Answer:
19. reflection (-1, -3)
20. translation (5, -3)
21. translation (0, -5)
22. reflection (1, 3)
23. translation (5, 6)
24. reflection (1, 3)
Step-by-step explanation:
Hello!
We are trying to describe the behavior of the graph given in the question.
To help us understand how to solve this question, we would need to understand <u>concavity.</u>
There are two types of concavity:
- Concave <em>up</em>
- Concave <em>down</em>
When a graph is concave up, the slope of the line would look like a "U".
When a graph is concave down, the slope of the line would look like a "U" that is flipped upside down.
In this case, we can see that the graph is concave down.
We can tell that the <em>slope</em> is negative due to the fact that the slope is going <u>down,</u> which results in the graph having a negative slope.
We can also tell that the graph is decreasing due to the fact that the line is doing downward.
Answer:
C). negative and decreasing
Answer:
Step-by-step explanation:
2005 AMC 8 Problems/Problem 20
Problem
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$
Solution
Alice moves $5k$ steps and Bob moves $9k$ steps, where $k$ is the turn they are on. Alice and Bob coincide when the number of steps they move collectively, $14k$, is a multiple of $12$. Since this number must be a multiple of $12$, as stated in the previous sentence, $14$ has a factor $2$, $k$ must have a factor of $6$. The smallest number of turns that is a multiple of $6$ is $\boxed{\textbf{(A)}\ 6}$.
See Also
2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 19 Followed by
Problem 21
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All AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
Answer: -4
Step-by-step explanation:
the answer for this question is -3
