Lisa wants to build a table and put a border around it. the table and border must have an area of 3,996 square inches. the table is 42 inches wide and 36 inches long without the border. which quadratic equation can be used to determine the thickness of the border, x?

a) 4x^2 + 156x - 2,484 = 0
b) 4x^2 + 156x - 3,024 = 0
c) 2x^2 + 156x - 3,996 = 0
d) x^2 + 78x + 3,996 = 0

Option A

The quadratic equation can be used to determine the thickness of the border, x is

Solution:

Given, Lisa wants to build a table and put a border around it.  

The table and border must have an area of 3,996 square inches.  

The table is 42 inches wide and 36 inches long without the border.  

To find the quadratic equation used to determine the thickness of the border:

So, area of table and border = 3996

Area = (length + 2x)(width + 2x)

Here “2x” represents the border around table

Hence, the equation is so option A is correct

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

the answer is a

step-by-step explanation: