Answer:
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.
Answer:

Step-by-step explanation:



The given function has no undefined points nor domain constraint. Thus, the domain is:
.
<h3>Domain and Range</h3>
The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined. An example, there is a restriction for the domain of fractions. The variable x in the denominator should be different of zero.
While the domain is related to the values of x, the range is related to the possible values of y that the function can have.
In this question, the function
has no undefined points nor domain constraint. Therefore, the domain is: 
Learn more about the domain here:
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Answer:
f(x) = 2(x - 5)² - 6
Step-by-step explanation:
Vertex Formula: <em>y</em><em> </em><em>=</em><em> </em><em>a</em><em>(</em><em>x</em><em> </em><em>-</em><em> </em><em>h</em><em>)</em><em> </em><em>+</em><em> </em><em>k</em>; Vertex: [<em>h</em><em>,</em><em> </em><em>k</em>]; there is a vertical stretch at <em>2</em><em> </em><em>=</em><em> </em><em>a</em><em>.</em><em> </em>The <em>-</em><em>h</em><em> </em>[phase shift (horizontal shift)] in parentheses gives you the OPPOSITE term of what it really is, so really, <em>5</em><em> </em><em>=</em><em> </em><em>h</em><em>.</em><em> </em>Now, <em>k</em><em> </em>[vertical shift] is the ONLY normal term, so <em>-</em><em>6</em><em> </em><em>=</em><em> </em><em>k.</em><em> </em>
Line of slope 4 and y_intercept 1
thus y=4x+1