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finlep [7]
4 years ago
9

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 6 hours of burning, a candle has a height of 17.4 centimeters. After 23 hours of burning, its height is 7.2 centimeters. What is the height of the candle after 11 hours?
Mathematics
1 answer:
Alborosie4 years ago
7 0
Assume that the rule connecting height of the candle to time is a linear one.  If you do, then we have to find the equation of this line, and then use this equation to predict the height of the candle after 11 hours.

Two points on this line are (6,17.4) and (23, 7.2).  The slope is thus
         7.2-17.4           -6
m = ---------------  =  -----------  or   -3/5.
           23-6                 10

Find the equation of the line.  I'm going to use the slope-intercept formula:

y = mx + b  =>   7.2 = (-3/5)(23) + b.  Solving for b,   b = 21.

Now    we know that y = (-3/5)x + 21

Let x=11 to predict the height of the candle at that time.

y = (-3/5)(11) + 21 = 14.4 inches  (answer)
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Answer:

x= 12/5

Step-by-step explanation:

Also, if you mean simplify, it can no longer be simplified, so it would just be

1/4x-3/5.

Hope this helps!!

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6 0
3 years ago
How can the Pythagorean theorem be used to help classify triangles
kompoz [17]

Answer:

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Step-by-step explanation:

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6 0
4 years ago
EM Company produces two types of laptop computer bags. The regular version requires $32 in capital and 4 hours of labor and sell
expeople1 [14]

Answer:

Step-by-step explanation:

Given that EM company produces two types of laptop computer bags.

Let regular version produced be R and deluxe version be D

Total capital required

= 32R+38D\leq 2100

Total labor hours required

=4R+6D\leq 280

Sales revenue = 46R+55D

Solving the two constraints we have

10D \leq 140

D can be atmost 14 and hence R can be 49

Otherwise if D is made 0, R = 65 maximum

If R is made 0, D maximum is 46

Thus corner points are (65,0) (0.,46) or (49,14)

Sales revenue for (65,0) = 2990

(0,46) is 2530

(49,14) is 3024

Maximum when R =14 and D is 49

5 0
4 years ago
B) y = log2 (4" - 4)<br> find the inverse of this equation
GuDViN [60]

Answer:

y =  \frac{1}{4}  \times  {2}^{x}  - 1

Step-by-step explanation:

Assuming the given logarithmic equation is

y =   \log_{2}( {4}{x }  - 4)

We interchange x and y to get:

x=   \log_{2}( {4}{y} - 4)

We solve for y now:

{2}^{x}  =  {4}{y}   - 4

We add 4 to both sides to get;

{2}^{x}  + 4 = 4y

Divide through by 4:

y =  \frac{1}{4}  \times  {2}^{x}  - 1

4 0
4 years ago
A dilation centered at the origin is applied to the line y = 3x + 5.
SOVA2 [1]

Answer:

"The question cannot be answered without knowing the scale factor."

Step-by-step explanation:

<u>The complete question:</u>

<em>A dilation centered at the origin is applied to the line y = 3x + 5.  What is true about the image of the line?</em>

  • <em>It is the same line. </em>
  • <em> It is another line parallel to y = 3x + 5. </em>
  • <em> The image is not a line. </em>
  • <em> The question cannot be answered without knowing the scale factor.</em>

<em />

A dilation, center at origin, with a scale factor of "k", will have a rule:

(x,y) = (kx,ky)

This basically means that the image after dilation will have the points kx and ky respectively.

If k ≠ 1, this means the image is parallel to the line y = 3x + 5

If k = 1, this means the image is same, it coincides with the line y = 3x + 5

<u><em>Thus, the scale factor is really important and we can't say anything about this dilation since scale factor isn't known.</em></u>

<em />

<em />

8 0
3 years ago
Read 2 more answers
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