Solve the following problems: 4. A car costs 6000. If a down payment of 15% is made, how much is still owed? 5. Factor the expression 3a2 + 3a - 18. 6. Simplify (x2-9)/(4x-12) / (x+3)/(2)$.

Here are the solutions to the problems. 4. Step 1: Calculate the amount of the down payment. The down payment is 15\% of the car's cost. Down payment = 0.15 × \6000 = \900 Step 2: Calculate the remaining amount to pay. The amount still to pay is the total cost minus the down payment. Amount to pay = \6000 - \900 = \5100 The correct option is d. The amount he still has to pay is \5100. 5. Step 1: Factor out the greatest common factor from the expression. The expression is 3a^2 + 3a - 18. The common factor is 3. 3a^2 + 3a - 18 = 3(a^2 + a - 6) Step 2: Factor the quadratic expression inside the parentheses. We need two numbers that multiply to -6 and add to 1. These numbers are 3 and -2. a^2 + a - 6 = (a+3)(a-2) Step 3: Combine the factors. 3(a^2 + a - 6) = 3(a+3)(a-2) The correct option is d. The factored and simplified expression is 3(a+3)(a-2). 6. Step 1: Factor the numerator and denominator of the first fraction. The numerator x^2 - 9 is a difference of squares: x^2 - 9 = (x-3)(x+3). The denominator 4x - 12 has a common factor of 4: 4x - 12 = 4(x-3). So the first fraction becomes ((x-3)(x+3))/(4(x-3)). Step 2: Rewrite the division as multiplication by the reciprocal of the second fraction. ((x-3)(x+3))/(4(x-3)) ÷ (x+3)/(2) = ((x-3)(x+3))/(4(x-3)) × (2)/(x+3) Step 3: Cancel common factors. Assuming x ≠ 3 and x ≠ -3, we can cancel (x-3) and (x+3). (x-3)(x+3)4(x-3) × (2)/(x+3) = (1)/(4) × 2 = (2)/(4) = (1)/(2) The correct option is b. The simplified expression