How many different ways can 6 plates be arranged

Step-by-step explanation:

This is a permutation since order matters.  We have 6 plates.  Once we put a specific plate in position 1, we only have 5 plates left to fill the next position.  After that, we only have 4 plates to fill the next position, and so on.  The formula for that would look like this:

₆P₆ = which simplifies to

₆P₆ = , where 0! = 1.  Therefore, our formula comes down to

₆P6 = 6 * 5 * 4 * 3 * 2 * 1 which is 720

This is a factorial, also, where 6 * 5 * 4 * 3 * 2 * 1 is the number of different ways all 6 plates can be arranged.  This is a total of 720 different ways to arrange them.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.