Find the average rate of change of h(x) = - x ^ 2 + 3x + 3 from x = 2 to x = 6 .

Answers

Answer 1

Answer:

The average rate of change is

Δy ÷ Δx = -20 ÷ 4

Δy/Δx = -20/4

          = -5      

Step-by-step explanation:

Given the function

[tex]h\left(x\right)\:=\:-x^2\:+\:3x\:+\:3[/tex]

Putting x = 6

[tex]h\left(6\right)\:=\:-\left(6\right)^2\:+\:3\left(6\right)\:+\:3[/tex]

         [tex]=-36+18+3[/tex]

          [tex]=-15[/tex]

Putting x = 2

[tex]h\left(2\right)\:=\:-\left(2\right)^2\:+\:3\left(2\right)\:+\:3[/tex]

         [tex]= -4 + 6 +3[/tex]

         [tex]= 5[/tex]

The change in y from 2 to 6 is

Δy = -15 - 5

    = -20

The interval from 2 to 6 has a width of

Δx = 6 - 2

     = 4

Therefore, the average rate of change is

Δy ÷ Δx = -20 ÷ 4

Δy/Δx = -20/4

          = -5      


Related Questions

PLEASE HELP!!!! 50 POINTS!!!
Find the solution(s) of the following equation.
x^2 = 100/361
Choose all answers that apply:
a) x = -10/9
b) x = -1/6
c) x = 5/18
d) x = 5/9
e) none of the above

Answers

Answer:i think its b im not sure tho

Step-by-step explanation:

Answer: The answer is A) x= -10/19

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 28 N acts on a certain
object, the acceleration of the object is 7 m/s². If the acceleration of the object becomes 3 m/s2, what is the force?

Answers

Answer:

Step-by-step explanation:

F=ma

28=7m

m=28/7=4

F=4a

when a=3 m/s²

F=4×3=12 N

tell whether the transformation appears to be a rigid motion. explain

Answers

Answer:

If you turn it or flip it over or move it it is essentially the same shape. If you try to stretch the paper or fold it you change what the shape is so it is not a rigid motion. Since the two circles are not the same size then it is not a rigid motion

Suppose that a company has fixed costs of $23 per unit and variable costs $10 per unit when 13,500 units are produced. What are the fixed costs per unit when 10,000 units are produced?

Answers

answer

32632 answer hai bro

The function t= 21.55 cos (pi/6(m-7)) + 43.75 models the average high temperature in degrees Fahrenheit each month

Answers

Answer:

B - 8

Step-by-step explanation:

Answer:

answer is letter b 8

Step-by-step explanation:

45×(−10)×45 STEP explanation ​

Answers

Answer:

-20,250

Step-by-step explanation:

PEMDAS

Multiply left to right

45 * -10 * 45

45* -10

-450 * 45 =

-20,250

How many times greater is the value of digit 1 in 21,648 than in 32,163?

Answers

Answer:

squirrel

Step-by-step explanation:

squirrel

Answer:

10

Step-by-step explanation:

An airplane travels 5152 kilometers against the wind in 7 hours and 6552 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

Answers

6552: 7=936 km/h in still air. 6552-5152:7=6552-736=5816 km/h rate of the wind

What is the meaning of the base of the function y= log(x)?
A. As y increases by 1, x increases by 10.
B. As y increases by 1, x increases by a factor of 10.
C. As y decreases by 1, x increases by a factor of 10.
D. As y decreases by 1, x increases by 10.

Answers

C .As y decrease by 1 c increase by a factor of 10hope this helps

what is equivalent to x+x ?
a)xx
b)2x
c)x^2
d)2^x

Answers

I’m pretty sure the answer is 2x

Answer:

b

Step-by-step explanation:

I think it is B because x+x is two x's so it would be 2x. I hope this helped have a good day

What would be the answee

Answers

I honestly dont kno neva dun dat before

best estimate for 563 / 15

Answers

Answer: 37 8/15 or 37.53

Step-by-step explanation:

use math_way its amazing for math problems, if i could give a rating it would definitely get 5 stars.

its a website and a app i believe it can be used for ios and android

aka apple and everything else

btw i had to add that (_) <that in the name because it wont let me say it normally

How many proportional relationships are shown

Answers

Answer:

2 I think thats the answer

Step-by-step explanation:

Help!! Please thanks

Answers

Answer:

i think you have chosen the right answer i don't really know its tricky for me

Step-by-step explanation:

5z + 3n -z2 ; n = 4.5 , z = 6 PLZ answer this

Answers

Answer:

5(6)+3(4.5)- 6(2)= 31.5

Step-by-step explanation:

Answer:

hmmmmm

Step-by-step explanation:

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

-0.4

Step-by-step explanation:

Answer:

Step-by-step explanation:

help please ASAP!!!!!
you can zoom in to see better

Answers

Answer:

true, false, and false

Step-by-step explanation:

AC=39 Find the length of AB

Answers

Answer:

AB = 12

Step-by-step explanation:

Write the equation of a line perpendicular to y=-5x that passes through the point (1,1) in slope intercept form. (This question is worth 2 points. One point for the correct slope and the second point is for the correct y intercept.)

