Given the function g(x) = x2 + 10x + 20, determine the average rate of change of
the function over the interval -9 < x < 0.

Answers

Answer 1

A function assigns the values. The average rate of change for the given function g(x) is 1.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The average rate of change of a function is given by the formula,

Average rate of change, = [f(b)-f(a)]/(b-a), [a,b]

Where a is the lower limit and b is the upper limit.

Given the upper limit for the function is 0, therefore, the value of a is 0, similarly, the value of b is -9. Thus,

a = 0

g(a) = 0²+10(0)+20 = 20

b = -9

g(b) = (-9)²+10(-9)+20 = 11

The average rate of change for the function g(x), can be written as,

[tex]\text{Average rate of change}= \dfrac{g(-9)-g(0)}{-9-0}=\dfrac{11-20}{-9} = 1[/tex]

Hence, the average rate of change for the given function g(x) is 1.

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Related Questions

Lets see if you know grade school math!! There were 22 bales of hay to be placed into 6 different tractors. what amount of hay would be placed in each tractor?​

Answers

Answer:

22 divided by 6 is about 3.67

Step-by-step explanation:

pls pls pls help me i am giving you a ton of points and pls explain how you got the answer.

Answers

The expected value of the defective skateboard will be 4/25. Then the correct option is B.

What is probability distribution?

Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.

It might be a function, a table, etc.

The table is shown below.

Then the expected value of the defected skateboard will be

p = 0 x 9/10 + 1 x 1/20 + 2 x 1/25 + 3 x 1/100

p = 1/20 + 2/25 + 3/100

p = 5/100 + 8/100 + 3/100

p = 16/100

p = 4/25

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What is the value of x when [tex](f°g)(x)=-8[/tex]

Answers

According to the table,

f(x) = -8   ⇒   x = -4

and according to the definition of g(x),

g(x) = -4   ⇒   x = 3

Then

(f o g)(x) = f(g(x)) = -8   ⇒   g(x) = -4   ⇒   x = 3

Solve the system of equations below using the linear combination method (elimination). Then, check your work.
x-2y=2
x-y=6

Answers

Answer: Solution- (10,4)

Step-by-step explanation:

x-2y=2   x-y=6              x-2(4)=2

-1(x-y=6)                        x-8=2

-x+y=-6                         +8  +8

                                      x=10

x-2y=2                            

-x+y=-6                           10-2(4)=2

-y=-4                                10-8=2

-1   -1                                  2=2

y=4

Need to be sure. The area of a circle is 9409pi square centimeters. Find the length of the radius. Round to the nearest whole number. I wrote the answer down but I'm not sure if I did it right.

Answers

Hi Student!

Looking at the question, lets extract the important values and information that we believe will be important for this problem.  First of all, we are given the area of a circle which is 9409π and we are told to find the radius (rounding it to the nearest whole number).

Now that we have gathered our information, we can move onto the part of solving for the unknown using the area of a circle formula.  We can do  this by just plugging in the information that we have and solving for r which is the radius.

Plug in the values

[tex]A = \pi\ *\ r^2[/tex][tex]9409\pi\ cm^2= \pi\ *\ r^2[/tex]

Divide both sides by pi to get r^2 by itself

[tex]\frac{9409\pi\ cm^2}{\pi}= \frac{\pi\ *\ r^2}{\pi}[/tex][tex]9409\ cm^2= \ r^2}[/tex]

Square root both sides to get down to just r

[tex]\sqrt{9409\ cm^2}= \sqrt{\ r^2}[/tex][tex]97\ cm= r[/tex]

Therefore, our final answer is that the length of the radius is 97 centimeters which we were able to find using the area and the area of a circle formula.

A triangle has sides with lengths of 30 millimeters, 40 millimeters, and 48 millimeters. Is it a
right triangle?
yes
no

Answers

Answer:

No, because a right angle must not have the least 90°/. degrees c

really need help please please help

Answers

Answer:

1000,000 2.0 77,255,0,0.84831,0,0,0 45,24 27,14 27,34

Step-by-step explanation:

Thanks Okay

The ratio of cats to dogs is
4:5. If there are 20 dogs,
how many cats are there?
29

Answers

I think if there are no cats but instead dogs so 0 cats?

Answer:

16

Step-by-step explanation:

Since the common ratio between cats and dogs is 4:5. We want to know cat and dogs in the ratio X:20. Thus, we can set up the equation as 4/5=X/50. Cross multiplication gets us 80=5X  Solving for  we get that 80/5 =X....16 =X Now, we know that the number of cats there are is 16

help me with this pls

Answers

Answer:

a. 1 triangle

Step-by-step explanation:

measure line QS=8.cm measure 85°on side Q

Answer:

will construct 1 triangle

Step-by-step explanation:

construct a line of Q to S 8cm

SQR let the angle stay in the middle of the letter (Q)

Q to R is 5cm

A cone has a radius of 2 feet and a height of 6 feet. How many cones of liquid would it take to fill a cylinder with a diameter of 4 feet and a height of 6 feet? Complete the explanation. The radius of the cylinder is the same as the radius of the cone. The height of the cylinder is double the height of the cone. So, it will take cones to equal the volume of the cylinder.

