f(x)=x^3-9x
What is the average rate of change of f over the interval (1,6]?

Answer:

zero

Step-by-step explanation:

the answer is zero brainley please don't delete this...  hope this helps with your question! please give me brainiest

The relationship "x divides y" is denoted by the notation x|y. The sign of y divided by x will be positive.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

The relationship "x divides y" is denoted by the notation x|y. Or, to put it another way, y is divisible by x and x is a factor of y.

For instance, the expression 3|15 denotes a division of 15 by 3 because 15=35 and 3 is a component of 15.

Therefore, The sign of y divided by x will be positive.

To learn more about division refer to :

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Answer:

[tex]x = 2/5y - 1, y = 5/2x + 5/2[/tex]

Step-by-step explanation:

Step 1:  Solve for x

[tex]5x / 5 = (2y - 5) / 5[/tex]

[tex]x = 2/5y - 1[/tex]

Step 2:  Solve for y

[tex]5x + 5 = 2y - 5 + 5[/tex]

[tex](5x + 5) / 2 = 2y / 2[/tex]

[tex]5/2x + 5/2 = y[/tex]

Answer:  [tex]x = 2/5y - 1, y = 5/2x + 5/2[/tex]

Answer:

$594.75

Step-by-step explanation:

Given

yearly salary of Stephen= $41,236

No of weeks in a year = 52

Therefore, one week salary of Stephen = $41,236/52 = $793

to get one week salary divide total salary by number of weeks

5 weeks salary of Stephen = 5*793 = $ 3,965

agency fees = 15% of Stephen's 5 week salary

                      (15/100)*($ 3,965)  = $594.75

Therefore, Stephen has to pay $594.75 to the agency.

Answer:

They are proportional

Step-by-step explanation:

Let's simplify the ratio of coffee to cost:

6:8 :: 3:4

9:12 :: 3:4

Both simplify to 3:4, so they are proportional

Answer:

Yes, proportional

Step-by-step explanation:

Price 'P' in dollars

No. of cups 'C'

P = kC

8 = 6k

k= 8/6

k = 4/3

12 = 9k

k = 12/9

k = 4/3

Same constant, so proportional

Answer:

(-3,0) and (0,-3)

Step-by-step explanation:

When you are looking for an intercept one of the coordinates is going to be 0.

The line or linear function which has a y-intercept at -3 will be that line that passes through (-3,0) and (0, -3).

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

F(x) = x is a line through the origin and is the parent linear function.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

A linear function has a single and unique constant slope.

In the given problem the line which intercepts y at -3 will be that line in which one y coordinate should be -3 since, it is coordinated with 0, -3)  hence, it will be the correct answer.

For more about the linear function

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Answer:

Final Answer B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer B is correct because all the side lengths are multiply by 3.

5 times 3= 15, 12 times 3=36, and 13 times 3=39.

Have a nice day and stay safe!

Answer:

the graph that represents the inequality is f.

0 is greater than or equal to and it is going to the right

Answer:

F

Step-by-step explanation:

f means x is above or at 0 and 0 counts because it is a closed circle, if it was open it would not have a line underneath.

Answer:

-7

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

-5 ÷ 5/7 = -7. the fives cancel each other out and you're left with -7.

Answer:

The length of the longest side of the triangle is 13 inches

Step-by-step explanation:

step 1

Find the value of x

we know that

The perimeter of triangle is equal to the sum of its three length sides

so

[tex]P=x+(2x+3)+(4x-8)[/tex]

[tex]P=(7x-5) \ in[/tex]

we have

[tex]P=30\ in[/tex]

substitute

[tex]30=(7x-5)[/tex]

solve for x

[tex]7x=30+5\\7x=35\\x=5[/tex]

step 2

Find the length of the longest side of the triangle

Remember that in a right triangle, the longest side is the hypotenuse

so

(2x+3) is the longest side

substitute the value of x

[tex]2(5)+3=13\ in[/tex]

Answer:

c) 94.37 is the correct answer.

