Asquare picture frame ocupies an area of 112ft^2. what is the length of each side of the picture in simplified radical form? show your work.

The area of a square is given by the equation: , where s is the length of the side.  Since the area of this picture frame is given (112), then the length of each side is the square root of the number.

However, 112 is not a perfect square.  You can simplify by breaking it down into smaller components.  First, find the largest factor of 112 which is also a perfect square.  In this case, this is 16.  You can write as since 16*7=112.  Then, you can take the square root of 16.

The final answer is .

Hope this makes sense!

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.