What is the average rate of change of the function over the interval x = 0 to x = 6?

f(x)=2x−1/3x+5 <--- This is a fraction
Enter your answer, as a fraction, in the box.

Answer:  

_______________________________________

→   x  = - 1 ±  i√7     ;

                  4    

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Or:  Write as:

_______________________________________

 →   x  = -1  +  i√7     ;   -1  −   i√7     ;

                   4                       4  

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Step-by-step explanation:

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Given:

 -2x² − x − 1 = 0 ;

Solve for " x " .

________________

First, let us multiply BOTH sides of the equation by "-1" ;

     to get rid of that "negative sign" in the coefficient:  " -2" ;

    →  as follows:

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  -1 * {-2x² − x − 1 } = 0 *{-1} ;

_________________

Rewrite the value: "x" on the "left-hand side" of the question; as:  "1x" ;

since "any value" ; multipled by "1" ; results in that same individual value:

_________________

    -1 * {-2x² − 1x − 1 } = 0 *{-1} ;  

________________

Note the "distributive property" of multiplication:

________________

 a(b + c) = ab + ac ;

________________

Likewise, from the "left-hand side" of the equation:

   -1 * {-2x² − 1x − 1 } =  {-1 * -2x²}  +  {-1 * -1x}  +  {-1* -1 } ;    

                                =      2x²       +  1x           + 1 ;

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Rewrite the "left-hand side" of the equation:

   2x² + 1x + 1 ;

Now, the "right-hand side of the equation:

            " { 0 * -1 } = 0 " .

Now, rewrite the entire equation:

    2x² + 1x + 1 = 0 ;

________________

Note:  This equation is written in "quadratic format" ;

that is:   " ax² + bx + c " ;   [a ≠ 0] ;

         →  in which:

                   a = 2 ;  b = 1 ; c = 1 ;

________________

 →  which means we can solve for the value(s) for "x" ; by using the

"quadratic equation formula" ;

   →  that is:

________________

   →    x  = -b ± √(b² − 4ac)       ;

                           2a                      

________________

 So;  to solve for the values for "x" ;  we substitute our known values for:

    "a" ; "b" ; and "c" ; and solve:

________________

   →   x  =   -1  ±  √(1² − 4*2 *1)       ;

                              4                    

_________________________

   →   x   =    -1  ±  √(1 − 8)       ;

                            4                              

_________________________

   →   x  =   -1  ±  √(-7)     ;

                         4        

_________________________

Note: "√(-7)"  ;  is the square root of a negative number.

Note that we use the lower case  letter, " i "  ;  

        as a symbol to represent the imaginary number:  " √(-1) " .

This is an "imaginary number" ;  since one cannot take the "square root" of a "number lower than zero."  

So, we write:  √-7 ;   as:   " i * 7 " ;  or, just:  " i √7 " ;  since:

  "i  = √-1" ;  and since:  " √-7"  would "factor out" to:  "√7  * √-1 " .

_________________________

Note:  In the mainstream U.S.A. , the concept of " i " as the  "imaginary number" — " √-1 "  ;  is usually introduced in the second year college-prep algebra class (after "first year high school algebra" in 9th grade; and after "geometry" in 10th grade).

_________________________

So;  we have:

→   x  = -1  ± √(-7)     ;

                   4        

___________

We can rewrite this as:

____________

→   x  = -1  ±  i√7    ;

                   4    

_____________

  We can leave our answer written like that.

We have two (2) solutions—so we can also write out both solutions for the value of x:

_____________

 →   x  = -1  +  i√7    ;   -1  +  i√7     ;

                   4                        4

_____________________________________________

Hope this explanation is helpful to you!

  Best of luck— and best wishes!

_____________________________________________

Answer:

the range for f(x) = (x-4) (x-2) is [-1,∞)

Step-by-step explanation:

all real numbers greater than or equal to -1

The range of the function is all real numbers greater than or equal to -1

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = ( x - 4 ) ( x - 2 )   be equation (1)

On simplifying , we get

f ( x ) = x ( x - 2 ) - 4 ( x - 2 )

f ( x ) = x² - 2x - 4x + 8

f ( x ) = x² - 6x + 8  

Now , the range of the function is set of possible y values

The vertex of the parabola is at ( 3 , -1 )

So , the range of the function is f ( x ) ≥ -1 and the interval is [ -1 , ∝ ]

Hence , the range of the function is f ( x ) ≥ -1

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The height of a rectangular prism is 8.3 cm.

The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface.

