The sum of the interior angles of a triangle is 180 degrees
2x-9+3x+x+3=180
6x-6=180
6x=186
x=31
A=2(31)-9
A=62-9
A=53
Answer:
<em>3.27*10^22</em>
Step-by-step explanation:
Given the expression 9.6x10^85/3x10^63, we are to write it on scientific notation as shown:
9.6x10^85/3x10^63
= (9.8/3) * (10^85/10^63)
= (9.8/3) * 10^{85-63}
= (9.8/3) *10^22
= 3.27 *10^22
<em>Hence the expression in scientific notation is 3.27*10^22</em>
The second one would be the answer. You want to plug in for this question. You can divide over the five leaving you with (x-2)^2 =25. Since you are squaring this answer, you want to get either 5 or negative five. Both -3 and 7 will do that.
C is your answer. Because 8 times 1.75$ = $14.00 and 5 times 1.25= $6.25. So $14.00+ $6.25 = $20.25
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.
