A lot of national flags are made up of three horizontal stripes.

1 answer:

7 0

How many different three colour flags (tricolors) can be designed using green, blue, red, yellow and black stripes if all three colours must be different?
6P3 = 6!/(6 - 3)! = 6!/3! = (6 x 5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 720/6 = 120 flags.

How many of them contain a red stripe?
The remaining two colours can be arranged in 5P2 = 5!/(5 - 2)! = 5!/3! = (5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 120/6 = 20ways
The red stripe can arranged in 3 ways
Therefore, number of flags having red stripe is 20 x 3 = 60 flags.

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Let us recall parallelogram properties, which states that opposite angles of parallelogram are congruent.

We can see from graph that side US is parallel to TR and measure of angle U equals to measure of angle R, therefore, quadrilateral drawn in our given graph is a parallelogram.

Since we know that opposite sides of parallelogram are congruent. In our parallelogram UT=SR and US=TR.

In our triangle STU and triangle TSR side TS=TS by reflexive property of congruence.

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PtichkaEL [24]

Answer:

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Step-by-step explanation:

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