ANSWER
The length of the rectangular field is 99 yards
EXPLANATION
Given information
The perimeter of a rectangle field is 372 yards
The width of the field is 87 yards
To find the length of the rectangular field, follow the steps below
Step 1: Write the formula for finding the perimeter of a rectangular field
Step 2: Substitute the given data into the formula in step 1
Hence, the length of the rectangular field is 99 yards
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.
1 1/<span>200 should be the answer</span>
Given the following values for a quadratic function, which is the graph of the function? (–1, 0), (0, 3), (1, 4), (2, 3), (3, 0)
Firdavs [7]
Answer:
The function of the graph is f(x) = - x² + 2x + 3
Step-by-step explanation:
Using the value of the graph we can say that the the function is negative x² because there are x-intercepts and the y-intercept if above 0.
Using the x-intercepts we can form the function of the graph:
-(x + 1)(x - 3) - we have a negative in front of the two brackets because the function is a negative. Now we multiply out the brackets and the negative at the end:
-(x² - 2x - 3)
- x² + 2x + 3 - So the function of the graph is:
f(x) = - x² + 2x + 3
