Find the length of the third side. If necessary, round to the nearest tenth. 10 14 ​

3.7 units

Explanation:

According to Pythagoras theorem, the square of length of the hypotenuse is equal to the sum of squares of lengths of other two sides.

Let the third side be x units.

Then,

x² + 10² = 14²

=> x² + 100 = 196

=> x² = 196 - 100

=> x² = 96

=> x = √96

=> x = 4√6

=> x = 3.79

=> x = 3.8 (Rounding to the nearest tenths)

So, the length of the third side is 3.8 units

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.

the third picture

step-by-step explanation: