1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Paladinen [302]
3 years ago
15

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 24.5 centimeters. After 23 hours of burning, its height is 17.5 centimeters. What is the height of the candle after 21
hours?
___ centimeters
Mathematics
1 answer:
natka813 [3]3 years ago
7 0

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)

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(9,\:24.5\right),\:\left(x_2,\:y_2\right)=\left(23,\:17.5\right)

m=\frac{17.5-24.5}{23-9}

m=-0.5

\mathrm{Plug\:the\:slope\:}-0.5\mathrm{\:into\:}y=mx+b

y=\left(-0.5\right)x+b

\mathrm{Plug\:in\:}\left(9,\:24.5\right)\mathrm{:\:}\quad \:x=9,\:y=24.5

24.5=\left(-0.5\right)\cdot \:9+b

24.5=\left(-0.5\right)\cdot \:9+b

-4.5+b=24.5

b=29

\mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=-0.5\mathrm{\:and\:}\mathbf{b}=29

y=-0.5x+29

Now plug in x=21, we get

y=-0.5*21+29=18.5

Thus the height of the candle after 21 hours is 18.5 centimeters.

You might be interested in
Which is the better buy?<br>12 bars of soap for $10.00 or 5 bars of soap for $4.00
Eddi Din [679]

Answer:

12 bars of soap for $10.00, but actullay the are both the same. if u buy 5 bars of soap for $4.00 then the next time u buy 7 bars of soap, your are still using the same amount of money.

Step-by-step explanation:


4 0
3 years ago
What is 1 1/4 × 4 3/4 =
Luden [163]
First, we need to turn this into an improper fraction. Therefore we have: 1 1/4 = 5/4 and 4 3/4 = 19/4
Now we multiply across and eliminate as needed.
5/4 * 19/4 = 95/16
Finally, we reduce and convert to a mixed fraction.
16 goes into 95, 5 times with a remainder of 15. Therefore, we can conclude that our answer is: 5 15/16.
4 0
3 years ago
Please help meeee PLEASEE no links :(
Tasya [4]

Answer:

C

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Some adults and children went to a movie.
aalyn [17]
4 adults and 8 children
3 0
3 years ago
Read 2 more answers
Help soon!!! tysm!!!
victus00 [196]

Answer:

36-b  ^ { 2  }  -c  ^ { 2  }  +2bc\\36-\left(b^{2}+c^{2}-2bc\right) \\6^{2}-\left(b-c\right)^{2} \\\boxed{\left(6-b+c\right)\left(6+b-c\right) }

Hope it helps ⚜

7 0
2 years ago
Other questions:
  • Write 720 as a product of its prime factors
    7·2 answers
  • As Jupiter revolves around the sun, it travels at a rate of approximately miles per second. Convert this rate to kilometers per
    10·1 answer
  • If the length and breadth of a rectangle are 10cm and 20cm respectively,find the length of its diagonal
    6·2 answers
  • Graph the line through points (-1, -3) and (7, -8)<br> From the graph, tell whether the slope is..
    15·1 answer
  • what is the greatest six digit number in which the thousands place is twice the digit in the tens place what is the least number
    6·1 answer
  • Alecia builds a box in the shape of a cube with an open top. She plans to paint the box. Alecia calculates that there are 256 sq
    7·2 answers
  • Help me mdkskkeeknsjeleksksk
    9·1 answer
  • Let |q| = 5 at an angle of 45° and |r| = 16 at an angle of 300°. What is |q – r|?
    9·2 answers
  • Multiply (5x^2-6x+2) x (4x^2-3x)
    7·1 answer
  • Eight values have a mean of 7. a ninth value is added. the new mean is 9. what is the new value
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!