Mathematics, 12.11.2019 03:31 jamerica0

Scratchpad
the chicken coup at the petting zoo is 10 by 14 feet. the farm would like to double the current area by adding the
same amount, x, to the length and width. what are the dimensions of the new enclosure? round to the nearest
hundredth of a foot.

Answers: 2

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Answer from: Ailany972

New width of coup =14.85 feet

New length of coup =18.85 feet

Step-by-step explanation:

Width of chicken coup = feet

Length of chicken coup= feet

Area of the coup = $length\times width = 10\times14=140\ ft^2$

New area is double the current area which is = $2\times140=280\ ft^2$

is added to both length and width.

New width of coup = 10+x feet

New length of coup = 14+x feet

New area of coup can be written as = $length\times width =(10+x)\times(14+x)$

So, we have

(10+x)(14+x)=280

Using FOIL method to multiply.

$(10\times14)+10x+14x+x^2=280\\140+24x+x^2=280$

Subtracting 280 both sides.

140+24x+x^2-280=280-280

Rearranging terms, we have the quadratic equation to solve.

x^2+24x-140=0

Using quadratic formula to find

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values.

$x=\frac{-24\pm\sqrt{24^2-(4(1)(-140))}}{2(1)}$

$x = \frac{ -24\pm\sqrt{576-(-560)}}{2}\\$

$x = \frac{ -24\pm\sqrt{1136}}{2}$

$x = \frac{-24\pm 4\sqrt{71}}{2}$

$x = \frac{-24}{2} \pm \frac{4\sqrt{71}}{2}$

$\therefore x=4.8523\approx 4.85\ and\ x=-28.8523\approx -28.85$

Since is the length, so it cannot be negative. So x=4.85

New width of coup = 10+x=10+4.85=14.85 feet

New length of coup = 14+x=14+4.85=18.85 feet

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

step-by-step explanation:

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