<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.
Answer:
y = x -7
Step-by-step explanation:
2x - 2y = 14
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
Subtract 2x from each side
2x - 2y -2x = -2x+14
-2y = -2x+14
Divide each side by -2
-2y/-2 = -2x/-2 +14/-2
y = x -7
The slope is 1 and the y intercept is -7
Answer:
The area of the triangle on left is 9
in², the area of the triangle on the right is 9
in², and the area of the rectangle is 108
in².
The area of the trapezoid is the sum of these areas, which is 126
in².
Answer:
31.5 hours studying English
Step-by-step explanation:
2 math hours = 3 english hours
21 math hours = ? english hours
21/2 = 10.5
10.5 * 3 = 31.5
Answer:
Yes
Step-by-step explanation:
Because 2 is a common factor
