The value \( V \) (in dollars) of a vehicle depends on the miles \( x \) that it has been driven. This is given in the formula \( V=22,000-0.25 x \). After one year, the value of a vehicle is between \( \$ 12,000 \) and \( \$ 15,000 \). Which range of miles driven corresponds to this range of values based on the given formula? \( 19,000 \leq x \leq 22,000 \) \( 28,000 \leq x \leq 40,000 \) \( 30,000 \leq x \leq 40,000 \) \( 13,000 \leq x \leq 19,000 \)

To find the range of miles driven that corresponds to values between \( \$12,000 \) and \( \$15,000 \), we can set up inequalities based on the given formula \( V = 22,000 - 0.25x \). 1. For \( V = 12,000 \): \[ 12,000 = 22,000 - 0.25x \] Rearranging gives: \[ 0.25x = 22,000 - 12,000 = 10,000 \implies x = \frac{10,000}{0.25} = 40,000 \] 2. For \( V = 15,000 \): \[ 15,000 = 22,000 - 0.25x \] Rearranging gives: \[ 0.25x = 22,000 - 15,000 = 7,000 \implies x = \frac{7,000}{0.25} = 28,000 \] Thus, the range of miles driven corresponding to this range of values is \( 28,000 \leq x \leq 40,000 \). Now, let's explore some interesting insights! Driving a car isn't just about the distance; it's also about how it ages over time. Did you know that the value drop in cars is mostly noticeable right after purchase? In fact, some vehicles can lose up to 20% of their value the moment they leave the dealership! This makes understanding depreciation crucial for potential buyers. If you're looking to maintain your vehicle's value, consider keeping track of your mileage and performing regular maintenance. Common mistakes include neglecting oil changes or ignoring warning lights. Keeping your car in good condition not only enhances safety but can also ward off the dreaded "yikes, my car lost so much value!" feeling when it’s time to sell.