Over what interval is the graph of f(x) = –(x + 8)2 – 1 decreasing?

The given function f(x) is decreasing on the interval : (-8, +∞)

Step-by-step explanation:

The function is given to be : f(x) = (x + 8)² - 1

To find the interval of decreasing, first find the critical points of the function f(x)

f(x) = (x + 8)² - 1

⇒ f'(x) = 2(x + 8)

Critical Point : x = -8

Now, Intervals are : (-∞ , -8) and (-8, +∞)

For the interval : (-∞ , -8)

f'(x) > 0 ⇒ f(x) is increasing on this interval.

For the interval : (-8, +∞)

f'(x) < 0 ⇒ f(x) is decreasing on this interval.

Hence, The given function f(x) is decreasing on the interval : (-8, +∞)

answer: 25.4 units

step-by-step explanation: radius = 12.7 units

diameter = twice the radius

diameter = 12.7 x 2

= 25.4

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

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