<h3>Given</h3>
- a rectangle x units wide and y units high divided into unit squares
<h3>Find</h3>
- The total perimeter of the unit squares, counting each line segment once
<h3>Solution</h3>
For each of the y rows of squares, there are x segments at the top, plus another x segments at the bottom. The total number of horizontal segments is then
... horizontal segment count = (y +1)x
Likewise, for each of the x columns of squares, there are y segments to the left, plus another y segments to the right of the entire area. Then the total number of vertical segments is
... vertical segment count = (x+1)y
The total segment count is ...
... total segments = horizontal segments + vertical segments
.. = (y+1)x +(x+1)y
... total segments = 2xy +x +y
_____
<u>Check</u>
We know a square (1×1) has 4 segments surrounding it.
... count = 2·1·1 +1 +1 = 4 . . . . (correct)
We know the 3×3 window in the problem statement has 24 segments.
... count = 2·3·3 +3 +3 = 18 +3 + 3 = 24 . . . . (correct)
We know a 1×3 row of panes will have 10 frame elements.
... count = 2·1·3 +1 +3 = 6 +1 +3 = 10
It looks like our formula works well.
Twice the number n will be expressed as 2n. So, that will be in our final answer. In order to decrease the number by 6, we will subtract 6. So there will be a - 6 in our final answer. Together, this is 2n - 6, and that is the same as the second option. So, the second option is the correct one.
Answer:
The answer is B
Step-by-step explanation:
2x+2y =10 and y= -x +5
These are not in the same form so thats the first step
2x+2y=10
we minus 2x from both side which turns into
2y=-2x+10 (the variable always comes first)
Secon step is to divide 2 from the y to everything so 2y divided by 2 = y
-2 divided by 2 is -x and 2 divided by 10 is 5 and now you have the same equations which leads to infinite
y=-x+5
Answer:
E
Step-by-step explanation:
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