Answers

Answer:

17 3/4 feet.

Step-by-step explan

question on similar triangles attatched

Answers

Answer:

h = 24 cm

Step-by-step explanation:

The triangles are similar.

Their dimensions are proportional.

Finding scale factor :

DC/AE10/201/2

Finding h :

h + h/2 = 363h/2 = 363h = 72h = 24 cm


Find the first four terms of the sequence given a = 31 and an+1 = an - 3.
A. 31, 26, 23, 20
B. 31, 28, 25, 22
C.31, 25, 22, 19
D. 31, 27, 26, 25

Answers

B is the correct answer

A bag contains 3 red and 5 green sweets.
Tim takes a sweet at random and eats it.
He then takes another sweet.

Find the probability that Tim takes 2 red sweets

Answers

Answer:

1/7

make sure to remember to remove a sweet when you take the second one, as it has been eaten.

A cube-shaped aquarium has edges that are 1.75 ft long. the aquarium is filled with water that has a density of 72" lb/f" "t" ^3.

(a) should the aquarium be placed on a table that can support a maximum weight of 150 lb? explain why or why not.
(b) would the density of the water change if the aquarium was only half full? explain.

Answers

Answer:

No and the density changes along with the weight.

Answer:

  (a) No. The weight is more than 150 lb.

  (b) No. Density is not a function of volume.

Step-by-step explanation:

The weight of the aquarium is the product of the volume and the density of the contents.

(a)

The volume of the aquarium is the product of its dimensions:

  V = LWH = (1.75 ft)(1.75 ft)(1.75 ft) = 1.75³ ft³ = 5.359375 ft³

The weight of its contents, at 72 lb/ft³ will be ...

  (72 lb/ft³)(5.359375 ft³) = 385.875 lb

The aquarium should not be placed on the table. The weight of the aquarium is too great for the load limit of the table.

__

(b)

The density of water is the ratio of its mass to its volume. Density does not change with depth or volume. It is essentially constant. (Water is considered to be virtually incompressible. Its density changes slightly with temperature,)

No, the density of the water would not change.

_____

Additional comments

The half-full aquarium would weigh about 385.875/2 lb ≈ 194 lb. This is still too heavy for the table.

The density of water is actually about 62.4 lb/ft³. We assume the extra 10 lb/ft³ might take into account the weight of the aquarium and any gravel or other non-water content.

PLEASE HELP MEEEEE I DONT LIKE PI

Answers

Answer:

I did the work and uploaded the picture i hope it helped!!

Janet and Bill leave their home at the same time, Janet has 60 miles to travel and drives at 40 mph. Bill has 80 miles to travel and also drives at 40 mph.
a) How long does Janet's journey take?
b) How much longer does Bill spend driving than Janet?

Answers

Answer:

Question 1 = 1 hour 30 minutes

Question 2 = he spent 30 more minutes driving

Step-by-step explanation:

time = distance ÷ speed

Answer:

Below in bold.

Step-by-step explanation:

Speed = distance / time.

a) Janet's journey:

40 = 60 / t

4ot = 60

t = 60/40 = 1 1/2 hours.

Janet's journey takes 1 1/2 hours.

b)  Bills journey:

40 = 80/t

t = 80/40 = 2 hours.

Bill travels for 1/2 hour more than Janet.

Please someone answer quick ( will give brainlessly)!!!!

Answers

Answer:

Step-by-step explanation:

For the length of AC

cosθ = 14/17

θ = arcCos 14/17

θ = 34.56

Let x = opposite

cot34.56  = 14/x

1.45=14/x

x1.45 = 14

x = 9.66

therefore, the length of AC is 9.66

For angle B is 34.56  

For angle C is 55.44

For Angle C :

90 + c + 34.56   = 180

c = 180 - 124.56

c = 55.44

Overall, about how many students prefer literature (poems, plays, or novels)?

I need help i sent in the graph

Answers

Answer:

3/8 or 37.5 percent, if there were 200 students there would be 75 students who enjoy literature.

A rectangular garden has a length of 6 feet and a width of 3 1/3 feet. Maria wants
to know the area of the garden so she can plan what to plant. Help Maria
determine the area.

Answers

Answer:

20 ft²

Step-by-step explanation:

Formula :

Area = length x width

Solving :

Area = 6 x 3 1/3Area = 18 + 2Area = 20 ft²
Here is the answer. Hope this helps!

Help me with this question please

Answers

Volume of a Cylinder = pi x r^2 x height

diameter = 10, so radius = 5

height = 6

Volume = pi x 5^2 x 6

Volume = pi x 25 x 6

Volume = 150pi

Answer: 150pi cubic feet

Hope this helps!

