Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after 9 hours of burning, a candle has a height of 17.5 centimeters. after 24 hours of burning, its height is 22 centimeters. what is the height of the candle after 22 hours?

 The candle has a height of 21.4 cm after burning for 22 hours.

Step-by-step explanation:

let x=hours, m=rate of change,  and  y= candle height

First you have to find the slope or, rate of change using the slope formula.  y2-y1 divided by x2-x1   .        

Here is our points    (9,     17.5)   and   (24,    22)

                                    x1       y1                 x2     y2

Now we put these into the equation and solve

  =

Now that we have the slope of 3/10 we can use this to find the y-intercept using the point-slope equation.

                y-17.5= .3(x-9) Solve

y-17.5=.3x-2.7                                        y  -14.8=      .3x

 +2.7         +2.7                                         +14.8               +14.8

y=.3x+14.8                     the y-intercept is 14.8

Now we use this equation to  plug in the 22 hours.

y=.3(22) +14.8

y=6.6+14.8

y= 21.4    The candle has a height of 21.4 cm after burning for 22 hours.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it