6. The line with equation \( y=4 x+c \), where \( c \) is a constant, meets the curve with equation \( y=x(x-3) \) at only one point. (a) Find the value of \( c \). (b) Hence find the coordinates of the point of intersection.

Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was \( \$ 420 \). Each envelope costs \( \$ 0.03 \) and they get paid \( \$ 0.06 \) per envelope stuffed. Let \( x \) represent the number of envelopes stuffed. (a) Express the cost \( C \) as a function of \( x \). (b) Express the revenue \( R \) as a function of \( x \). (c) Determine analytically the value of \( x \) for which revenue equals cost. (a) \( C(x)=\square \) (C in dollars) (b) \( R(x)=\square \) ( \( R \) in dollars) (c) Revenue equals cost when \( x=\square \)

Linear Application The function \( E(t)=3848-77.1 t \) gives the surface elevation (in feet above sea level) of Lake Powell \( t \) years after 1999. Interpret the Slope in this situation. The surface elevation of Lake Powell is Select an answer \( \vee \) at a rate of

(c) \( 3 x^{2}-x=x^{2}-5 x+6 \)

(c) \( 3 x^{2}-x=x^{2}-5 x+6 \)

Rationalize the Denominator: \( \frac{4+\sqrt{7}}{3+\sqrt{7}} \)