You are enlarging a [b][i]5[/i][/b]-inch by [b][i]7[/i][/b]-inch photo by a scale factor of [i][b]x[/b][/i] and mounting it on a mat. You want the mat to be twice as wide as the enlarged photo and [b][i]2[/i][/b] inches less than twice as high as the enlarged photo.[br][br][u][b]a.[/b][/u] Draw a diagram to represent the described situation. Label the dimensions.[br][br][b][u]b.[/u][/b] Write a model for the area of the mat around the photograph as a function of the scale factor.

Use a verbal model. Use the diagram to find expression for the labels.[br][br][b]Area of mat = Total Area - Area of photo[br][/b][br]Area of mat = [b][i]A[/i][/b]   (square inches)[br][br]Total area = [math]\left(10x\right)\left(14x-2\right)[/math] (square inches)[br][br]Area of photo = [math]\left(5x\right)\left(7x\right)[/math] (square inches)[br][br]Algebraic Model[br][br][math]A=\left(10x\right)\left(14x-2\right)-\left(5x\right)\left(7x\right)[/math][br][br] [math]=140x^2-20x-35x^2[/math][br][br] [math]=105x^2-20x[/math][br][br]A model for the area of the mat around the photograph as a function of the scale factor [b][i]x[/i][/b] is[br][br][math]A=105x^2-20x[/math]