Answer:
6x ≥ -24
x ≥ -4
Step-by-step explanation:
the inequality of Six times a number x is at least −24
6x ≥ -24
Divide each side by 6
6x/6 ≥ -24/6
x ≥ -4
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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
Angle 1= 180-111 =69 degree
angle 2=1 so ,69 degree(vertically oppsite angle)
angle 3= 180-111= 69 degrees(corresponding angle to 111 degree)
angle angle 6 =108 (vertically opposite angle)
angle 4 =108(corresponding angle)
angle 5=180-108 =72 (alternate angle)
Inequality 9d+10>72
Num of hot dogs needed to be eaten per min, 7.
T(14 - 5) = 14t - 5t or t(14) - t(5)
