After simplification, the value of 1-2/1(1+2)-3/(1+2)(1+2+3)-4/(1+2+3) (1+2+3+4)-...-100/(1+2+...+99)(1+2+ ...+100) is a proper fraction in its lowest form. Find the difference of its numerator and denominator.

The area of a rectangle is 54x^9y^8 square yards.if the length of the rectangle is 6x^3y^4 yards,which expression represents the width of the rectangle in yards

For [tex]f(x) = 4x + 1[/tex] and (x) = [tex]g(x)= x^{2} -5,[/tex] find [tex](\frac{g}{f}) (x)[/tex]a. [tex]\frac{x^{2} - 5 }{4x +1 },x[/tex] ≠ [tex]-\frac{1}{4}[/tex]b. x[tex]\frac{4 x +1 }{x^{2} - 5}, x[/tex] ≠ ± [tex]\sqrt[]{5}[/tex]c. [tex]\frac{4x +1}{x^{2} -5}[/tex]d.[tex]\frac{x^{2} -5 }{4x + 1}[/tex]

The base of a rectangular pyramid is 13 inches long and 12 inches wide. the height of the pyramid is 8 inches. what is the volume of the pyramid