Option C:
Area of the remaining paper = (3x – 4)(3x + 4) square centimeter
Solution:
Area of the square paper = 
sq. cm
Area of the square corner removed = 16 sq. cm
Let us find the area of the remaining paper.
Area of the remaining paper = Area of the square paper – Area of the corner
Area of the remaining = 
= 
Using algebraic formula: 
Area of the remaining paper = (3x – 4)(3x + 4) square centimeter
Hence (3x – 4)(3x + 4) represents area of the remaining paper in square centimeters.
Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
29 and 31
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