Please help me. I'm lost.

What is the average rate of change of the function f(x) on the interval 6 < x < 8

Rainbow [258]

Answer:

Step-by-step explanation:

The

average rate of change

of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the

secant line

connecting the 2 points.

To calculate the average rate of change between the 2 points use.

∣

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

a

f

(

b

)

−

f

(

a

)

b

−

a

∣

−−−−−−−−−−−−−−−

f

(

9

)

=

9

2

−

6

(

9

)

+

8

=

35

and

f

(

4

)

=

4

2

−

6

(

4

)

+

8

=

0

The average rate of change between (4 ,0) and (9 ,35) is

35

−

0

9

−

4

=

35

5

=

7

This means that the average of all the slopes of lines tangent to the graph of f(x) between (4 ,0) and (9 ,35) is 7.

8 0

3 years ago

Which of the following does not factor as a perfect square trinomial?

Ede4ka [16]

Answer:

Option C. x^2-18x-81

Step-by-step explanation:

A. 16a^2-72a+81

x^2-2xy+y^2=(x-y)^2

x^2=16a^2→sqrt(x^2)=sqrt(16a^2)→x=sqrt(16) sqrt(a^2)→x=4a

y^2=81→sqrt(y^2)=sqrt(81)→y=9

2xy=2(4a)(9)→2xy=72a equal to the second term of the expression, then we can factor as a perfect square trinomial:

16a^2-72a+81=(4a-9)^2

B. 169x^2+26xy+y^2

a^2+2ab+b^2=(a+b)^2

a^2=169x^2→sqrt(a^2)=sqrt(169x^2)→a=sqrt(169) sqrt(x^2)→a=13x

b^2=y^2→sqrt(b^2)=sqrt(y^2)→b=y

2ab=2(13x)(y)→2ab=26xy equal to the second term of the expression, then we can factor as a perfect square trinomial:

169x^2+26xy+y^2=(13x+y)^2

C. x^2-18x-81

a^2+2ab+b^2=(a+b)^2

This expression does not factor as a perfect square trinomial because the third term is negative (-81).

D. 4x^2+4x+1

a^2+2ab+b^2=(a+b)^2

a^2=4x^2→sqrt(a^2)=sqrt(4x^2)→a=sqrt(4) sqrt(x^2)→a=2x

b^2=1→sqrt(b^2)=sqrt(1)→b=1

2ab=2(2x)(1)→2ab=4x equal to the second term of the expression, then we can factor as a perfect square trinomial:

4x^2+4x+1=(2x+1)^2

4 0

3 years ago

If a 4 x 16 riangle has the same area as a square, what is the length of a side of the square

m_a_m_a [10]

Answer: $\bold{4\sqrt2}$

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

$A_{triangle}=\bigg(\dfrac{1}{2}\bigg)b\times h$

$A_{triangle}=\bigg(\dfrac{1}{2}\bigg)4\times 16$

$=\bigg(\dfrac{1}{2}\bigg)64$

$=32$

$A_{square}= s^2$

$32 = s^2$

$\sqrt{32}=s$

$\sqrt{\underline{2\cdot 2}\cdot \underline{2\cdot 2}\cdot 2}=s$

$2\cdot 2\sqrt{2}=s$

$4\sqrt{2}=s$

7 0

3 years ago

What is 1/2 • 1 • 2 please help

BabaBlast [244]

Answer:

1

Step-by-step explanation:

1/2x1x2

1

8 0

2 years ago

The table shows the times of the top six swimmers in the women’s 100 meter butterfly at the 2012 Olympic Games. A 2-column table

DENIUS [597]

Answer:

The difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds.

Step-by-step explanation:

The first positioned swimmer took 55.98 seconds and the second positioned swimmer took 56.87 seconds to complete the race.

So, the difference is (56.87 - 55.98) = 0.89 seconds.

The second positioned swimmer took 56.87 seconds and the third positioned swimmer took 56.94 seconds to complete the race.

So, the difference is (56.94 - 56.87) = 0.07 seconds.

The third positioned swimmer took 56.94 seconds and the fourth positioned swimmer took 57.17 seconds to complete the race.

So, the difference is (57.17 - 56.94) = 0.23 seconds.

The fourth positioned swimmer took 57.17 seconds and the fifth positioned swimmer took 57.27 seconds to complete the race.

So, the difference is (57.27 - 57.17) = 0.10 seconds.

The fifth positioned swimmer took 57.27 seconds and the sixth positioned swimmer took 57.35 seconds to complete the race.

So, the difference is (57.27 - 57.35) = 0.08 seconds.

Therefore, the difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds. (Answer)

5 0

3 years ago

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