What is the average rate of change of the function f (x) = between x = 1 and
x= 3?

[tex]\pm 8, \pm 4, \pm 2, \pm 1, \pm \frac{1}{2}[/tex]

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Explanation:

The first coefficient is 2. The last term is 8.

To find the possible rational roots, we look at factors of 2 and 8

factors of 2 = 1, 2

factors of 8 = 1,2,4,8

Then you divide each factor of 8 over the factor of 2. More generally, we divide the factors of the last term over the factors of the first coefficient.

A table is recommended so you can keep everything organized. See the diagram below.

The table shows 8, 4, 2, 1 and 1/2 as the unique results in each cell.

The table only shows the positive results, but the negative results will basically be identical except for the negative sign of course. The plus minus is to account for things like saying "-2 is a factor of 8 since -2*(-4) = 8". I find its easier to just focus on the positive and then stick plus minus at the end when all is said and done.

This is why choice B is the answer.

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Extra info:

Keep in mind this list is the possible rational roots and it does not mean they are all actual rational roots of the given polynomial. You'll need to plug each one into the polynomial to see if you get 0 as an output.

For instance, plugging x = 2 into y = 2x^2-10x+8 leads to y = -4 showing that x = 2 is not a root; however, x = 1 is a root because plugging x = 1 into y = 2x^2-10x+8 leads to y = 0. There's one other rational root for this polynomial.

Answer:

Step-by-step explanation:

Ans 1: 250m/8.6s=29.07m/s(average velocity)

Ans 2: 0.12m/s*3s= 0.36m (it travelled 0.36m in 3 sec)

Ans 3: 467m/5.6/s= 83.4s (time Mychal was riding his bike)

Ans 4: 227 772.18m-200 000m= 27772.18m

finding per minute = 31.7/s*60

19902m/min

time on cruise control= 200 000m/19902/m

=105.15min

Abel was on cruise control for 105.15min

Answer:

The diameter is 12

Step-by-step explanation:

Since it is 1 to 2

The diameter is double the radius.

The radius is 6 and 6 times 2 is 12.

The diameter of the circle Russell drew is 12 centimeters.

A circle is a bounded figure with a point from the center to its circumference is equidistant.

A diameter is a straight line from one point on the circumference of the circle to another point on the circumference of the circle.

Radius is a line from the center of the circle to the circumference of the circle.

The ratio of radius to the diameter is 1 : 2. This means that the diameter is two times the length of the radius.  If the radius is 6cm, the diameter = 6 x 2 = 12 cm.

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Answer:

$516

Step-by-step explanation:

Price of lunch: $400

Sales tax: 11% of $400

Tip: 18% of $400

The sales tax and tip combined were 29% of $400 since 11% of $400 + 18% of $400 = 29% of $400.

We calculate the combined sales tax and tip:

29% of $400 =

= 0.29 * $400

= $116

The combined sales tax and tip were $116.

Now we add the combined sales tax and tip to the $400 price of dinner.

total = $400 + $116

total = $516

Answer:

y=8.25x-15

Step-by-step explanation:

From the information provided, the algebraic expression will need to indicate that your earnings during the first week, y, would be equal to multiplying $8.25 for the number of hours, x, minus $15. According to that, the algebraic expression is:

y=8.25x-15

Answer:

I got a decimal

Step-by-step explanation:

0.857142857

Answer:

Step-by-step explanation:

Answer:YAY

Step-by-step explanation: :)

Answer:

a =  cf - b(d-e)

        c(d-e)

Step-by-step explanation:

Kindly check correct question as attached!

