Which expression below gives the average rate of change of the function g(x)= -x^2 -4x on the interval 6 ≤ x ≤ 8?

Answers

Answer 1

The average rate of change of a function, g(x), over an interval [a, b] is given by

[tex]Average\ rate\ of\ change= \frac{g(b)-g(a)}{b-a} [/tex]

Thus, the average rate of change of [tex]g(x)=-x^2-4x[/tex] over the interval [tex]6\leq x\leq8[/tex] is given by:

[tex]Average\ rate\ of\ change= \frac{[-(8)^2-4(8)]-[-(6)^2-4(6)]}{8-6} \\ \\ = \frac{(-64-32)-(-36-24)}{2} = \frac{-96-(-60)}{2} = \frac{-96+60}{2} = \frac{-36}{2} \\ \\ -18[/tex]

Related Questions

PLZ HELP ASAP CIRCLES

Answers

First we need to convert the given equation to standard form, then we can write the center and radius directly from it.

[tex] x^{2} -16x+ y^{2} -36=0 \\ \\ x^{2} -2(x)(8)+ y^{2} = 36 \\ \\ x^{2} -2(x)(8)+ 8^{2}+ y^{2} =36 +8^{2} \\ \\ (x-8)^{2}+y^{2}=100 [/tex]

Thus, we can say now:

Center of the circle is (8,0) and its radius is 10.

you plant 30 african violet seeds and 9 of them sprout use experimental probability to predict how many will sprout if you plant 20 seeds

Answers

Given that out of 30 planted seeds only 9 of the m sprouted, then:
Experimental probability =(number of occurrence of event)/(total number of trials made)
=9/30
=3/10
thus the number of seeds that will sprout given that 20 seeds we planted will be:
3/10×20
=6 seeds

6 seeds are required that will sprout if you plant 20 seeds.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

It is given that out of 30 planted seeds only 9 of them sprouted, then

Experimental probability =(number of occurrences of the event)/(total number of trials made)

=9/30

=3/10

thus the number of seeds that will sprout given the 20 seeds we planted will be

3/10×20

=6 seeds

Therefore, 6 seeds are required that will sprout if you plant 20 seeds.

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Hey can you please help me posted picture of question

Answers

C.
____________________

G(x) = F(x + 4) + 2

Addition of a number to x indicates a shift towards left. Since 4 is being added to x, this means function is shifted to left by 4 units.

Addition of a number to the function represent an upward shift. Since 2 is being added to the function value, this mean function is shifted up by 2 units.

So, G(x) is obtained by shifted F(x) 4 units to left and 2 units up.

Thus, option C is the correct answer

Linda bought circular table clothe that was a radius of 3 feet. What is the circmference to the nearest foot of linda's table cloth? (using Pie 3.14

Answers

we know that
[circumference]=2*pi*r
for r=3 ft
[circumference]=2*pi*3-----> 18.84 ft-------> nearest foot-----> 19 ft

the answer is
19 ft

what happens when you add 1 to a number

Answers

um the value of the number increases by 1

Trica's mother let her play outside for 15 minutes. When she went outside,she played with her dog for 5 minutes.Then she rode her bike for 4 minutes .She spent the rest of her time catching bugs.how many minutes did Trica spent catching bugs?

Answers

to get the answer, you subtract the time she spent playing with her dog (5 minutes) from 15. 15-5=10. then you subtract the time she rode her bike (4 minutes). 10-4=6. since there are 6 minutes left, she spent 6 minutes catching bugs

easy 6 minutes because the other minutes trica spent doing something else equal 9 minutes and we need 15 minutes so 6 +9 =15 right so that is y it is 6 ur welcome

Identify the figure formed by the net.

•Square pyramid
•Hexagonal prism
•Cylinder
•Cube

Answers

Hello!

the answer is CUBE

I hope this helps, and have a nice day!

