Multi-Step Inequalities 23
The average cost of gas where you live is $3.50 per gallon. You are trying to
decide whether to buy a hybrid or a standard car. The hybrid gives you 45
miles per gallon (mpg) and the standard gives you 25 mpg. The hybrid car
costs $8,960 more than the standard.
What is the minimum miles you would need to drive in order for your savings
on fuel to surpass the additional cost of the hybrid vehicle?

inverse property is the answer

step-by-step explanation:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west