What's the sequence and drawing scheme of f(x)=x^(1/3)?​

Answers

I thought I knew css this looked familiar but I don’t if I find the answer I will be back to answer

NEED HELP PLEASE ANSWER ASAP! (45)

Answers

Answer:

   45. (4) (2, 2)

Step-by-step explanation:

Question 45

Equate the equationsx = x² - 2x² - x = 2x(x - 1) = 2

Solutions

x = 2x - 1 = 2 ⇒ x = 3

We'll take x = 2 as no options with x = 3 are listed.

y = xy = 2

Ordered pair

(x, y)(4) (2, 2)

The mean number wins of a team is 37 wins that is normally distributed. The standard deviation is 3 wins. What would be the sections that are one standard deviation from the mean? Select all that apply.
31
34
37
40
43

Answers

Using the normal distribution, it is found that the sections that are one standard deviation from the mean are 34 and 40.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 37, \sigma = 3[/tex]

The measures that are one standard deviation from the mean are given by X when Z = -1 and Z = 1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1 = \frac{X - 37}{3}[/tex]

X - 37 = -3

X = 34

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1 = \frac{X - 37}{3}[/tex]

X - 37 = 3

X = 40

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Which of the following expressions is equivalent to ab2 + 6ab + 7a3 – 14a?

Answers

Answer:

−4a^2+2ab+8a

Step-by-step explanation:

−4a^2+2ab+8a is expressions of equivalent to ab2 + 6ab + 7a3 – 14a.

Which expression is equivalent to st6?

1 Answer. s(6) × t(6) is equivalent to (st)(6).

Which expression is equivalent to FG )( 4 )?

Thus, the expression (f + g)(4) is equal to f(4) + g(4).

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(3,-3) and (2,-6) as a linear equation in y=mx+b form

Answers

Answer:

y=3x-12

Step-by-step explanation:

We need to find the m of y = mx+b which is the slope:

-3-(-6)/3-2 = 3 as our slope

We know have y = 3x+b.

If we keep applying slope to the point (2,-6) and go downwards. We hit (0,-12). That's our y intercept. So we replace b with our y intercept which is -12. We know get y = 3x-12


Which inequality has an open circle when it is graphed on a number line?
x greater-than three-fifths
StartFraction 4 over 7 EndFraction greater-than-or-equal-to x
x less-than-or-equal-to 12
x greater-than-or-equal-to negative 6

Answers

Answer:

A.) X greater than 3/5


Open circles are used for numbers that are less than or greater than (< or >). Closed circles are used for numbers that are less than or equal to and greater than or equal to (≤ or ≥).








Step-by-step explanation:

Have a great rest of your day
#TheWizzer

The correct inequality that  has an open circle when it is graphed on a number line is,

1) x greater-than three-fifths

We have to given that,

All the expressions are,

1) x greater-than three-fifths

2) Start Fraction 4 over 7 End Fraction greater-than-or-equal-to x

3) x less-than-or-equal-to 12

4) x greater-than-or-equal-to negative 6.

We can write all the inequality as,

1)  x greater-than three-fifths

⇒ x > 3/5

Since, it has symbol '>' which represent open circle.

Hence, It is true.

2) Start Fraction 4 over 7 End Fraction greater-than-or-equal-to x.

4/7 ≥ x

Since, it has symbol '≥' which represent closed circle.

Hence, It is not true.

3) x less-than-or-equal-to 12

x ≤ 12

Since, it has symbol '≥' which represent closed circle.

Hence, It is not true.

4) x greater-than-or-equal-to negative 6.

x ≥ - 6

Since, it has symbol '≥' which represent closed circle.

Hence, It is not true.

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If anyone can help me with this, please feel free to answer

Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and balance scale.

Answers

Answer:

Step-by-step explanation:

   Number of candies that her sister gave = x

Total candies that Pam has now = 27

  x +  15 = 27

 

Inverse operation:

       x + 15 = 27

   x + 15 - 15 = 27 - 15

               x  = 12

Answer:

Equations :

27 - 15 = x

15 + x = 27

Step-by-step explanation:

So, we know that 1. Pam starts with 15 candies. and 2. Pam ends up having 27 candies. This means, that she gained candy.

To figure out how many candies her sister gave, her, we have to find the difference between 27 and 15 becuase she goes from having 15 to having 27 after her sister had given some.

x will represent how many cadies Pams' sister had given her :

27 -  15 = x

12 = x

This means Pams' sister gave 12 candies to Pam. To make sure we are correct, we can simply start with how many candies Pam started with (15). And add how many we think her sister added (12)

15 + 12

15 + 12 = 27

Therefore proving, and meaning, that Pams' sister gave her 12 candies.

Possible Equations :

27 - 15 = x

End total (27) minus starting total (15).

15 + x = 27

Starting total (15) plus how many she gained (x) equal to end total (27).

Solve for x: Answer: -13x+8 = -8x - 7 Submit Answe​

Answers

[tex]-13x+8=-8x-7\\\\8=5x-7\\\\15=5x\\\\3=x[/tex]

the value of x is 3.

Answer: X=3

Step-by-step explanation:

How do you find area of a figure ?

Answers

Length × Width = Area

Answer:

The length x the widith. If there's more then 4 sides I think you just multiply them all together

Step-by-step explanation:

How many different 6-digit numbers can you write using each of the digits 0, 1, 2, 3,
4, 5 exactly once?

Answers

720, because 6x5x4x3x2x1=720
Pretty sure that how you do it sorry if it’s wrong.
Hope this helps.
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