Solution

(a+b/c)(d-e) = f

a + b/c = f/d-e

a = [f/d-e] - [b/c]

Lcm = c(d-e)

a =  cf - b(d-e)

        c(d-e)

The equivalent value of the expression is a = [ f / ( d - e ) ] - ( b/c )

Given data ,

Let the equation be represented as A

Now , the value of A is

( a + b/c ) ( d - e ) = f

On simplifying the equation , we get

( a + b/c ) ( d - e ) = f

So , the left hand side of the equation is equated to the right hand side by the value of f

Divide by ( d - e ) on both sides , we get

a + b/c = f / ( d - e )

Subtracting b/c on both sides , we get

a = [ f / ( d - e ) ] - ( b/c )

a = [ f / ( d - e ) ] - ( b/c )

Therefore , the value of a = [ f / ( d - e ) ] - ( b/c )

Hence , the expression is a = [ f / ( d - e ) ] - ( b/c )

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Answer:

Step-by-step explanation:

To get the median of the ages given

2, 4, 5, 6, 7, 8, 8, 8, 0, 3, 5, 9, 1, 4, 7, 6, 1, 2, 4, 4, 8

First we will need to rearrange the median ages in ascending order (from lowest to highest)

0, 1, 1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9

Next is to locate the middle value of the arranged data

(0, 1, 1, 2, 2, 3, 4, 4, 4, 4), 5, (5, 6, 6, 7, 7, 8, 8, 8, 8, 9)

The total values in both parenthesis are the same(10 in numbers) leaving 5 as the middle number.

Hence the median age of the people in the pool is 5years

Answer:

11

Step-by-step explanation:

I just assumed D is the midpoint; and if D is the midpoint,

GD=DH, GD+DH=GH

5.5+5.5=11

The graph of equation y=−3x+4 has been drawn below.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

After that, we need to substitute the values of x's and y's into the coordinate geometry.

Given a linear function y=−3x+4

In order to plot a graph, we need to assume one x value, and corresponding to that need to calculate the y value.

Lets say x = 0 than

y = -3(0) + 4

y = 4 ⇒ (0.4) will be the first coordinate of the line.

Now let's say y = 0 than

0 = -3x + 4

x = 1.33 ⇒ (1.33, 0) will be the second coordinate of the line.

So,

Draw a straight line by passing both points gives us an f the equation y=−3x+4.

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The graph of the equation y = -3x + 4 is shown in the figure attached with the answer.

We have the following equation of a straight line y = - 3x + 4.

We have to plot the equation of this straight line.

The general equation of a straight line is as follows -

y = mx + c

where -

m - slope of line

c - intercept of line on y - axis.

According to the question -

The equation of line = - 3x + 4

Now, comparing this line with the general equation of line -  y = mx + c, we get -

m = -3

c = 4

Hence, the graph of the equation is shown in the figure attached with the answer.

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Answer:

6a-2

Step-by-step explanation:

Fist wright the equation

2a+4a-1-1

add like terms

2a+4a=6a

-1+-1=-2

Combine

6a-2

Hope this helps! Plz award Brainliest : )

Answer:

250

Step-by-step explanation:

60% is 3/5. Meaning, for every 5 shots taken, the archer only makes 3.

So, they would need to make 250 shots before they get 100.

Hope this helps!

Plz name brainliest if possible!

Answer:

5/8

Step-by-step explanation:

There are 4 possible outcomes on the first spinner and 4 outcomes on the second spinner for 4*4 = 16 outcomes

We want 5 or more

1+4

2+3

2+4

3+2

3+3

3+4

4+1

4+2

4+3

4+4

These are the positive outcomes  10

10/16 = 5/8

Answer:You earn 5% commission on the first $2000 of sales and 8% commission on all sales over $2000. If you sold $7740, what is your total ...

Step-by-step explanation:

Answer:

(4,0)

Step-by-step explanation:

So we have the system of equations:

[tex]y=-2x+8\\y=x-4[/tex]

To solve, we can use substitution.

