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mrs_skeptik [129]
2 years ago
13

Ralph wants to build a rectangular deck with a predefined area of 66 feet squared. One side of the deck will be 5 feet longer th

an the other. To find the side lengths, he first writes the equation (x)(x+5)=66 and later simplifies (x-6)(x+11)=0 it to , where x is the length of the shorter side. Which of these are the side lengths, in feet, of the rectangular deck? Select all that apply
Mathematics
1 answer:
Lorico [155]2 years ago
4 0

Answer:

<h2>The shorter side is 6 ft and the longer side is 11 ft</h2>

Step-by-step explanation:

The options are not given, but we could solve and arrive at an answer

say the shorter side is x

and the longer side is x+5

we know that the area of a rectangle is given as

x*(x+5)=66

open the bracket

x^2+5x=66

x^2+5x-66=0

Find two factors of  -66  whose sum equals the coefficient of the middle term, which is   5 .

the factors are 11 and -6

splitting the middle term using the two factors  11  and  -6

x2 +11x - 6x - 66=0

x(x+11)-6(x+11)=0

(x-6)=0

x=6

(x+11)=0

x=-11

The shorter side is 6 ft and the longer side is 11 ft

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\left(x-5\right)^3-1=-3

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\mathrm{For\:}g^3\left(x\right)=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}

Thus, the input values are:

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And the real input is:

x=-\sqrt[3]{2}+5

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