Answers

Answer:

y= 1/5x + 0.8

Step-by-step explanation:

Hope this helps

An integer is 15 more than 2 times another. If the product of the two integers is -27, then find the integers

Answers

Answer:

The required integers are x=3 and y= -9

Step-by-step explanation:

Let one the integers be x and y

An integer is 15 more than 2 times another: x=15+2y

product of the two integers is -27: x*y=27

[tex]x=15+2y ---eq(1)\\x*y=-27----eq(2)[/tex]

Solving both equations to find values of x and y

Putting value of x from equation 1 in equation 2

[tex](15+2y)*y=-27\\15y+2y^2=-27\\Rearranging:\\2y^2+15y-27=0[/tex]

This can be solved using quadratic formula:

[tex]$y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

Putting values and finding factors

[tex]$y=\frac{-(15)\pm\sqrt{(15)^2-4(2)(-27)}}{2(2)}$\\$y=\frac{-(15)\pm\sqrt{225+216}}{4}$\\$y=\frac{-(15)\pm\sqrt{441}}{4}$\\$y=\frac{-(15)\pm21}{4}$\\$y=\frac{-(15)+21}{4} \ or \ y=\frac{-(15)-21}{4}$\\$y=\frac{6}{4} \ or \ y=\frac{-36}{4}$\\$y=\frac{3}{2} \ or \ y=-9$[/tex]

Since y is integer so, we consider only y= -9

The value of x will be:

[tex]x*y=-27\\x*(-9)=-27\\x=\frac{-27}{-9} \\x=3[/tex]

So, the value of x is x=3

The required integers are x=3 and y= -9

Why is it important for mathematicians to graph functions? Select all that apply.
A. For them to determine if a function can be inverted.
B. For them to visualize the function.
C. For them to extrapolate beyond the known data.
D. For them to determine if the function can be graphed.
E. For them to determine characteristics of the function.

Answers

Answer:

e

Step-by-step explanation:

s

Work out (7×10^5) ÷ (2×10^2)
Give
your answer in standard form.​

Answers

Answer:

3.5 X 10^3

Step-by-step explanation:

Simplify the expression:

8(x - 5) + 7(3x + 4)​

Answers

Answer:

29x-12

Step-by-step explanation:

29x-12

Step-by-step explanation:

8•x=8×

8•-5=-40

7•3x=21x

7•4=28

-40+28=-12

21x+8x=29x

2×2+31×1+1+1+1+1+11×4×4×4×4×4×4×4×4×4

Answers

Answer:

I think it is 13107200

Step-by-step explanation:

I think the answer might be 2,883,623. Hopefully, this helps you! :)

Emile paid $3.96 for 4 songs.

What is the unit rate and what does it mean?

Enter your answers in the boxes.

Answers

Answer:

$0.99

Unit rate is cost for 1 individual (song)

Step-by-step explanation:

$3.96/4

0.99

99 cents

In a particular​ game, the probability of winning $95 is 1/36 and the probability of losing $7 is 35/36. What is the expected value after playing this​ game? Round to the nearest cent.

Answers

Answer:

1.53

Step-by-step explanation:

1

36

(

85

)

+

(

35

36

)

(

4

)

=

E

V

 

85

36

140

36

=

E

V

55

36

=

E

V

E

V

$

1.53

Ella swims four times a week at her clubs pool. She swims the same number of labs on Monday, Wednesday, and Friday, and 15 laps on Saturday. She swims a total of 51 labs each week. How many laughs does she swim on Monday?

Answers

52 laps is the correct answer. Explaining. Don’t have to I just took the test and got a 100

Free brainliest timmmmmmme :)


What is 2+2?
A. 69
B. 420
C:666
D:21

PLEASE HELP WORTH 4 POINTS

Answers

Answer:

2+2=4

Step-by-step explanation:

lol tell me the subject and ill research and give u n answer

Who wanna help me ???

25 points and brainlest

Answers

Answer:

2/5

Step-by-step explanation:

8/20=2/5

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.05?

If it was later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?

a. If the confidence level is increased, then the sample size would need to increase because a higher level of confidence increases the margin of error.
b. If the confidence level is increased, then the sample size would need to decrease because increasing the sample size would create an even larger interval.
c. If the confidence level is increased, then the sample size would need to decrease because we would like the proportion of people who buckle up to be around 50%.
d. If the confidence level is increased, then the sample size would not be affected.

Answers

Answer:

The value  is  [tex]n = 384 [/tex]

The correct option is a

Step-by-step explanation:

From the question we are told that

   The margin of error is  E =  0.05

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of   is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally since the sample proportion is not given we will assume it to be

      [tex]\^ p = 0.5[/tex]

Generally the sample size is mathematically represented as  

    [tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]

=>   [tex]n = [\frac{ 1.96 }{0.05} ]^2 *0.5 (1 - 0.5) [/tex]

=>   [tex]n = 384 [/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }[/tex]

Generally if the level of confidence increases,  the critical value of  [tex]\frac{\alpha }{2}[/tex]  increase and from the equation for margin of error we see the the critical  value varies directly with the margin of error , hence the margin of error  will increase also  

So  If the confidence level is increased, then the sample size would need to increase because a higher level of confidence increases the margin of error.

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