Joan wants to buy a rug for a room that is 1111 feet by 1414 feet. she wants to leave a uniform strip of floor around the rug. she can afford 8888 square feet of carpeting. what dimensions should the rug have?

Solution:

Let  x be the width of the strip.

Width of rug = 1111 - 2x

Length of rug = 1414 - 2x

Area of carpet = 8888

Area = Length * Width

8888 = (1414 - 2x) (1111 - 2x)

8888 = 1570954 - 2222x - 2828x + 4x²

4x² - 5050x + 1562066 = 0

2x² - 2525x + 781033 = 0

x = 720.5, 542

So, the value of x is 542.

Width of rug = 1111 - 2(542) = 27

Length of rug = 1414 - 2(542) = 330

Hence, the dimensions are 330, 27.

where is the figure

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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