The graph of a hyperbola is shown. what is the length of the transverse axis

Answers

the transverse axis is the distance between the two vertices ( where the lines cross the x axis)

the one on the left is at (0,-9) the one on the right is st (0,9)

distance between -9 and 9 = 18

the length of the transverse axis is 18

The length of the transverse axis is 18 units.

What is the transverse axis of a hyperbola?

"The transverse axis is a line segment that passes through the center of the hyperbola and has vertices as its endpoints."

Given, the vertices of the hyperbola are at (-9, 0) and (9, 0).

Therefore, the length of the transverse axis is

[tex]= (9+9) units\\= 18 units[/tex]

Therefore, the length of the transverse axis is 18 units.

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The raised vegetable garden in Susan's yard is in the shape of a rectangular prism with a volume of 48 cubic feet and a height of 3/4 foot.
PLEASE DO THE WORK AND SHOW ME!!!!!
Please answer, and I'll ask this and I'll do the question again, and I'll do the same points.
Please thankyou
No jokes!!!!!!!!!

Answers

Final answer:

To find the dimensions of the raised vegetable garden, we need to solve for the length and width using the given volume and height.

Explanation:

To find the volume of the raised vegetable garden, we multiply the area of the base by the height. In this case, the base is a rectangle, so its area is length times width. Let's call the length of the garden L and the width W. The volume (V) is given as 48 cubic feet and the height (H) is 3/4 foot. Therefore, we have the equation V = L x W x H. Substituting the given values, we get 48 = L x W x 3/4. To solve for L and W, we need to choose possible values for them that satisfy the equation. Let's start by considering possible values for L and W: L = 16 feet and W = 3 feet. Substituting these values into the equation, we have 48 = 16 x 3 x 3/4. Simplifying, we get 48 = 144/4, which is not true. Therefore, our initial guess for the values of L and W is incorrect. Let's try another set of values: L = 12 feet and W = 4 feet. Substituting these values into the equation, we have 48 = 12 x 4 x 3/4. Simplifying, we get 48 = 144/4, which is true. Therefore, the raised vegetable garden is 12 feet long and 4 feet wide.

At the ice-cream parlor you can choose from 4 flavors of ice cream, 2 types of sauce, and 3 different toppings when ordering a sundae. How many possible sundaes can be ordered?

Answers

possibilities are 4*2*3 = 24 different sundaes

Which expression represents the volume of the box? use the formula v=lwh 3x+1, 2x-1 ×+2

Answers

The expression of the volume of the box with dimensions of
(3x+1) by (2x-1) by (x+2) will be:
volume, V=lwh
plugging the values we get:
V=(3x+1)(2x-1)(x+2)
Expanding the above we get:
V=(3x+1)(2x^2+3x-2)
V=3x(2x^2+3x-2)+1(2x^2+3x-2)
V=6x^3+9x^2-6x+2x^2+3x-2
V=6x^3+11x^2-3x-2
Hence the expression for the volume will be:
V=6x^3+11x^2-3x-2

Hey can you please help me posted picture of question

Answers

6(6 sided) choices for the die, and 8 choices(sections), so there are 6*8 = 48 total possibilities :)

there are 6 numbers on a die

the spinner has 8 sections

total possibilities = 6 x 8 = 48
the answer is B.

Julius is buying beverages for brunch he needs to buy a total of 5 gallons of beverages he decides to buy two containers of each of the following beverages 2 pints of milk 2 quarts of orange juice 16 cups of milk 32 oz of lemonade . how many gallons of beverages did he buy

Answers

This will be calculated as follows:
1 pint=0.125 gallons
1 quart=0.25 gallons
1 cup = 0.0625 gallons
1 oz = 0.0078125 gallons
thus amount of :
milk bought
0.125*2=0.25 gallons

orange juice bought:
0.25*2=0.5 gallons

milk bought:
16*0.0625=1 gallon

lemonade bought:
32*0.0078125=0.25 gallons

Thus total gallons made was:
0.25+1+0.5+0.25
=2 gallons

The amount of beverages did he buy will be 2 gallons.

