d. Write the equation of the line that is perpendicular to the graph of \( y=25 x+99 \) and crosses the point \( (1,37) \). e. What is the relationship between the graphs of \( y=-27 x+15 \) and \( y=-27 x+5 \). f. What is the relationship between the graphs of \( y=-0.125 x+10 \) \( y=8 x+1 \).

(b) \( \frac{3}{x-1}<\frac{2}{x} \)

Subtract the polynomials: \( (5x^{3} + 2x^{2} - 7) - (3x^{3} - x^{2} + 4) \)

Roger was told to think of a number, add 20 , then divide the result by 3 . The answer was Jower than Roger's original number. Deteruine the range of possible numbers Roger may have originally chosen.

In the \( x y \)-plane, a parabola has vertex \( (9,-14) \) and intersects the \( x \)-axis at two points. If the equation of the parabola is written in the form \( y=a x^{2}+b x+c \) where \( a, b \), and \( c \) are constants, which of the following could be the value of \( a+b+c \) ? (A) -23 (B) -19 (D) -12

8. \( \frac{\sqrt{27 a^{3} b^{6}}}{\sqrt{3 a b^{6}}-5 a b^{2}}= \)