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      


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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

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Answers

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Step-by-step explanation:

PEMDAS

Multiply left to right

45 * -10 * 45

45* -10

-450 * 45 =

-20,250

Why is it important for mathematicians to graph functions? Select all that apply.
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D. For them to determine if the function can be graphed.
E. For them to determine characteristics of the function.

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Answer:

e

Step-by-step explanation:

s

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

F=ma

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when a=3 m/s²

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What is the meaning of the base of the function y= log(x)?
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C .As y decrease by 1 c increase by a factor of 10hope this helps

Work out (7×10^5) ÷ (2×10^2)
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Step-by-step explanation:

Free brainliest timmmmmmme :)


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Answer:

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Step-by-step explanation:

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

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Emile paid $3.96 for 4 songs.

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Enter your answers in the boxes.

Answers

Answer:

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Step-by-step explanation:

$3.96/4

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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

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

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Step-by-step explanation:

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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

Simplify the expression:

8(x - 5) + 7(3x + 4)​

Answers

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29x-12

Step-by-step explanation:

29x-12

Step-by-step explanation:

8•x=8×

8•-5=-40

7•3x=21x

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2×2+31×1+1+1+1+1+11×4×4×4×4×4×4×4×4×4

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Step-by-step explanation:

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

What would be the answee

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I honestly dont kno neva dun dat before

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.
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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]

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      [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  

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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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Answers

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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

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Answers

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Answers

Answer:

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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:

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?

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answer

32632 answer hai bro

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