The function f(x)= -(x+5)(x+1) is down. what is the range of the function?

(-∞, 4)

Step-by-step explanation:

"The function f(x)= -(x+5)(x+1) is down" should be "The function f(x)= -(x+5)(x+1) has a parabolic graph that opens down."

Expanding f(x)= -(x+5)(x+1), we get  f(x) = -[x^2 + 6x + 5] = -x^2 - 6x - 5.

Here the coefficients are a = -1, b = -6 and c = -5.  Thus, the axis of symmetry is

         -(-6)

x = = -3.  

        2(-1)

The maximum value of the function occurs  when x = -3.

We must also find the actual max value.  

It is f(-3) = -(-3)^2 - 6(-3) - 5, or 4.

The max value is 4.  Thus, the range of this function is (-∞, 4)

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,