Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Two hot air balloons are flying above a park. One balloon started at a height of 3,000 feet above the ground and is decreasing in height at a rate of 40 feet per minute. The second balloon is rising at a rate of 50 feet per minute after beginning from a height of 1,200 feet above the ground. Given that h is the height of the balloons after m minutes, determine which system of equations represents this situation. A. h = 3,000 - 40m h = 1,200 50m B. m = 3,000 - 40h m = 1,200 50h C. h = 3,000 40m h = 1,200 - 50m D. h = 3,000m - 40 h = 1,200m 50

Sagot :

Answer:

A. h = 3,000 - 40m; h = 1,200 + 50m

Step-by-step explanation:

Linear Equations

The equation of a linear function is

                                                y = mx + b,

where m is the slope or rate of change--can be positive or negative--and b is the y-intercept or the initial value of the function when x = 0.

[tex]\dotfill[/tex]

Breaking down the Problem

One balloon starts at an altitude of 3,000 feet before the first minute struck, this is our b value. It then decreases by 40 feet every minute, so -40 is our slope value.

So, the equation for the first balloon is

                                           y = -40x + 3000,

or

                                           h = -40m + 3000,

where m is the number of minutes that pass--no longer the rate of change--, and h is the elevation after m minutes.

The second balloon starts at an altitude of 1,200 feet before the first minute struck, this is our b value. Its altitude increases by 50 feet every minute, so 50 is our slope value.

So, the equation for the second balloon is

                                            y = 50x + 1200,

or

                                           h = 50m + 1200.

Both equations of this system match answer choice A, so that's our answer!

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.