What is conversion?

Conversion means to convert the same thing into different units.

Julius is buying beverages for brunch he needs to buy a total of 5 gallons of beverages he decides to buy two containers of each of the following beverages 2 pints of milk, 2 quarts of orange juice, 16 cups of milk, and 32 oz of lemonade.

We know the conversion

1 pint = 0.125 gallons

1 quart = 0.25 gallons

1 cup = 0.0625 gallons

1 oz = 0.0078125 gallons

Then the amount of beverages did he buy will be

Milk bought

0.125 x 2 = 0.25 gallons

Orange juice bought:

0.25 x 2 = 0.5 gallons

Milk bought:

16 x 0.0625 = 1 gallon

Lemonade bought:

32 x 0.0078125 = 0.25 gallons

Thus total gallons made will be

→ 0.25 + 1 + 0.5 + 0.25

→ 2 gallons

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Find the lowest common denominator of the following fractions. 5/n-2 and n+2/n^2-4

Answers

The denominator of the second fraction is the difference of squares, so can be factored using the formula for that.
(n^2 -4) = (n -2)(n +2)

Now, you will note that the second fraction has a numerator that is equal to one of the factors in the denominator. In other words, the whole fraction can be simplified to ...
(n +2)/((n +2)(n -2)) = 1/(n -2) . . . . with the restriction n≠-2

This reduced form of the fraction has the same denominator as the first fraction, so you can say that the lowest common denominator is that: (n -2).

_____
If there is some reason you don't want to reduce the second fraction, the lowest common denominator will be (n -2)(n +2).

Final answer:

The lowest common denominator of the fractions 5/(n-2) and[tex](n+2)/(n^2-4)[/tex] is[tex]n^2 - 4,[/tex] which is the factored form of the denominator of the second fraction.

Explanation:

The question asks to find the lowest common denominator (LCD) of two fractions: 5/(n-2) and (n+2)/[tex]n^2 - 4,[/tex]. To do this, we need to factor each denominator, if possible, and then determine the LCD. The second denominator can be factored into (n+2)(n-2) since it is a difference of squares. For the LCD, we need each factor present at least as many times as it occurs in any one of the denominators. The first fraction is already missing the (n+2) factor, so we multiply the numerator and the denominator of this fraction by (n+2) to have an equivalent fraction with the common denominator.

The common denominator then is (n+2)(n-2), equivalent to[tex]n^2 - 4,[/tex] So the LCD of the two fractions is[tex]n^2 - 4.[/tex] We can use this denominator to combine fractions or compare them. No further steps are necessary because the second fraction already has the LCD. Therefore, the LCD for both fractions is [tex]n^2 - 4.[/tex]

If f(x)=x-6 and g(x)=x1/2(x+3), find g(x) times f(x)

Answers

To solve this problem you must apply the proccedure shown below:
1. You have the following functions given in the problem above:
[tex]f(x)=x-6 [/tex] and [tex]g(x)=x1/2(x+3)=x(x+3)/2 [/tex]
2. You have that g(x) times f(x) can be written as g(x)*f(x). Therefore, you must multiply f(x) * g(x), as following:
[tex]g(x)*f(x)=(x-6)*x(x+3)/2 [/tex]
3. Applying the distributive property, you have:
[tex]g(x)*f(x)=( x^{3} + 3x^2 - 6x^{2} -18x)/2[/tex]
[tex]g(x)*f(x)=(x^{3} - 3x^{2} -18x)/2 [/tex]
The answer is: [tex]g(x)*f(x)=(x^{3} - 3x^{2} -18x)/2[/tex]

Simplify radical expression. Leave in radical form. the squarefoot of 7(the squarefoot of 14+the squarefoot 3)

Answers

To solve this problem you must apply the proccedure shown below:

1- You have the following radical expression given in the problem above:

(√7)(√(14)+√(3))

2- When you apply the distributive property, you obtain:

(√7)(√(14))+ (√7)(√(3))

3-Simpliying, you have:

(7√2)+(√21)

4- Therefore the answer is: (7√2)+(√21)

What is the domain of the function log(x-4) +4?

