9. wade has 126 inches of 1-inch wide bias tape for a border
on a rectangular banner. if the banner needs to be 48
inches long, what is the maximum width it could be?

Let 'x' represent the width.

2*48 + 2x = 126

x = 15 in

The maximum width could be 15 inches.

X²+y²-10x-6y = 23
(x²-10x)+(y²-6y)=23
We need to complete square for x and y groups.
(x²-2*5x+5²) + (y²- 2*3y+3²)=23 +5² +3²
(x-5)²+(y-3)² = 57  - sometimes this form is called standard
(x-5)²+(y-3)² = (√57)² 
(5,3) is vertex of the circle, and √57 is the radius of the circle.
Sometimes this form called is standard: