Ahot air balloon is 10 meters above the ground and rising at a rate of 15 meters per minute. another balloon is 150 meters above the ground and descending at a rate of 20 meters per minute. what is the solution of the system of equations? make sure you write the answer as an ordered pair.

(4, 70)

Step-by-step explanation:

Let's call

x: time, in minutes

y: height of the balloon, in meters

The height of the rising balloon is modeled as follows:

y = 15x + 10 (eq. 1)

The height of the descending balloon is modeled as follows:

y = -20x + 150 (eq. 2)

Combining equations 1 and 2:

15x + 10 = -20x + 150

15x + 20x  = 150 - 10

35x = 140

x = 140/35 = 4

Replacing it in equation 1:

y = 15(4) + 10 = 70

So, the solution is (4, 70), that is, after 4 minutes both balloons will have the same height, which is 70 meters.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.