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LuckyWell [14K]
2 years ago
11

Let f (x) = -1/2(x + 2)+ 5

Mathematics
1 answer:
bogdanovich [222]2 years ago
8 0

Answer:

Rate of change = -1

Step-by-step explanation:

Given:

f(x) = -½(x + 2)² + 5

Required:

Average rate of change from x = -3 to x = 1

Solution:

Rate of change = \frac{f(b) - f(a)}{b - a}

Where,

a = -3,

f(a) = f(-3) = -½(-3 + 2)² + 5 = -½(-1)² + 5 = 4.5

b = 1,

f(b) = f(1) = -½(1 + 2)² + 5 = -½(9) + 5 = 0.5

Plug in the values into the formula:

Rate of change = \frac{0.5 - 4.5}{1 - (-3)}

Rate of change = \frac{-4}{4}

Rate of change = -1

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The answer is:  [D]:  " 24 + 2w " .
___________________________________________
Explanation:
___________________________________________
Given: The formula for the Perimeter of a rectangle:
___________________________________________
   P = 2L + 2w ; 
  
                 in which:
                                P = perimeter ;
                                L = length = 12 units (given); 
                                w = width = unknown;
_______________________________________________________
           Find the perimeter, "P", in terms of "w" ; since "w" (width) is unknown; and considering the answer choices given; along with the information provided in the problem, we only have enough information to solve for the perimeter, "P", in terms of "w" ; 
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         So, given the formula/equation for the perimeter, "P" :
_____________________________________________________
       P = 2L + 2w ;  we know that:  " L = 12 units " ;
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       P = 2*12  +  2w  =  24 + 2w ;  which is:  "Answer choice: [D]" .
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