Substitute the second equation into the first. So:

[tex]x-4=-2x+8[/tex]

Add 2x to both sides. The right cancels:

[tex]3x-4=8[/tex]

Add 4 to both sides:

[tex]3x=12[/tex]

Divide both sides by 3:

[tex]x=4[/tex]

Now, let's substitute this back into the second equation to find y:

[tex]y=x-4[/tex]

Substitute 4 for x:

[tex]y=4-4[/tex]

Subtract:

[tex]y=0[/tex]

So, our solution is (4,0).

And we're done!

Answer:

800 ÷ 40

=20

It will take Carmen 20 to pay back her loan

Answer:

20 Months

Step-by-step explanation:

800 / 40 = 20

Answer:

6ft

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the actual dimension were different from 28 inches by more than 1/2 inch, it would be reported as a different dimension. So, the minimum that will be reported as 28 is 27.5. The maximum that will be reported as 28 will be 28.4999999.... ≈ 28.5

The maximum and minimum length of the sheet are 28.5 inches and 27.5 inches, respectively.

Answer:

About 7

Step-by-step explanation:

245/35 = 7

So, 246/35 = 7.02, which is about 7.

Hope this helps!

Plz name brainliest if possible!

Answer:

[tex] \sqrt{30} [/tex]

can not be simplified further.

Decimal = 5.477225575

Answer:

B. all expected frequencies > 5

Step-by-step explanation:

The expected number np(i) in any of the classes or cells should not be less than 5. So when the expected number np(i) in any  class is less than 5 , we may combine this class with one or more other classes to meet this requirement.

It is clear that chi square  will be small when all ni are close to their expected values npi. The chi square will become larger when the difference becomes larger. The chi square thus measures the amount of deviation ( or agreement ) between the observed and expected results.

Thus it is a good approximation if all the expected values npi are sufficiently large and hence chi square distribution confirms with the ( k-1) degrees of freedom.

Answer: Can you give more details

Step-by-step explanation:

Answer:

The number is 138,695,157.

If you want to know the value of a particular number, then follow the steps:

1) Start at the decimal point (in the right) and count the places until you reach the desired number.

For example, the 3 is in the 8th position, so here we take n = 8.

2) Now that you find n, multiply your number by 10^(n-1)

in this case we have:

3*10^(8 - 1) = 3*10^7 → (this means that you add 7 zeros at the right of the 3)

                     3*10^7 = 30,000,000

So that is the value of the 3 in the given number. (3 ten-millions)

Answer:

Since all views look like a circle, the solid would be a ball, which is also called a sphere.

The answer is Sphere

The geometrical name of the solid given is Sphere.

Answer:

17/30

Step-by-step explanation:

2/3-1/10=

20/30-3/30=

17/30

Answer:

Tomorrow = 25 students

In 2 days = 44 students

In 40 days = 40 students

Step-by-step explanation:

Let A =  watch more than an hour

     B = watch less than an hour

First of all we need to make a transition matrix

[tex]P = \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} \binom{A}{B}[/tex]

Also we are given,

X = [100, 100]

       A       B

Therefore,

[tex]XP=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}[/tex]

     = [25, 175]

Thus, 25 students will watch television for an hour or more tomorrow.

Now for 2 days,

[tex]XP^2=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}[/tex]

       = [43.75, 156.25]

Hence, 44 students will watch television for an hour or more in 2 days.

Now in 40 days,

[tex]XP^40=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}^{40}[/tex]

But instead of multiplying the above matrix 40 times, we can we can find the long term division method.

Let

x =  long term distribution of students watching television >1 hour

y =   long term distribution of students watching television <1 hour

Therefore,

[tex]\begin{bmatrix}x & y\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} = \begin{bmatrix}x & y\end{bmatrix}[/tex]

⇒ 0.25 y = x

And we know that x + y = 200

∴ 0.25 y + y = 200

∴ y = 160

And x = 40 ( ∵ x + y = 200)

Thus 40 students will watch televisions in the 40 days for an hour or more.

Answer:

20.75

Explanation:

20+3/4

= 20.75

= 2075