State the name of the angle

The ten sides of a regular decagon are colored with five different colors, so that all five colors are used, and sides that are

const2013 [10]

Answer:

<u>120</u>

Explanation:

Number the sides of the decagon: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, from top (currently red) clockwise.

The side number one can be colored of five different colors (red, orange, blue, green, or yellow): 5

The side number two can be colored with four different colors: 4

The side number three can be colored with three different colors: 3

The side number four can be colored with two different colors: 2

The side number five can be colored with the only color left: 1

Each of the sides six through ten can be colored with one color, the same as its opposite side: 1

Thus, by the multiplication or fundamental principle of counting, the number of different ways to color the decagon will be:

5 × 4 × 3 × 2 ×1 × 1 × 1 × 1 × 1 × 1 = 120.

Notice that numbering the sides starting from other than the top side is a rotation of the decagon, which would lead to identical coloring decagons, not adding a new way to the number of ways to color the sides of the figure.

6 0

3 years ago

. Use the quadratic formula to solve each quadratic real equation. Round

Liono4ka [1.6K]

Answer:

A. No real solution

B. 5 and -1.5

C. 5.5

Step-by-step explanation:

The quadratic formula is:

$\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}$ , with a being the x² term, b being the x term, and c being the constant.