We have,

Surface Area = 288 square cm

Base length = 4 cm and width = 9 cm

So, SA of rectangular prism

288 = 2(lw+ wh + lh)

144 = (36 + 9h + 4h)

13h = 144- 36

13h = 108

h = 8.30 cm

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Answer: [tex]\sqrt{2}[/tex]

Step-by-step explanation:

In a 45 45 90 triangle the two sides are 1 wile the hypothenuse is [tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

(-2, 2)   (2, -3)

(-3 - 2)/(2 + 2)

-5/4 the slope

y - 2 = -5/4(x + 2)

y - 2 = -5/4x - 5/2

y- 4/2 = -5/4x - 5/2

y = -5/4x - 1/2

Answers:

#1: infinite solutions;  #2: no solutions

Step-by-step explanations:

Steps for #1

3(2x+7)=13+4(x+2)+2x

6x+21=13+4x+8+2x

6x+21=21+6x

6x=6x

x=x

After completing the steps to find the value of x using Order of Operations, we see that in the end, the answer we have is x=x. We can easily conclude that x is equal to any number because the final answer in this exercise is always whatever the value of x is. For example, if x=4, our final answer would be 4.

Steps for #2

5(6x+8)=9x-10+21x

30x+40=30x-10

40=-10

Here, we see that once we've completed the steps using the Order of Operations, we come out with the answer 40=-10, which is not true on any terms. Therefore we can simply conclude that the answer for #2 is "no solutions."

If you have any trouble figuring out how I got my answers, please refer back to the steps I used to get the answers.

Thank you!

Answer: u have to cross out 3x and change into a positive and u try to find the other side of da equation. I hope dis helps :3

Step-by-step explanation:

Answer:

You performed better relative to the class average in your economics class.

Step-by-step explanation:

There are two classes.

AP statistics class and Economic class

Using the z score formula,

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

In the AP statistics class, you scored a percentage of 65%. The class average was 60%

x is the raw score = 65%

μ is the population mean = 60%

σ is the population standard deviation = 6%

z = (x-μ)/σ

z = (65 - 60)/6

z = 5/6

z = 0.8333333333

In the Economics classes, you scored a percentage of 78% with a class average of 75%

x is the raw score = 78%

μ is the population mean = 75%

σ is the population standard deviation = 2.5%

z = (x-μ)/σ

z = (78 - 75)/2.5

z = 3/2.5

z = 1.2

Comparing the z score of both exams taken from different classes,we can see that your z score was higher in the Economics class compared to the A.P statistics class.

Therefore, you performed better relative to the class average in your economics class.

Answer:

5

Step-by-step explanation:

Using the formula of a trapezoid, we can solve this!

Formula is A=1/2(b1+b2)h.

A=1/2(2+8)1

A=1/2(10)1

A=1/2(10)

The area would be 5 cubic in2.

Please tell me if im wrong! im just a student .m.

Answer:

5 units²

Step-by-step explanation:

a for a trapezoid = [tex]\frac{a+b}{2} *h[/tex]

[tex]\frac{8+2}{2} *1[/tex] = [tex]\frac{10}{2} * 1[/tex] = 5*1 = 5

The area is 5 units²

Answer:

Time taken = 6.2 hours

Step-by-step explanation:

Firstly, we will calculate the rate of each person per hour. Then we combine the rates and afterward divide the number of envelope they could address by the combined rate.

Casey can address 20 envelopes at the rate of 20 per hour.

Casey rate = 20 envelope per hr

Anne can address 44 envelope in 2 hours

Anne rate = 22 envelope per hr

Paula can address 68 envelope in 3 hours

Paula rate = 68/3 envelope per hr

Time it will take them to address 400 envelope can be solved below

Add their rate = 20 + 22 + 68/3 = 42 + 68/3 = (126 + 68)/3 = 194/3

Time = 400 ÷ 194/3 = 400 × 3/194 = 1200/194 = 6.1855670103

Time taken = 6.2 hours

Answer:

0.6

Step-by-step explanation:

9÷15=0.6

Answer: 25 pi

Step-by-step explanation:

Answer:

[tex]3m/s^2[/tex]

Step-by-step explanation:

the information that we have is:

mass: [tex]m=20kg[/tex]

force applied: [tex]F=60N[/tex]

since we need to find the acceleration, we can use Newton's second law of motion:

[tex]F=ma[/tex]

Where [tex]F[/tex] is the force applied to a mass [tex]m[/tex] which creates an acceleration [tex]a[/tex].

we solve this equation for the acceleration:

[tex]a=\frac{F}{m}[/tex]

and we substitute the known values:

[tex]a=\frac{60N}{20kg} \\\\a=3m/s^2[/tex]

the acceleration of the load is: [tex]3m/s^2[/tex]

Answer: 5/6

Step-by-step explanation:

Answer:

the answer is

100÷83

Step-by-step explanation:

hope this helps

Answer:

=7/6 pls mark me as brainlist

Step-by-step explanation:

1/2+2/3

=find lcm = 6

=1x3/2x3 +2x2/3x2

3/6+4/6

=7/6

Answer:

1/2 + 2/3 = 1 1/6

Step-by-step explanation:+

1/2 + 2/3 = ?

Find the common denominator.

3/6 + 4/6 = 7/6

Turn your improper fraction into a mixed number.

