Let g(x)=x²-1.
(a) Find the average rate of change from 2 to 6.
(b) Find an equation of the secant line containing (-2, g(-2)) and (6, g(6)).
Answers
Answer:
Step-by-step explanation:
To find the average rate of change from 2 to 6, we can use the formula for the average rate of change, which is given by (y2 - y1) / (x2 - x1). In this case, the function we are working with is g(x) = x² - 1, so we need to plug in the values of x1 and x2 into the function to get the corresponding values of y1 and y2.
a) The average rate of change from 2 to 6 is given by:
(g(6) - g(2)) / (6 - 2)
Plugging in the values of x1 and x2 into the function g(x), we get:
(g(6) - g(2)) / (6 - 2) = (6² - 1 - 2² + 1) / (6 - 2) = (35 - 3) / 4 = 32 / 4 = 8
Therefore, the average rate of change from 2 to 6 is 8.
b) To find an equation of the secant line containing the points (-2, g(-2)) and (6, g(6)), we need to first find the slope of the secant line. The slope of the secant line is given by the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points on the secant line.
In this case, the coordinates of the two points on the secant line are (-2, g(-2)) and (6, g(6)). Plugging these values into the formula for the slope, we get:
m = (g(6) - g(-2)) / (6 - (-2)) = (6² - 1 - (-2)² + 1) / (6 + 2) = (35 + 5) / 8 = 40 / 8 = 5
Now that we know the slope of the secant line, we can use the point-slope form of a line to write the equation of the secant line. The point-slope form of a line is given by the formula y - y1 = m(x - x1), where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of a generic point on the line.
In this case, we know that the point (-2, g(-2)) is on the secant line, and we know that the slope of the secant line is 5. Plugging these values into the point-slope form of a line, we get:
y - g(-2) = 5(x - (-2))
We can then simplify this equation to get:
y - (-2² - 1) = 5(x + 2)
y + 3 = 5x + 10
Finally, we can move all of the terms containing x to one side of the equation and all of the constant terms to the other side of the equation to get the standard form of the equation of the line:
y = 5x + 7
Therefore, an equation of the secant line containing the points (-2, g(-2)) and (6, g(6)) is y = 5x + 7.
Related Questions
The floor plan of a house is shown below 20 ft 12 ft 7 ft 8 ft 8 ft 34 ft After installing new hardwood flooring , you also need to install base board around the bottom of the walls How many feet of base board will you need to buy ?
Answers
Given
The floor plan of a house is,
After installing new hardwood flooring , you also need to install base board around the bottom of the walls.
To find: How many feet of base board will you need to buy?
Explanation:
It is given that,
The floor plan of a house is,
After installing new hardwood flooring , you also need to install base board around the bottom of the walls.
That implies,
The perimetr of the base board is,
\(\begin{gathered} Perimeter=20+12+12+7+7+8+8+34 \\ =108ft \end{gathered}\)Hence, we need to buy 108ft of base board.
45% of the students of a Padampur Shiksha Niketan School play basketball, 40% play cricket and 30% play both. If 360 students play neither basketball nor cricket, use Venn-diagram and find the number of students in the school. Also, find the number of students who play only basketball. Ans: 800, 120
Answers
Then we have:
n(B) = 45% of the total number of students
n(C) = 40% of the total number of students
n(B ∩ C) = 30% of the total number of students
n(Not B and Not C) = 360 students
We want to find the total number of students, which is given by the formula:
n(Total) = n(B) + n(C) - n(B ∩ C) + n(Not B and Not C)
Substituting the given values, we get:
n(Total) = 45% + 40% - 30% + 360
n(Total) = 55% + 360
n(Total) = 800
Therefore, the total number of students in the school is 800.
To find the number of students who play only basketball, we can use the formula:
n(B only) = n(B) - n(B ∩ C)
Substituting the given values, we get:
n(B only) = 45% - 30%
n(B only) = 15%
Since 15% of 800 is 120, we can conclude that 120 students play only basketball.
Can you help me
The Celtics won 70% of their 30 games this season. The Celtics won 4 out of 6 games when Jason Tatum is playing. Are the events "the Wildcats win
the game" and the "Wildcats win the game when Elena started the game "dependent or independent events?
For questions 1 and 2, write your answer as a percentage, rounded to the nearest whole number WITH the percent sign (Ex. 65%)
1. P(Win)
2. P(Win I Jason Tatum)
3. Are these events independent or dependent (write the word, spelled correctly)?
Hint: Independent means same probabilities and dependent means the different probabilities) to
Answers
1) The probability of the Celtics winning a game is 21/30, or 70%.
2) The probability of the Celtics winning a game when Jason Tatum played is 4/6, or 67%.
