Patrick has just finished building a pen for his new dog. the pen is 3 feet wider than it is long. he also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base. after putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen. he also finds that the perimeter of the pen is 3 times greater than the perimeter of the doghouse if x represents the length of the pen and y represents the area of the doghouse, then which of the following systems of equations can be used to determine the length and width of the pen and the area of the doghouse? . a. 178 = 12 + 3.5 - y -6 = 41 - 3y + y b. 178 = 12 + 3 "-6 = 41 – 3y c. 178 = 12 + 3.1 -6 = 41 – 3y d. 178 = 12 – 31 - y 6 = 41 – 37

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! : )

cretdit to source

it's 100

step-by-step explanation:

22, 28, 34, 40, 46

b)   f(n) = 6n + 16

  n = what is the number of the row ( 22 would be row 1) so if we replaced n with 1, we would get 22

c)   the  14th  row will have 100 seats

(1)   (2)   (3)   (4)   (5)   (6)   (7)   (8)   (9)   (10) (11) (12) (13) (14)

22 | 28 | 34 | 40 | 46 | 52 | 58 | 64 | 70 | 76 | 82 | 88 | 94 | 100

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