Answers

[tex]\log(x-4)+4\\\\\text{the domain:}\\\\x-4 > 0\ \ \ |+4\\\\x > 4\to x\in(4;\ \infty)[/tex]

the log of 0 is not defined, so the criterion to use here is that the input to the log function must be greater than zero.

Thus, x-4 ≥ 0, or x ≥ 4 (answer)

two angles are supplementary. One of the angles has a measure of 60 degrees. What is the measure of the other angle?

Answers

Answer:

120°

Step-by-step explanation:

One researcher wishes to estimate the mean number of hours that high school students spend watching tv on a weekday. a margin of error of 0.23 hour is desired. past studies suggest that a population standard deviation of 1.9 hours is reasonable. estimate the minimum sample size required to estimate the population mean with the stated accuracy.

Answers

Margin of error, e = Z*SD/Sqrt (N), where N = Sample population

Assuming a 95% confidence interval and substituting all the values;
At 95% confidence, Z = 1.96

Therefore,
0.23 = 1.96*1.9/Sqrt (N)

Sqrt (N) = 1.96*1.9/0.23

N = (1.96*1.9/0.23)^2 = 262.16 ≈ 263

Minimum sample size required is 263 students.

Answer:the answer is 236 students

Step-by-step explanation:

Leo, Kush and Mai share some money in the ratio 3:5:8
Kush receives £750 more than Leo.
Calculate total amount of money that they shared.

Answers

Let the amount Leo received be £x Kush received be £(x+750)
The ratio in which they received cash is 3:5:8
the difference in ration between Kush and Leo=£(5-3)=£2
Total ratio is: 16
thus the total amount was:
16/2×750
=£6000

Q # 2 Graph TWX and it's image after a rotation of 90° counterclockwise about the origen

Answers

For a rotation of 90o: (x, y) ⇒ (–y, x)
T(3,4) ⇒⇒⇒ T'(-4,3)
W(-2,-1) ⇒⇒⇒ W'(1,-2)
x(-3,3) ⇒⇒⇒ x'(-3,-3)

see the attached figure

Please help the answer are
12
4
X
X+4
-16
16
X+12
X^2

Answers

Step 1:
x² + 4x = 192

Step 2:
Take x common:
x ( x + 4) = 192

Length is x and width is x+4

Step 3:

x² + 4x - 192 = 0

Step 4:

x² + 16x - 12x - 192 = 0
x(x+16) - 12(x+16) = 0
(x-12)(x+16) = 0

⇒ x=12, x=-16

Because the length can't be -16, the length is 12.

Step 2: {4, x+4}
Factoring x²+4x, you get x(x+4). If you call the length x, then the width is the other factor, x+4.

Step 4: {16}
You know this two ways. -192/-12 = 16, and 4 -(-12) = 16, where 4 is the coefficient of x in step 3.

Last line: {-16, 16}
The values of x that make the factors zero are -16 and 12. Since these are supposed to represent lengths, an appropriate answer cannot be negative (-16). The width is x+4 = 12+4 = 16.

A taco stand sells tacos for $3.25 each. The stands expenses for the day are $210. Define your variables and write an inequality to represent the amount of tacos they need to sell per day to make a profit, and then slice the inequality. Provide your conclusion as a complete sentence.

Answers

Given:

Let P= profit
let n= no. of tacos sold per day

Sol'n:

P= 3.25n-210
the profit needs to be positive, thus

3.25n>210

n>210/3.25

n> 64.615

they can only sell whole tacos, therefore they must sell at least 65 tacos to make a profit and that profit is:

P=3.25n-210

P=3.25*65 - 210

P= 211.25 -210

P= 1.25

$1.25 profit

Jill earns $18.59 per hour. what is her gross earnings if she worked 46 hours. jill earns time and a half for overtime work.

