Answer:
8.5/10 or 8.5:10
Step-by-step explanation:
A proportion can be written as a fraction or a ratio. 85% of 100 points is 85 points. The proportion becomes 85/100, which can be simplified to 8.5/10 or 8.5:10.
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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:
The correct answer to this problem is the final option, angle BTA is congruent to angle ATC.
Step-by-step explanation:
To solve this problem, we first have to unpack the meaning of the given information. First, let's remember that CPCTC means that corresponding parts of congruent triangles are congruent. This means that the same parts of two different triangles that are stated to be congruent (the same) are thus also congruent (the same).
In this case, triangle BAT and triangle CAT are stated to be congruent. This means that line segment BA and CA are congruent, angles BAT and CAT are congruent, and more because of CPCTC (explained above).
The correct answer to this problem is the final option, angle BTA is congruent to angle ATC. We can figure this out simply by looking at the triangle names. Angle ATC is the same as angle CTA (the letters are just in reverse order). From the congruence statement, we can tell that BTA and CTA are congruent angles due to the fact that triangle BAT and CAT are congruent using CPCTC. Looking at the figure, this makes sense because these two angles appear to be the same measure.
Also, we can eliminate the other answer choices, since they are not corresponding parts of the two triangles (the line segments and angles do not represent two congruent pieces of the triangle - they are not matched up correctly).
Hope this helps!