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3 years ago

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The width of a rectangle is the length minus 3 units. The area of the rectangle is 40 units. What is the width, in units, of the

rectangle?

1 answer:

marusya05 [52]3 years ago

5 0

Width of the rectangle is 5 units

<u>Explanation:</u>

Let length (l) = l units

Given,

width (b) = l-3 units

Area of rectangle = 40 units

We know,

Area of rectangle = l X b

$40= l(l-3)\\40=l^{2} - 3l\\l^{2} - 3l -40=0\\l=8units$

If l = 8 units then, b = 8-3 units

b = 5 units

Therefore, width of the rectangle is 5 units.

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

mariarad [96]

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.

4 0

3 years ago

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