Answers

We assume Jill's full-time work week is 40 hours, so that any hours in excess of that are overtime.

There are a couple of ways to think about overtime pay.
1) Figure the number of overtime hours, and multiply that number by 1.5 times the base pay. (OT pay) = (OT hours)*(1.5*(base pay))

2) Figure the number of overtime hours, and multiply that number by 1.5, then by the base pay. (OT pay) = ((OT hours)*1.5)*(base pay)

You can see the product is the same, only the sequence of computation is changed.

Then Jill's gross earnings can be computed as ...
(40 h +(6 h)*1.5)*(base pay)
(49 h)*($18.59/h) = $910.91

Jill's gross earnings for 46 hours' work will be $910.91.

Find the nth term of the sequence, then find the 20th term, 100th term and the series for each?

2/5, 1/15, -4/15,....

Answers

[tex]a_1=\dfrac{2}{5}=\dfrac{6}{15}\\\\a_2=\dfrac{1}{15}\\\\a_3=-\dfrac{4}{15}\\\\a_2-a_1=\dfrac{1}{15}-\dfrac{6}{15}=-\dfrac{5}{15}=-\dfrac{1}{3}\\\\a_3-a_2=-\dfrac{4}{15}-\dfrac{1}{15}=-\dfrac{5}{15}=-\dfrac{1}{3}[/tex]

It's an arithmetic sequence where

[tex]a_1=\dfrac{2}{5}\ and\ d=-\dfrac{1}{3}[/tex]

nth term of the arithmetic sequence is equal:

[tex]a_n=a_1+(n-1)d[/tex]

Substitute:

[tex]a_n=\dfrac{2}{5}+(n-1)\cdot\left(-\dfrac{1}{3}\right)\\\\a_n=\dfrac{2}{5}-\dfrac{1}{3}n+\dfrac{1}{3}\\\\a_n=\dfrac{6}{15}+\dfrac{5}{15}-\dfrac{1}{3}n\\\\\boxed{a_n=\dfrac{11}{15}-\dfrac{1}{3}n}[/tex]

Other form:

[tex]a_n=\dfrac{11}{15}-\dfrac{5}{15}n\\\\\boxed{a_n=\dfrac{11-5n}{15}}[/tex]

[tex]a_{20}=\dfrac{11-5\cdot20}{15}=\dfrac{11-100}{15}=\dfrac{-89}{15}\\\\a_{100}=\dfrac{11-5\cdot100}{15}=\dfrac{11-500}{15}=\dfrac{-489}{15}=-\dfrac{163}{5}[/tex]

the temperature at 10 am was -7°F. By noon, the temperature had dropped 12°F. By 2 pm, it had dropped another 5°F. what was the temperature at 2 pm?

Answers

-7°F minus 12°F equals -19°F minus another 5°F is -24°F

Tanisha cut a triangle with angles of 34°, 67°, and 79° in three pieces so that each piece had one angle of the triangle. She arranged the three angles connected together such that the three corners of the triangle were all touching. What type of angle was formed and what does this show?

Answers

A straight angle was formed when Tanisha arranged the three angles. This shows that the sum of the measures of the three angles in the triangle is equal to the straight angle, that is, the angle sum is 180 degrees. Also, this shows that whatever the position of the three sides of the triangle is, the total degrees of the angles is always 180.

Employee Earnings per month($) 1 1,200 2 2,600 3 1,800 4 1,450 5 3,500 6 2,800 7 12,500 8 3,200 Which measure of spread is best for the data in the table?

Answers

Answer: Interquartile range

Step-by-step explanation:

Interquartile Range:

Q3 - Q1 Find Q2 then Q3 then Q1. Then subtract Q3 and Q1.

This is the most accurate out of all measures of spread.

Hope this helps :)

The measure of spread is best for the data in the table is mean absolute deviation.

What is data table?

Tables are a useful tool used to present data in an organized and easy-to-understand format. They typically consist of rows and columns that contain information, and can even be structured in more complex ways. Tables are often used in communications, research, and data analysis.

