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kykrilka [37]
4 years ago
9

The expression

6" alt="x {?}^{2} - 16" align="absmiddle" class="latex-formula">
is equivalent to
Mathematics
1 answer:
skad [1K]4 years ago
5 0
Hi Mpmolina, 

x² - 16
= (x)² - (4)²
= (x - 4)(x + 4)
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Given the function f(x)=x^2-8x+13f(x)=x, determine the average rate of change of the function over the interval −1≤x≤6.
Ann [662]

Given:

Consider the given function is:

f(x)=x^2-8x+13

To find:

The average rate of change of the function over the interval -1\leq x\leq 6.

Solution:

The average rate of change of the function f(x) over the interval [a,b] is:

m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}

We have,

f(x)=x^2-8x+13

At x=-1,

f(-1)=(-1)^2-8(-1)+13

f(-1)=1+8+13

f(-1)=22

At x=6,

f(6)=(6)^2-8(6)+13

f(6)=36-48+13

f(6)=1

Now, the average rate of change of the function f(x) over the interval -1\leq x\leq 6 is:

m=\dfrac{f(6)-f(-1)}{6-(-1)}

m=\dfrac{1-22}{7}

m=\dfrac{-21}{7}

m=-3

Therefore, the average rate of change of the function f(x) over the interval -1\leq x\leq 6 is -3.

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<h3>Answer:</h3>

For each birdhouse built, the total cost increases by $3.50.

<h3>Step-by-step explanation:</h3>

Let's try some of the answers and see if they work.

The "initial cost" will be the cost when 0 birdhouses are built.

... f(0) = 3.5·0 +24 = 24 . . . . . clearly, not $3.50

Then increasing the number of birdhouses by 1, the cost is ...

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Clearly the total cost to build 1 birdhouse is not $3.50. (It is $27.50.)

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... For each birdhouse built, the total cost increases by $3.50.

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