Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are (2x^2-16) feet and (-x^2+4x+1) feet. Which expression represents the total perimeter of the table, and if x=3, what is the length of the entire rubber bumper? x^2+4x-15 3 feet x^2+4x-15 6 feet 2x^2+8x-30 6 feet 2x^2+8x-30 12 feet

To find the perimeter rectangle, we add up the lengths of all four sides. Since the table is rectangular, opposite sides are equal in length. Therefore, the perimeter (P) can be calculated using the formula:<br /><br />\[ P = 2 \times (\text{length} + \text{width}) \]<br /><br />Given the dimensions of the table are \( (2x^{2}-16) \) feet and \( (-x^{2}+4x+1) \) feet, we can substitute these into the perimeter formula:<br /><br />\[ P = 2 \times ((2x^{2}-16) + (-x^{2}+4x+1)) \]<br /><br />Simplify the expression inside the parentheses:<br /><br />\[ P = 2 \times (2x^{2} - x^{2} + 4x - 16 + 1) \]<br />\[ P = 2 \times (x^{2} + 4x - 15) \]<br /><br />Now, distribute the 2:<br /><br />\[ P = 2x^{2} + 8x - 30 \]<br /><br />So, the expression representing the total perimeter of the table is \( 2x^{2} + 8x - 30 \).<br /><br />Next, we need to find the length of the entire rubber bumper when \( x = 3 \). Substitute \( x = 3 \) into the expression for the perimeter:<br /><br />\[ P = 2(3)^{2} + 8(3) - 30 \]<br />\[ P = 2(9) + 24 - 30 \]<br />\[ P = 18 + 24 - 30 \]<br />\[ P = 42 - 30 \]<br />\[ P = 12 \]<br /><br />Therefore, the length of the entire rubber bumper when \( x = 3 \) is 12 feet.<br /><br />The correct answer is:<br /><br />\[ 2x^{2} + 8x - 30 \text{ 12 feet} \]