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Ipatiy [6.2K]
2 years ago
14

The area of a rectangular piece of cardboard is represented by

Mathematics
1 answer:
Liula [17]2 years ago
5 0

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

A = wl

w(2w + 3) = 9

From this, we get that:

l = 2w + 3, A = 9

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

In this question:

w(2w+3) = 9

2w^2 + 3w - 9 = 0

Thus a quadratic equation with a = 2, b = 3, c = -9

Then

\Delta = 3^2 - 4(2)(-9) = 81

w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5

w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

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A) 
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Hope this helps!
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3 years ago
A sum of money is shared among Ben, Jack, and Sarah in the ratio 6 : 8 : 10.
alexdok [17]

Answer:

B:J:S

6:8:10

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8 0
2 years ago
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Which expressions are equivalent to 2(2x + 4y + x − 2y)?
joja [24]

Answer: 2(3x + 2y) and 6x + 4y

Step-by-step explanation:

Hi, to answer this question we have to solve the expression.

2(2x + 4y + x − 2y)

First we have to simplify the expression within the brackets.

2 (2x + x +4y -2y)

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We have the first equivalent expression. Now to obtain the second expression we apply distributive property:

2 (3x) + 2 ( 2y)

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In conclusion 2(3x + 2y) and 6x + 4y are equivalent expressions to 2(2x + 4y + x − 2y).

Feel free to ask for more if it´s necessary or if you did not understand something.

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3 years ago
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