In what interval is the function f(x)=squareroot x^2+5x+4 defined

9514 1404 393

  (-∞, -4] U [-1, ∞)

Step-by-step explanation:

The quadratic expression factors as ...

  x^2 +5x +4 = (x +4)(x +1)

The zeros of this expression are where these factors are zero, at x=-4 and x=-1. The product is negative when one factor is negative and the other is positive, in the region -4 < x < -1. It is non-negative elsewhere. f(x) is defined where the quadratic is not negative, on the union of intervals ...

  (-∞, -4] U [-1, ∞)

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i