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

n-4 ≥ 13

Add 4 to each side

n-4+4 ≥ 13+4

n ≥17

There will be a closed circle at 17  because of the equal sign and the line will go to the left because of the greater than sign

Answer:

D 12

Step-by-step explanation:

The product of the lengths of the segments of one chord equal the product of the segments of the other.

x*4 = 6*8

4x = 48

Divide each side by 4

4x/4 = 48/4

x = 12

Answer:

Step-by-step explanation

two and a half batches?

Final answer:

Pauline used 1 cup of sugar and each batch of cookies requires 2/5 cup. By dividing 1 cup by 2/5 cup, we get 2.5 giving us ≈2 batches.

Explanation:

The question asks how many batches of cookies Pauline was able to make if she used 1 cup of sugar, with each batch requiring 2/5 of a cup of sugar. To find this, we can use a simple division process as our conversion factor. You divide the total amount of sugar used by the amount needed per batch.

Steps to calculate the number of batches:

Pauline uses 2/5 of a cup of sugar for each batch of cookies.

She used a total of 1 cup of sugar yesterday.

To find the number of batches made, divide the total amount of sugar by the amount per batch: 1 cup / (2/5 cup per batch) = 5/2 = 2.5 batches.

However, since you cannot make half a batch of cookies, Pauline must have made 2 batches.

Answer:

-6x+y=0

Step-by-step explanation:

y+6=-6(x+1)

y+6=-6x-6

-6x+y=0

On converting y + 6 = -6(x + 1) to Ax+By=C form, get 6x + y = -6 with A=6, B=1, and C=-6.

To rewrite the equation y + 6 = -6(x + 1) in the Ax+By=C form, where A, B, and C are integers, we need to distribute the -6 and then move all terms involving variables to one side of the equation and the constant term to the other side.

First, distribute the -6:

y + 6 = -6x - 6

Now, move the variable terms to one side by adding 6x to both sides:

6x + y + 6 = 0

Finally, subtract 6 from both sides to isolate the constant:

6x + y = -6

Now the equation is in the desired format with A=6, B=1, and C=-6.

Answer:

Cylinder

explanation:

The formula for the volume of a cylinder is V=πr²h

To find the volume of a cylinder, the formula V = πr²h is used, where you multiply the square of the radius by π and then by the height, ensuring consistent units throughout.

To get the volume of a cylinder, you need to use the formula V = πr²h, where V stands for volume, π is a mathematical constant approximately equal to 3.14159, r represents the radius of the cylinder's base, and h denotes the height of the cylinder. To calculate the volume, first square the radius, then multiply that by π, and finally multiply by the cylinder's height. For example, if a cylinder has a radius of 0.750 cm and a height of 5.25 cm, you would calculate the volume as follows: 3.142 × (0.750 cm)2 × 5.25 cm, which equals approximately 9.278 cm3. Remember to use consistent units throughout the calculation.

Answer:

D

Step-by-step explanation:

If (2,-7) and (8,15) is the end points of the diameter, they must be on the circle.

Here is a graph: search up  https:// www .  desmos. com /calculator/ yl9uiyhttps, sorry I couldn't put up a link cause of brainly. Type it in without spaces.

Answer:

D

Step-by-step explanation:

The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal, it is obtained by Pythagoras theorem.

Step-by-step explanation:

The given are,

           From ΔABC,

                    AB= 6

                    BC= 10

                    AC = x

           From ΔDEC,

                    CD= 28

                    DE= 21

                    CE = y

Step:1

        Pythagoras theorem from  ΔABC,

                    [tex]BC^{2}=AB^{2} + AC^{2}[/tex]...............(1)

       Substitute the values,

                   [tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]AC^{2}[/tex]

                  100 = 36 + [tex]AC^{2}[/tex]

                   [tex]AC^{2}[/tex] = 100 - 36

                           = 64

                    AC = [tex]\sqrt{64}[/tex]

                    AC = 8

                  AC = x = 8

Step:2

        Pythagoras theorem for ΔDEC,

               [tex]CE^{2} = CD^{2} + DE^{2}[/tex]................(2)

       From the values,

              [tex]CE^{2}[/tex] = [tex]28^{2}[/tex] + [tex]21^{2}[/tex]

             [tex]CE^{2}[/tex] = 784 + 441

                     = 1225

              CE = [tex]\sqrt{1225}[/tex]

              CE = 35

             CE = y = 35

Result:

         The values are x=8 and y=35, if the given ΔABC and ΔDEC are equal.

