1. Given the following system of equation, solve for p and q ( 10 points) 23p + 45q = 181 10p + 15q = 65 2. Given the following quadratic equation 12p2 - 7p + 1 = 0, find the value of p that will make the equation true. (10 points) 3. Find the values of x for the following non-linear equation (x4 + 1) (4 + x) = 0(10 points) 4. Find the domain of the function f defined by the formula ( 10 points) f (x) = 1/(x2 + x+ 1) 5. Let f (t) = 9 - (t - 3)2, compute 3f (3) + f(-6). ( 15 points) 6. Find the slopes and the equation of the lines passing through the following pairs of points of (2, -6) and (5, 8) (15 points) 7. Solve the following equations for x: 10x2-2x+2 = 100 (15 points) 8. Suppose demand D for a good is a linear function of its price per unit, P. When price is $10, demand is 200 units, and when price is $15, demand is 150 units. Find the demand function. ( 15 points)