3) These events are dependent.
Now, we can use the formula:
P(Win) = (number of wins) / (total number of games)
Substituting the given values, we get:
P(Win) = (0.7 * 30) / 1 P(Win) = 21
Therefore, the probability of the Celtics winning a game is 21/30, or 70%.
Hence, P(Win) = 70%
This means that the Celtics won 70% of their 30 games this season.
And, we can use the formula:
P(Win I Jason Tatum) = (number of wins when Jason Tatum played) / (total number of games Jason Tatum played)
Substituting the given values, we get:
P(Win I Jason Tatum) = 4 / 6 P(Win I Jason Tatum) = 0.67
Therefore, the probability of the Celtics winning a game when Jason Tatum played is 4/6, or 67%.
3) These things are linked together. The likelihood of the Celtics winning a game is impacted by Jason Tatum's participation in that game. If the two events were separate, whether Jason Tatum played or not would not have an impact on the outcome of the first event, the game.
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A pattern contains 3, 11, 5, 13, 7, and 15 dots. What are the next two terms of the sequence?
O9, 17
O 7, 13
O9, 15
O 7,11
Answers
Find the X- Intercept for this 3/2y + 3
(?,?)
Answers
Answer:
\((3,0)\)
Step-by-step explanation:
A bag is filled with an equal number of red, yellow, green, blue, and purple marbles. The theoretical probability of Jonah drawing 2 red marbles from the bag with replacement is one fifth. If the experiment is repeated 100 times, what is a reasonable prediction of the number of times he will select 2 red marbles?
one fifth
5
20
25
Answers
Answer:
20
Step-by-step explanation:
The theoretical probability of drawing 2 red marbles from the bag with replacement is one-fifth, which means that the probability of drawing 2 red marbles in any one trial is 1/5 or 0.2.
The number of times Jonah is expected to select 2 red marbles in 100 trials can be predicted using the expected value formula:
Expected value = (Number of trials) x (Probability of success in one trial)
Expected value = 100 x 0.2
Expected value = 20
Therefore, a reasonable prediction of the number of times Jonah will select 2 red marbles in 100 trials is 20. Therefore, the answer is 20.
Answer: 20 i took the test
Step-by-step explanation:
Solve the equation.
4 (6 – x) + 4 = 2 (3x + 1) - 6
Answers
Answer:
x = 2.4
Step-by-step explanation:
Simplify.
24 - 4x + 4 = 6x + 2 - 6
Combine like terms (24 + 4 = 28, sorry for the confusion!)
28 - 4x = 6x - 4
Add x and add 4 to both sides.
10x = 32
x = 3.2
Answer:
x=3 1/5 or 3.2
Step-by-step explanation:
Trevor packed 22.5 pounds of potatoes into several bags. If there are 2.5 pounds of potatoes in each bag, how many
bags did he pack?
Answers
22.5/2.5 = 9 bags
Answer:
9
Step-by-step explanation:
22.5÷2.5=9 this is how you solve it
6 minutes 20 seconds into seconds.
Answers
Answer:
380 seconds
Step-by-step explanation:
Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360
Now add the 20 seconds.
360 + 20 = 380
6 minutes and 20 seconds are equal to 380 seconds.
(x+5)²=81
need help quick
Answers
x-5=positive/negative 9
x=14, and -4
If 4m =130 does 4m÷4=130
Answers
Answer:
no
Step-by-step explanation:
if 4m=130 then that means m=32.5
if 4m/4=130 then that means m=130 which is not the same as 4m=130
1. Jamar has two bowls of fruit from which he can choose a
snack when he gets home from school. One bowl has 1 yellow,
1 red, and 2 green apples. The other bowl has 5 each of
boysenberries, strawberries, blueberries, and blackberries.
What is the probability that he gets a yellow apple and a
boysenberry when he reaches into the bowls?
Answers
Answer:
One bowl has 1 yellow, 1 red, and 2 green apples. The other bowl has 5 each of boysenberries, strawberries, blueberries, and blackberries.
Step-by-step explanation:
In response to nutrition concerns raised last year about food served in school cafeterias, the Smallville School District entered into a one-year contract with the Healthy Alternative Meals (HAM) company. Under this contract, the company plans and prepares meals for 2,500 elementary, middle, and high school students, with a focus on good nutrition. The school administration would like to survey the students in the district to estimate the proportion of students who are satisfied with the food under this contract. Two sampling plans for selecting the students to be surveyed are under consideration by the administration. One plan is to take a simple random sample of students in the district and then survey those students. The other plan is to take a stratified random sample of students in the district and then survey those students. (a) Describe a simple random sampling procedure that the administrators could use to select 200 students from the 2,500 students in the district. (b) If a stratified random sampling procedure is used, give one example of an effective variable on which to stratify in this survey. Explain your reasoning>
Answers
The students corresponding to those 200 numbers would beasked to participate in the survey.