Answer:

x=-17 and x=-19

Step-by-step explanation:

-17+18=1

-19+18=-1

|-1| =1

Answer:

-17 and -19

Step-by-step explanation:

Absolute value equations have two problems and two solutions unless the original answer equals a negative-then it would be no solution.

x + 18 =1 subtract 18 from both sides to get x by itself

x = 1-18

x= -17

x +18 = -1  subtract 18 from both sides to get x by itself

x= -1 -18

x= -19

Answer:

(0,1)

Step-by-step explanation:

The equation for slope is y=mx+b.

The b value stands as the y - intercept.

Answer:

96 degrees

Step-by-step explanation:

A center angles degree measurement is the same as the ark it is on

Somebody once told me the world is gonna roll me

I ain't the sharpest tool in the shed

She was looking kind of dumb with her finger and her thumb

In the shape of an "L" on her forehead

Well the years start coming and they don't stop coming

Fed to the rules and I hit the ground running

Didn't make sense not to live for fun

Your brain gets smart but your head gets dumb

So much to do, so much to see

So what's wrong with taking the back streets?

You'll never know if you don't go

You'll never shine if you don't glow

Answer:

1.333...

Step-by-step explanation:

because irrational numbers can be repeating decimals, numbers that aren't perfect squares,and numbers that can not be in fraction form.

Answer:2 root 3

Or 3.464101615

Step-by-step explanation:

Answer:

b. 3

Step-by-step explanation:

Answer:

n < 5

Step-by-step explanation:

8n+6 < 46

1. subtract 6 from both sides

       8n < 40

2. Divide both sides by 8

40/8 = 5

So n<5

Answer:

(explanation)

Step-by-step explanation:

[tex]8n + 6 < 46\\8n +6 (-6) < 46 - 6\\8n < 40\\\frac{8n}{8} <\frac{40}{8}\\ n < 5[/tex]

Answer:The other guy Lied it’s A

Step-by-step explanation:Just took test

Answer:

Erin has $200

Step-by-step explanation:

Kevin = K

Erin = E

30% of Erin = 0.3E

K = E - 0.3E

K = 140

Substitute

140 = E - 0.3E

140 = 0.7E

Divide both sides of the equation by 0.7

E = 200

Erin has $200

Hope this helps :)

Answer:

4x-2

Step-by-step explanation:

hope this helps

Answer:

You find the area first

L x W of the rectangle only.

To find volume : you find the depth of the square and multiply this by the area above.

Whatever the number is you add 'unit sq'

Lets say the rectangular prism measured L12 units x W6units x D4units

A =72unit square

V = D4 x A72 = 4 x 72 = 288unitsq cubes

Step-by-step explanation:

Answer: Mechanics and Kinematics

Step-by-step explanation:

The study of motion with regard to the forces or energies that may be involved is called Mechanics

The study of motion without regard to the forces or energies that may be involved is called kinematics

Therefore, the correct answer is (D) [tex]$(12.61,16.39)$[/tex]

To calculate the confidence interval for the mean age of cars in the commuter lot, we'll use the formula:

[tex]\[ \text{Confidence interval} = \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \][/tex]

where:

- [tex]\(\bar{x}\)[/tex] is the sample mean age (14.5 years),

- [tex]\(s\)[/tex] is the sample standard deviation (4.6 years),

- [tex]\(n\)[/tex] is the sample size (16),

- [tex]\(t\)[/tex] is the critical value from the t-distribution corresponding to the desired confidence level (90% in this case).

