Answer:
y = x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 0) and (x₂, y₂ ) = (0, - 1) ← coordinates of intercepts
m = =
=
The y- intercept is - 1 ⇒ c = - 1
y = x - 1
First of all, note that all integers are either 0,1, or 2 modulo 3 (if you're not familiar with this terminology, it means that every integer is either a multiple of 3, or it is 1 or 2 away from a multiple of 3).
So, we can think of our numbers as
In order to make sure that the sum of any three adjacent numbers is divisible by 3, we have to make sure that any group of 3 three adjacent numbers contains a 0, a 1 and a 2. This is possible only if we arrange our 9 numbers in 3 groups of 3 numbers containing 0,1 and 2 exactly once, repeating always the same pattern.
For example, we could arrange our numbers following the pattern
or
We have possible patterns. Suppose for example that we choose the pattern
One possible way of following this pattern would be the arrangement
In fact, we substituted every '0' with a multiple of 3 (3, 6 or 9), every '1' with a number 1 away from a multiple of 3 (1, 4 or 7) and every '2' with a number 2 away from a multiple of 3 (2, 5 or 8).
This means that, once we fix a patter, we have 3 choices for the first 3 slots, 2 choices for the next 3 slots, and the final slot will be fixed. So, we have
possible ways of following a fixed pattern. Since the number of patterns was 6, we have
possible arrangements.
The school council will have 216 small sandwiches.
Step-by-step explanation:
Sandwiches ordered = 12
Length of one sandwich = 6 feet
1 foot = 12 inch
6 feet = 12*6 = 72 inches
Length of one sandwich in inches = 72 inches
As one small sandwich is 4 inches,
Number of small sandwiches in one sandwich =
One sandwich = 18 small sandwiches
12 sandwiches = 18*12 = 216 small sandwiches
The school council will have 216 small sandwiches.
Keywords: multiplication, division
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