What is corresponding ?
Having or participating in the same relationship (such as kind, degree, position, correspondence, or function) especially with regard to the same or like wholes (such as geometric figures or sets) corresponding parts of similar triangles. : related, accompanying.
Have given,
a) The administrators could number an alphabetical list of students from 1 to 2,500.Then use a random number generator from a calculator or computer to generate 200 unique random numbers from 1 to2,500.(if you don’t say “unique”, then say “ignoring repeats”)The students corresponding to those 200 numbers would beasked to participate in the survey.
b) One advantage is that stratified random sampling guarantees that each of the school-level strata will have some representation, because it is possible that a simple random sample would miss one or more of the strata completely.(NOTE: It is NOT sufficient to say that a stratified sample “makes it MORELIKELY that all school-levels are represented in the sample”… the student must state that stratifying by school level GUARANTEES or ENSURES that all school levels are represented in the sample.)
The students corresponding to those 200 numbers would beasked to participate in the survey.
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Subtract these polynomials.
(3x2 – 2x + 5) – (x2 + 3) =
Answers
Answer:
D. 2x^2 - 2x + 2
Step-by-step explanation:
(3x2 – 2x + 5) – (x2 + 3) add or subtract like terms
3x^2 - x^2 - 2x - 3 + 5 = 2x^2 - 2x + 2
Answer:
2x^2 - 2x + 2
Step-by-step explanation:
Ape-x
find the base of the triangle, if its area is 18 hectares and height is 60 dam
Answers
Answer:
Step-by-step explanation:
The formula for the area of a triangle is:
1/2×base×height
If you know the area of the triangle and height you can apply the area formula:
A=1/2×base×height
in reverse to calculate the length of the base:
b=2A/h
given, h=60dam
A=18
so, b=2×18/60
b=36/60
b=0.6
The answer is 0.6
select all of the lines that have a slope of 2/5
Answers
the slope 2/5 is written in the formula rise/run. So u can use this method to determine which line has a slope of 2/5.
please helppp
here is the picture is about Row Ops
Answers
Multiplying row 1 of the matrix by 1 / 4 would give a resultant matrix of [ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ].
How to multiply the matrix row ?The question wants to multiply the first row of the matrix alone, with the fraction, 1 / 4.
First step is then to multiply the first row by the fraction of 1 / 4 :
( 1 / 4 ) x 2 = 1 / 2
( 1 / 4 ) x 0 = 0
( 1 / 4 ) x 3 = 3 / 4
The results acquired can then be input into the matrix which would then give a resultant matrix of :
[ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ]
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when some population elements are excluded from the process of selecting the sample
Answers
Specific individuals in a population are unfairly left out of a study, which is known as exclusion bias. When researchers design a study that inadequately represents specific segments of the community, undercoverage bias emerges.
when a sample is unrepresentative of the population as a whole?When a sample is not chosen that accurately represents the full population of data, a statistical error known as sampling error arises. As a result, the sample's findings do not accurately reflect the outcomes that the complete population would produce.
What is the procedure for choosing a sample from the population called as?When a sample is chosen from a population based on the idea of randomization, this practise is known as probability sampling.
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Help please!!!!!!!!!!!
Answers
Answer:
9/40
Step-by-step explanation:
9/2 is 4.5 and 1/5 is 0.20 so 4.5 times 0.30 is 22.5 and 22.5 into a fraction is 9/40.
making $40 payments each Friday,
6. Emily borrowed $1,000 from her parents to put towards a down payment on a car. She has
already paid back $350. Her parents do not charge any interest and Emily is planning on
Write an equation that represents the number of weeks it will take Emily to repay her
b. Is the solution to the equation the actual number of weeks it will take Emily to repay her
Lesson 1.5.
parents? Explain your answer.
a.
parents if she pays $40 each Friday.
Answers
Use the ALEKS graphing calculator to find all the real zeros of the quadrat
f(x)=-3x²+2x+2
Round to the nearest hundredth.
If there is more than one answer, separate them with commas.
If there are no real zeros, click on "None".
real zero(s):
0
0,0,...
X
None
S
Answers
The quadratic function f(x) = -3x² + 2x + 2 has no genuine zeros, rounded to the closest hundredth.
Utilising the graphing calculator ALEKS, do the following procedures to calculate the real zeros of the quadratic function f(x) = -3x² + 2x + 2
Launch the graphing calculator ALEKS.
Input the calculator's f(x) = -3x² + 2x + 2 function.