1 1/6

Answer:

y = x(0.75)^t

the cost to rent a dvd 5 years ago is $8.43

Step-by-step explanation:

Let x represent the cost to rent a dvd 5 years ago;

And y the cost to rent a dvd t years after.

The cost to rent a dvd has decreased 25% per year, this can be written as an exponential function;

y = x(100% -25%)^t

y = x(1-0.25)^t

y = x(0.75)^t .....1

if the current cost is $2;

t = 5 years

y = $2

Substituting the values into equation 1;

2 = x(0.75)^5

2 = x(0.2373046875)

x = 2/(0.2373046875)

x = 8.427983539094

x = $8.43

Answer:

Domain- {IR} all real numbers or {infinity,infinity}

Range-{0,infinity}

Step-by-step explanation:

plug into calculator

Answer:

176

Step-by-step explanation:

Answer:

The area of triangle DEF is 588 cm²

Step-by-step explanation:

Given;

triangle  DEF with base, b = 42 centimeters

triangle  DEF with height, h = 28 centimeters

triangle  DEF other side length, L = 35 centimeters

Area of a triangle is half of the product of the triangle base and height.

Represented in formula as;

A = ¹/₂bh

where;

b is the base of the triangle

h is the height of the triangle

A = ¹/₂ x 42 x 28

A = 588 cm²

Therefore the area of triangle DEF is 588 cm²

Answer:

588

Step-by-step explanation:

Answer:

B: x = -y+6

Step-by-step explanation:

Since y = x+6:

Bring x and y to their opposite sides:

x = -y+6

I hope this helps and plz mark me brainliest!!

Answer:

They are the same equations. (I don't know what you mean by "true.")

Step-by-step explanation:

If you divide 2x + 2y = 6 by 2, it turns into x + y = 3. This means that the graphs of the lines are the same, or there are infinite solutions.

I am really sorry if this is wrong because I am not really sure what you meant by "Which statement is true?"

Answer:

1. 1 3/8- 1 /1/8

2. 11/8- 9/8

3. 1 3/8- 9/8

Step-by-step explanation:

Options A, B, D, and E are correct answers such that the probability of the usage of social media by 8th and 9th-grade students is given.

A. There is no association between using social media and grade level.

B. The probability a student uses social media, given that he or she is in 9th grade, is 81%.

D. An 8th grader is more likely to use social media than not.

E. Knowing a student’s grade level does not help determine if he or she uses social media.

Probability is the ratio of the favorable outcomes to the total outcomes.

Given that, a group of 8th and 9th graders were surveyed about whether they use social media to communicate with their friends.

We can see that, there is no relationship between the usage of social media and grade level so, we can say that there is no association between using social media and grade level.

Probability of using social media by a 9th grader is-

P(9) = 0.81 / 1 x 100 = 81%

Probability of using social media by a 8th grader is-

P(8) = 0.84 / 1 x 100 = 84%

We cannot define the usage of social media depending on the grade level.

Thus, Options A, B, D, and E are correct answers.

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The table is attached

Answer:

Each side is 14 ft.

Step-by-step explanation:

If there are 4 equal sides, you divide 56 by 4. That equals 14.

Answer:

x=6      x=-5

Step-by-step explanation:

f(x) = (x-6)(x + 5)

To find the zeros, set the function equal  to zero

0 =  (x-6)(x + 5)

Using the zero product of property

0 = x-6    0=x+5

x=6      x=-5

Answer:

im pretty sure it's c

Step-by-step explanation:

Answer:

its C

Step-by-step explanation:

Answer:

B  4i sqrt(2)

Step-by-step explanation:

sqrt(-2) = sqrt(-1) * sqrt(2) = i sqrt(2)

sqrt(-18) = sqrt(-1) sqrt(2) sqrt(9) = 3i sqrt(2)

Add them together

i sqrt(2) + 3i sqrt(2)

4i sqrt(2)

Answer:

B.) [tex]4\sqrt{2}i[/tex]

Step-by-step explanation:

Simplify both radicals from negative form (the square root of -1 is i ):

[tex]\sqrt{-1*2} +\sqrt{-1*18} \\\\\sqrt{2}i+\sqrt{18}i[/tex]

Simplify [tex]\sqrt{18}[/tex] :

[tex]\sqrt{9*2}\\\\\sqrt{9}*\sqrt{2}\\\\ 3\sqrt{2}i[/tex]

Add:

[tex]1\sqrt{2}i+3\sqrt{2}i\\\\4\sqrt{2}i[/tex]

:Done

Answer: C

Step-by-step explanation:

Length: 6in

Width: 8in

Height: 9in

[tex]A=2(wl+hl+hw)\\A=2[(8in)(6in)+(9in)(6in)+(9in)(8in)]\\A=2(48in^2+54in^2+72in^2)\\A=2(174in^2)\\A=348in^2[/tex]