Solve the following problems: 4. A car costs 6000. If a down payment of 15% is made, how much is still owed?…

Question

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)$.

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Here are the solutions to the problems.

4.

Calculate the amount of the down payment.
The down payment is $15\%$ of the car's cost. $\text{Down payment} = 0.15 \times \$6000 = \$900$
Calculate the remaining amount to pay.
The amount still to pay is the total cost minus the down payment. $\text{Amount to pay} = \$6000 - \$900 = \$5100$ The correct option is d.
The amount he still has to pay is \boxed{\text{\5100}}$.

5.
Factor out the greatest common factor from the expression.
The expression is $3a^2 + 3a - 18$ . The common factor is 3.
$3a^2 + 3a - 18 = 3(a^2 + a - 6)$
Factor the quadratic expression inside the parentheses.
We need two numbers that multiply to $-6$ and add to 1. These numbers are 3 and $-2$ .
$a^2 + a - 6 = (a+3)(a-2)$
Combine the factors.
$3(a^2 + a - 6) = 3(a+3)(a-2)$
The correct option is d.
The factored and simplified expression is $\boxed{3(a+3)(a-2)}$ .

6.
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 $\frac{(x-3)(x+3)}{4(x-3)}$ .
Rewrite the division as multiplication by the reciprocal of the second fraction.
$\frac{(x-3)(x+3)}{4(x-3)} \div \frac{x+3}{2} = \frac{(x-3)(x+3)}{4(x-3)} \times \frac{2}{x+3}$
Cancel common factors.
Assuming $x \neq 3$ and $x \neq -3$ , we can cancel $(x-3)$ and $(x+3)$ .
$\frac{\cancel{(x-3)}\cancel{(x+3)}}{4\cancel{(x-3)}} \times \frac{2}{\cancel{x+3}} = \frac{1}{4} \times 2 = \frac{2}{4} = \frac{1}{2}$
The correct option is b.
The simplified expression

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)$.

Answer

Step-by-step solution

Calculate the amount of the down payment.

Calculate the remaining amount to pay.

Factor out the greatest common factor from the expression.

Factor the quadratic expression inside the parentheses.

Combine the factors.

Factor the numerator and denominator of the first fraction.

Rewrite the division as multiplication by the reciprocal of the second fraction.

Cancel common factors.

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