First, we need to find the critical value \(t\) for a 90% confidence level with [tex]\(n-1 = 15\)[/tex] degrees of freedom. Using a t-distribution table or calculator,[tex]\(t \approx 1.753\).[/tex]

Now, we can plug in the values:

[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \left( \frac{4.6}{\sqrt{16}} \right) \][/tex]

[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \times \frac{4.6}{4} \][/tex]

[tex]\[ \text{Confidence interval} = 14.5 \pm 1.753 \times 1.15 \][/tex]

[tex]\[ \text{Confidence interval} = 14.5 \pm 2.12595 \][/tex]

[tex]\[ \text{Confidence interval} = (12.37405, 16.62595) \][/tex]

Complete question:

Ignacio is curious about the average age of cars in the commuter lot at his large university. He takes a random sample of 16 cars and finds that their average age is [tex]$\bar{x}=14.5$[/tex] years and their standard deviation is [tex]$s_x=4.6$[/tex]years. The distribution of ages in the sample was roughly symmetric with no obvious outliers.

Based on this sample, which of the following is a [tex]$90 \%$[/tex] confidence interval for the mean age of cars (in years) in this commuter lot?

Choose 1 answer:

(A) [tex]$(6.44,22.56)$[/tex]

(B) [tex]$(12.05,16.95)$[/tex]

(c) [tex]$(12.48,16.52)$[/tex]

(D)[tex]$(12.61,16.39)$[/tex]

(E) [tex]$(13.35,15.65)$[/tex]

The 90% confidence interval for the mean age of cars in the commuter lot is (12.48, 16.52). The correct answer is: c) (12.48, 16.52)

Step 1

To determine the 90% confidence interval for the mean age of cars in the commuter lot, we can use the formula for the confidence interval of the mean for a normally distributed sample:

[tex]\[ \text{CI} = \bar{x} \pm t \left(\frac{s}{\sqrt{n}}\right) \][/tex]

Where:

- [tex]\(\bar{x}\)[/tex] is the sample mean (14.5 years)

- [tex]\(s\)[/tex] is the sample standard deviation (4.6 years)

- n is the sample size (16)

- t is the t-value for the 90% confidence level with [tex]\(n-1\)[/tex] degrees of freedom (df = 16 - 1 = 15)

First, we find the t-value for 90% confidence and 15 degrees of freedom. Using a t-table or a calculator, the t-value (two-tailed) is approximately 1.753.

Step 2

Next, we calculate the margin of error:

[tex]\[ \text{Margin of Error} = t \left(\frac{s}{\sqrt{n}}\right) = 1.753 \left(\frac{4.6}{\sqrt{16}}\right) = 1.753 \left(\frac{4.6}{4}\right) = 1.753 \times 1.15 \approx 2.016 \][/tex]

Now, we calculate the confidence interval:

[tex]\[ \text{CI} = 14.5 \pm 2.016 \][/tex]

So, the lower bound is:

[tex]\[ 14.5 - 2.016 = 12.484 \][/tex]

And the upper bound is:

[tex]\[ 14.5 + 2.016 = 16.516 \][/tex]

Thus, the 90% confidence interval for the mean age of cars is approximately:

[tex]\[ (12.48, 16.52) \][/tex]

This interval suggests that we are 90% confident that the true mean age of cars in the commuter lot lies between 12.48 and 16.52 years.

Complete question : Ignacio is curious about the average age of cars in the commuter lot at Mis large university. He takes a random sample of 16 cars and finds that their average age is 2 = 14.5 years and their standard deviation is 8, = 4.6

years. The distribution of ages in the sample was roughly symmetric with no obvious outliers. Based on this sample, which of the following is a 90% confidence interval for the mean age of cars (in years) in this commuter lot?

a) (6,44,22,56)

b) (12,05,16,95)

c) (12,48,16,52)

d) (12,61,16,39)

e) (13,35,15,65)