To view the function's graph, click the "Graph" button.
Find the points where the graph and x-axis meet.
These dots represent the function's real zeros.
To determine the precise coordinates of these junction locations, use the "Trace" or "Zero" feature on the calculator.
The x-coordinates should be rounded to the nearest hundredth.
We shall discover that the real zeros of the function f(x) = -3x2 after taking these actions.
After following these steps, we will find that the real zeros of the function f(x) = -3x² + 2x + 2 are approximately -0.44 and 1.22.
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PLEASE HELP ON QUESTION ASAP! 30PTS!
I WILL ALSO GIVE YOU A THANKS RATE YOU FIVE STARS AND MAYBE EVEN BRAINLIEST any silly answeres will be reported / deleted
Hiba needs 40g sugar to make 15 biscuits. she also needs three times as much flour as sugar . Hiba is going to make 60 biscuits . work out the amount of flour she needs .
Answers
40.3=120g flour➡️15 biscuits
60 biscuits = 16.4➡️120.4 = 480g flour
She needs 480g flour to make 60 biscuits
the degree of non constant zero polynomial is
Answers
Answer:
it is zero . zero is the degree of zero polnomial
List all 2-digit multiples of 27
Answers
Answer:
Solution: The multiples of 27 are, 27, 54, 81, 108, 135, 162, 189,... Among these, the multiples of 27 that lie between 110 and 170 are 135 and 162. Among these two multiples, the one with an odd digit in its one's place is 135.
Step-by-step explanation:
Answer:
27, 54, 81
Step-by-step explanation:
The n-th multiple of 27 is 27n. For 0 < n < 4, the multiples will be 2-digit.
27×1 = 27
27×2 = 54
27×3 = 81
The 2-digit multiples of 27 are 27, 54, 81.
can someone help me with this I need to find .the vertical asymptote, the horizontal asymptote , the x-intercept and the y-intercept
Answers
the vertical asymptote and horizontal asymptote
\(\begin{gathered} f(x)=\frac{x^2-1}{x^2+3x+2} \\ f(x)=\frac{(x-1)(x+1)}{(x+1)(x+2)} \\ f(x)=\frac{x-1}{x+2} \end{gathered}\)The vertical asymptote is x+2 = 0, x = -2
The horizontal asymptote is x - 1 = 0, x = 1
the x-intercept and the y-intercept
The intercept with x is calculated as 0 f(x)
\(\begin{gathered} f(x)=0 \\ \frac{x-1}{x+2}=0 \\ (x-1)=0 \\ x=1 \\ \end{gathered}\)The intercept with x is (1,0)
The intercept with y is calculated for x = 0
\(\begin{gathered} f(0) \\ \frac{x-1}{x+2} \\ \frac{0-1}{0+2} \\ \frac{-1}{2} \\ \end{gathered}\)The intercept with y is (0,-1/2)
The perimeter of a rectangle garden is 364 feet. If the width of the garden is 85 feet, what is it length?
Answers
P=2(L+W)
P=364
L=99
sub and find W
364=2(99+W)
divide both sides by 2
182=99+w
subtract 99 from both sides
83=W
w=83ft
Given the equation y = 2 csc(7π/4x-21π/2)
The horizontal shift is:
units to the Select an answer (right or left)
The exact period (give as an integer or fraction) is:
Answers
The horizontal shift is to the right.
The exact period is 8/7.
How to find the the horizontal shiftIn a trigonometric function, written of the form
y = A csc (Bx - C)
the parameters are interpreted as follows
A is the amplitude
B is period / 2π
C is the horizontal shift
comparing with the equation y = 2 csc (7π/4x - 21π/2). we have that
horizontal shift = -21π/2 since it is positive it is to the right
The exact period is
Period = 2π / (7π/4)
= 8/7
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What's the sum of ⅖ and ¾? О A. % • в. ⅐ • C. % O D. 1%0
Answers
Write and solve an equation for the word problem below
Chanel is renting a DVR from her cable company. It has a start-up fee of $45 plus $5 per month (m). If Chanel has a budget of $250, how many months
can she rent the DVR?
Answers
Answer:
41
Step-by-step explanation:
250-45=205
205/5=41
The student population at King Middle School is 52% female.
There are 637 girls at King Middle School. What is the total student
population King Middle School?
Answers
Answer:There are a total of 1225 students at King Middle School. If the population is 52% female, then 1225 x .52 = 637 female. 1225 - 637 = 588 male students.
Step-by-step explanation:
Answer:
1225
Step-by-step explanation:
To find the total amount of kids there are at King Middle School you do 100/52 because 52/100 is female and we are reversing the operation. 100/52 times 637 is 1225. There are a total of 1225 students and King Middle School.