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Oksi-84 [34.3K]
3 years ago
6

Nirmala graphed the relationship between the duration (in hours) of using an oil lamp and the volume (in milliliters) of oil rem

aining. what feature if the graph represents how long Nirmala can use the lamp before it runs out of oil?

Mathematics
2 answers:
Ksju [112]3 years ago
6 0

Answer:

the answer is

x-intercept

Step-by-step explanation:

im doing the quiz right now

mariarad [96]3 years ago
4 0

Answer:

Nirmala can use the lamp for 31.66 hours before it runs out of oil.

Step-by-step explanation:

From the graph,

Take any two points, let say

(15, 25)

(25, 10)

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

\left(x_1,\:y_1\right)=\left(15,\:25\right),\:\left(x_2,\:y_2\right)=\left(25,\:10\right)

m=\frac{10-25}{25-15}

m=-\frac{3}{2}

The equation of line in slope-intercept form

y = mx + b

Putting m=-\frac{3}{2}  and any point, let say (25, 10), to find the y-intercept 'b'

10=-\frac{3}{2}\left(25\right)+b

-\frac{3}{2}\left(25\right)+b=10

-\frac{75}{2}+b=10

\mathrm{Add\:}\frac{75}{2}\mathrm{\:to\:both\:sides}

-\frac{75}{2}+b+\frac{75}{2}=10+\frac{75}{2}

b=\frac{95}{2}

b=47.5

So the equation of line will be:

y = mx + b

y=-\frac{3}{2}x+47.5

In order to find how long Nirmala can use the lamp before it runs out of oil, we need to find x-intercept which can be obtained by putting y = 0, and solve for x, as duration lies on x-axis.

so

y=-\frac{3}{2}x+47.5

Putting y = 0

0=-\frac{3}{2}x+47.5

-\frac{3}{2}x+47.5=0

-\frac{3}{2}x=-47.5

\mathrm{Multiply\:both\:sides\:by\:}2

2\left(-\frac{3}{2}x\right)=2\left(-47.5\right)

-3x=-95

\mathrm{Divide\:both\:sides\:by\:}-3

\frac{-3x}{-3}=\frac{-95}{-3}

x=\frac{95}{3}

x=31.66

Therefore, Nirmala can use the lamp for 31.66 hours before it runs out of oil.

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