Suppose that the height (in centimeters) of a candle is a linear function of
the amount of time (in hours) it has been burning.
Let x be the amount of time in hours
Let y be the heoght of a candle in centimeters
The two points are then as (9,24.5) and (23,17.5).
![\mathrm{Find\:the\:line\:}\mathbf{y=mx+b}\mathrm{\:passing\:through\:}\left(9,\:24.5\right)\mathrm{,\:}\left(23,\:17.5\right)](https://tex.z-dn.net/?f=%20%5Cmathrm%7BFind%5C%3Athe%5C%3Aline%5C%3A%7D%5Cmathbf%7By%3Dmx%2Bb%7D%5Cmathrm%7B%5C%3Apassing%5C%3Athrough%5C%3A%7D%5Cleft%289%2C%5C%3A24.5%5Cright%29%5Cmathrm%7B%2C%5C%3A%7D%5Cleft%2823%2C%5C%3A17.5%5Cright%29%20)
![\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%20%5Cmathrm%7BSlope%5C%3Abetween%5C%3Atwo%5C%3Apoints%7D%3A%5Cquad%20%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20)
![\left(x_1,\:y_1\right)=\left(9,\:24.5\right),\:\left(x_2,\:y_2\right)=\left(23,\:17.5\right)](https://tex.z-dn.net/?f=%20%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%289%2C%5C%3A24.5%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%2823%2C%5C%3A17.5%5Cright%29%20)
![m=\frac{17.5-24.5}{23-9}](https://tex.z-dn.net/?f=%20m%3D%5Cfrac%7B17.5-24.5%7D%7B23-9%7D%20)
![m=-0.5](https://tex.z-dn.net/?f=%20m%3D-0.5%20)
![\mathrm{Plug\:the\:slope\:}-0.5\mathrm{\:into\:}y=mx+b](https://tex.z-dn.net/?f=%20%5Cmathrm%7BPlug%5C%3Athe%5C%3Aslope%5C%3A%7D-0.5%5Cmathrm%7B%5C%3Ainto%5C%3A%7Dy%3Dmx%2Bb%20)
![y=\left(-0.5\right)x+b](https://tex.z-dn.net/?f=%20y%3D%5Cleft%28-0.5%5Cright%29x%2Bb%20)
![\mathrm{Plug\:in\:}\left(9,\:24.5\right)\mathrm{:\:}\quad \:x=9,\:y=24.5](https://tex.z-dn.net/?f=%20%5Cmathrm%7BPlug%5C%3Ain%5C%3A%7D%5Cleft%289%2C%5C%3A24.5%5Cright%29%5Cmathrm%7B%3A%5C%3A%7D%5Cquad%20%5C%3Ax%3D9%2C%5C%3Ay%3D24.5%20)
![24.5=\left(-0.5\right)\cdot \:9+b](https://tex.z-dn.net/?f=%2024.5%3D%5Cleft%28-0.5%5Cright%29%5Ccdot%20%5C%3A9%2Bb%20)
![24.5=\left(-0.5\right)\cdot \:9+b](https://tex.z-dn.net/?f=%2024.5%3D%5Cleft%28-0.5%5Cright%29%5Ccdot%20%5C%3A9%2Bb%20)
![-4.5+b=24.5](https://tex.z-dn.net/?f=%20-4.5%2Bb%3D24.5%20)
![b=29](https://tex.z-dn.net/?f=%20b%3D29%20)
![\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=-0.5\mathrm{\:and\:}\mathbf{b}=29](https://tex.z-dn.net/?f=%20%5Cmathrm%7BConstruct%5C%3Athe%5C%3Aline%5C%3Aequation%5C%3A%7D%5Cmathbf%7By%3Dmx%2Bb%7D%5Cmathrm%7B%5C%3Awhere%5C%3A%7D%5Cmathbf%7Bm%7D%3D-0.5%5Cmathrm%7B%5C%3Aand%5C%3A%7D%5Cmathbf%7Bb%7D%3D29%20)
![y=-0.5x+29](https://tex.z-dn.net/?f=%20y%3D-0.5x%2B29%20)
Now plug in x=21, we get
![y=-0.5*21+29=18.5](https://tex.z-dn.net/?f=%20y%3D-0.5%2A21%2B29%3D18.5%20)
Thus the height of the candle after 21 hours is 18.5 centimeters.
Answer:
6 times
Step-by-step explanation:
well just divide 4.5 by 0.75 to get
Gg easey
perimiter is jsut the sum of the measures of the sides
P=2.3x+14+2x-0.2x+15
group like terms
P=2.3x+2x-0.2x+14+15
add
P=4.1x+29
answer is first one
I agree those answers make more sense to be true ^^^^
Answer:
42 - 6 - 6 - 6 - 6 - 6 - 6 - 6 = 0
or
42 - 7 - 7 - 7 - 7 - 7 - 7 = 0