intop?

Mathematics

2 answers:

Lostsunrise [7]3 years ago

6 0

The answer is 300 inches and 25 feet!!

Annette [7]3 years ago

4 0

The answer is 300 inches and 25 feet

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

MAVERICK [17]

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.

8 0

3 years ago

Math - Use unit conversion factor to convert the units.

nlexa [21]

Answer: 240 minutes, 20 cups, 4000 pounds

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

Use the following conversions:

1 hour = 60 minutes

2 cups = 1 pint

2 pints = 1 quart

1 ton = 2000 pounds

$4\ hours\times \dfrac{60\ minutes}{1\ hour}=\large\boxed{240\ minutes}\\\\\\\\5\ quarts \times \dfrac{2\ pints}{1\ quart}\times \dfrac{2\ cups}{1\ pint}=\large\boxed{20\ cups}\\\\\\\\2\ tons\times \dfrac{2000\ pounds}{1\ ton}=\large\boxed{4000\ pounds}$