The given data is 1200, 2600, 1800, 1450, 3500, 2800, 12500 and 3200.

Mean absolute deviation (MAD) is a measure of variation in a data set, calculated by taking the average of the absolute differences between each data value and the mean. It gives an indication of how far each data point is from the mean, providing an easy way to detect the spread of the data. MAD is a useful tool for understanding the range of values within a data set, and it can be used to compare different sets of data to each other.

Therefore, the measure of spread is best for the data in the table is mean absolute deviation.

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the function f(x)=2^x. the function f(x)= 2^x+k and K < 0. which of the following statements is true

Answers

from experience it is f of x equals two to the square root of x

State the domain of the relation

Answers

Domain is all of the x values of the points in a graph.

The domain is {-2,0,1,2,3,4}, assuming there is a point at (4,6).

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Ssl (secure sockets layer) operates at which layer of the osi model Developing a hypothesis is which step in the scientific method When p is divided by 12, the quotient is q with a remainder of 5, where p and q are positive integers. what is the remainder when p is divided by 6? I would like to nominate my friend Angela Consolo for class president. Angela is an excellent student who participates in many extracurricular activities. She has always had a knack for leadership. She currently acts as captain of the soccer team and president of the honor society. I believe that Angela could help our class reach its goals over the next school year. Jason wrote a letter to nominate his friend Angela for class president. Do the examples Jason provided in this part of his letter support his position? A)no, because they do not explain why Angela wants to be president B)yes, because they support the idea that Angela is an excellent leader C)no, because they do not tell readers what Angela would do as president D)yes, because they show readers how popular Angela is with other students a car traveling at 24 m/s starts to decelerate steadily. It comes to a complete stop in 6 seconds what is its acceleration? It would take an hour for plane A to meet plane B which is flying towards it. If the distance between them will be 200 miles after 45 minutes, how far apart are they now? Gould and colleagues summarized their findings by stating that there are two major "strains" of burnout. these two strains are _________ and _________ in nature. (5 points)Points A and B are two of the vertices of a right triangle. They are the endpoints of the hypotenuse AB of the triangle. The third vertex of the triangle lies in the first quadrant.Plot a point at the location of the third vertex. A dilation produces a smaller figure. Which is a possible scale factor? 2 1/31 4 my opponent thinks that he would make an effective class president. but he received Cs and Ds on recent test. is this kind of person you want to serve in office? which logical fallacy is used in this passage? a.circular reasoningb.bandwagonc.slippery sloped.ad hominem attack The point, (-4, 1) is located in which quadrant? If I have a 40 % and my teacher puts in 3 100% whats my grade ? virginia's therapist notes that virginia jumps from one topic to another and her replies are only tangentially related to the therapist's questions. this describes which symptom of schizophrenia? What is required for a person to have sickle-cell disease?A. the person is homozygous and has malaria B. the person is heterozygous and has malariaC. the person is heterozygous for the traitD. the person is homozygous for the trait Explain the degree to which Shakespeare used outside sources and ideas in his plays? If a hydrogen atom in the ground state absorbs a photon of energy 12.09 ev, to which state will the electron make a transition? What museum did the fearless five infiltrate in Mexico city In the general plan for balancing redox equations, when a reaction takes place in basic solution, you will need to add Sound waves travel at about 259 meters per second through gaseous carbon dioxide. They travel at about 1,162 meters per second through liquid ethanol. And they travel at 1,960 meters per second though solid lead. Which of the following statements about electromagnetic waves is true? A. Electromagnetic waves travel faster than sound waves through all media. B. Electromagnetic waves travel faster than sound waves through gases but not through liquids. C. Electromagnetic waves travel faster than sound waves through liquids but not through solids. D. Sound waves travel faster than electromagnetic waves through all media. Hailey works in a spa. Today, there was a sale on a particular color of nail polish. Twenty customers came in asking for the nail polish. Which qualification helped Hailey make it through the day without getting frustrated?