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3 years ago

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A builder cuts a rectangular hole in a ceiling to install an exhaust fan. The width is 3 in. less than the length and the area i

s 180 in². Find the length and width of the hole.

1 answer:

slavikrds [6]3 years ago

8 0

Area of a rectangle = l * w

A = Area of a rectangle

l = length

w = width

In our problem,

l = x

w = x - 3

A = 180 square inches

Plug our numbers into the area formula of a rectangle

180 square inches = x(x-3)

Distribute the x into (x-3)

180 square inches = x^2 - 3x

subtract 180 from both sides

0 = x^2 - 3x -180.

Factor the express on the left side of the equation

0 = (x-15) (x+12).

Set each term equal to zero and solve for x

x+12 = 0.

Subtract 12 from both sides

x = -12 <--- lengths of a rectangle cannot be negative, therefore, we need to check the other term we factored.

set x-15 equal to zero

x-15 = 0.

Add 15 to both sides

x = 15.

We know l = x so now we know that the length i = 15 inches.

We also know that the width = length - 3

w = 15 - 3

w = 12

The width is 12 inches and the length is 15 inches

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well, from the 1st equation, we know what "c" is already, so let's just plug that in the 2nd equation and solve for "b".

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well, now let's plug that "b" into our 3rd equation and solve for "a".

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3 years ago

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Please help! question attached

Svetradugi [14.3K]

Answer:

36. y=x

37. x=4

38. y=3x-10

39. y=-25x+49

40. $y=-\dfrac{1}{18}x-\dfrac{89}{18}$

41. y=-x+3

Step-by-step explanation:

36. Parallel lines have the same slope. The slope of the line $y=x+42$ is $m=1,$ so the equation of a parallel line is

$y=x+b$

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$2=2+b\\ \\b=0$

and the equation of the line is $y=x$

37. The line $x=03$ is vertical ine, so parallel line is also vertical line with equation $x=a.$ Substitute the coordinates of the point (4,3):

$4=a$

hence the equation is $x=4$

38. Parallel lines have the same slope. The slope of the line $y=3x+24$ is $m=3,$ so the equation of a parallel line is

$y=3x+b$

This line passes through the point (2,-4), so its coordinates satisfy the equation:

$-4=3\cdot 2+b\\ \\b=-10$

and the equation of the line is $y=3x-10$

39. Parallel lines have the same slope. The slope of the line $y=-25x+35$ is $m=-25,$ so the equation of a parallel line is

$y=-25x+b$

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$-1=-25\cdot 2+b\\ \\b=49$

and the equation of the line is $y=-25x+49$

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The equation is

$y=-\dfrac{1}{18}x+b$

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and the equation of the line is $y=-\dfrac{1}{18}x-\dfrac{89}{18}$

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The equation is

$y=-x+b$

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$-1=-4+b\\ \\b=3$

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3 years ago

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Answer:

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