QUESTION A candle is 16 in. tall after burning for 3 hours. After 5 hours, it is 15.5 in. tall. Write a linear equation to model the relationship between height (h) of the candle and time (t). Predict how tall the candle will be after burning 2 hours.

For the linear equation you have two points (3, 17) and (5, 15) so the equation is: h-17=(15-17)/(5-3)*(t-3), solve for h= -t+20.

For predicting, only replace t=8 into you equation (h= -t+20) and you will get h=-8+20=12

Using the data given, you should create 2 points: (time,inches)

The 2 points should be: (3,17) and (5,15)

Then use the slope formula: (y2-y1)/(x2-x1)

(15-17)/(5-3)

-2/2

-1

So the slope end up equaling -1

Then use y=mx+b

m is the slope, and it doesn’t matter what points we plug in for x and y, but they have to be from the same point. For this, I’m gonna use (17,3)

3=(-1)(17)+b

Now solve for b

3=-17+b

+17 +17

20=b

Now your equation is: y=-1x+20

Now it asks how long after 8 hours, so we plug in 8 for x:

Y=(-1)(8)+20

Y=-8+20

Y=12

So the candle will be 12 inches long after 8 hours.

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation:

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.