This table represents a quadratic function with a vertex at (1, 1). What is the
average rate of change for the interval from x = 5 to x = 6?
OA. 26
OB. 13
O C. 7
OD. 9
1
2
3
4
5
X
1
2
LO
5
10
17
y
Answers
The average rate of change on the interval (5, 6) is 9. So the correct option is D.
How to find the average rate of change on the interval?
Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).
This is just:
\(r = \frac{f(6) - f(5)}{6 - 5}\)
\(f(x) = a*x^2 + b*x + c\)
I we look at the table we see that:
\(f(1) = 1 = a + b + c\)
\(f(2) =2 = 4a + 2b + c\)
\(f(3) = 5 = 9a + 3b + c\)
This is a system of equations.
If we subtract the second and first functions, we get:
\(2 - 1 = (4a + 2b +c) - (a + b + c)\\1 = 3a + b = a + b + c\)
From that we take two relations:
\(1 - 3a = b\\2a = c\)
Now we can replace these two in the last equations so we get:
\(5 = 9a + 3b + c\\\\5 = 9a + 3*(1 - 3a) + 2a\\\\5 = 9a + 3 - 9a + 2a\\\\5 = 3 + 2a\\\\5 - 3 = 2a\\\\2 = 2a\\\\a = 1\)
Now that we know the value of a:
\(c = 2a = 2*1 = 2\\\\b = 1 - 3a = 1 - 3 = -2\)
The quadratic equation is:
\(f(x) = x^2 - 2x + 2\)
Evaluating this in x = 6 we get:
\(f(6) = 6^2 - 2*6 + 2 = 26\)
And from the table we know that f(5) = 17, then the average rate of change is:
\(r = \frac{f(6) - f(5)}{6 - 5} = \frac{26-17}{1} = 9\)
The correct option is D.
If you want to learn more about average rates of change:
https://brainly.com/question/8728504
#SPJ1
Related Questions
Candice is taking a group nature hike in a park. There is a
$11.00 fee just to enter the park. In addition, the tour
group charges $0.14 per mile they hike. She brought
$81.00 with her. Find the maximum amount of miles
Candice can hike.
Answers
Answer:
500 miles
Step-by-step explanation:
81-11 is 70. 70 divided by .14 is 500 so that's 500 miles she can bike.
Answer:
500 miles
Step-by-step explanation:
To find out how many miles Candice can hike at max, use the equation 11 + 0.14x = 81.
11 + 0.14x = 81
Subtract 11 from both sides. This undoes the +11.
0.14x = 81 - 11
Subtract 11 from 81 to get 70.
0.14x = 70
Divide both sides by 0.14. This undoes the multiplication by 0.14.
x = 70/0.14
I recommend converting 0.14 into a fraction. That would be 7/50.
x = 70/(7/50)
Find the reciprocal of 7/50 (50/7). Switch the sign from division to multiplication.
x = (70 * 50)/7
Multiply 70 by 50 to get 3500.
x = 3500/7
Divide 3500 by 7 to get 500.
x = 500
At max, Candice can hike 500 miles.
Find only the margin of error to construct a 98% confidence interval for p1 - P2. Assume the samples are random and independent. Do not construct a confidence interval. Sample statistics: nâ = 1000, x1 = 250, and n2 = 1200, x2 = 195
Answers
The required margin of error construct a 98% confidence interval for p1 - P2 is 0.0403.
What is margin of error?Margin of errors, in statistics, is the level of blunder in results got from irregular examining overviews. A higher wiggle room in measurements shows less probability of depending on the consequences of a review or survey, for example the certainty on the outcomes will be lower to address a populace.
According to question:given data
n1 =1 000 x1 = 250
pˆ1 = x1n1 = 2501000 = 0.250
n2 = 1200 x2 = 195
pˆ2 = x2n2 = 1951200 = 0.1625
We have given confidence interval ,
98% ci for p1−p2.
Then,
α = 1 - 0.98 = 0.02
\(Z_{\alpha /2}\) = \(Z_{0.01}\) = 2.326
Again,
E = \(Z\sqrt{\frac{p1(1-p1)}{n1}+ \frac{p2(1-p2)}{n2} }\)
E = \(2.326\sqrt{\frac{0.250(1-0.250)}{1000}+ \frac{0.1625(1-0.1625)}{1200} }\)
E = 0.0403
Thus, required margin of error is 0.0403.
To know more about margin of error Visit:
brainly.com/question/10501147
#SPJ4
the numbers 1447, 1005, and 1231 have something in common: each is a 4-digit number beginning with 1 that has exactly two identical digits. how many such numbers are there?
Answers
If each is a 4-digit number beginning with 1 that has exactly two identical digits , then there are 432 such numbers .
In the question ,
Suppose that the two identical digits are both 1.
and since the thousands digit must be 1, only one of the other three digits can be 1. This means that the possible forms for the required numbers are
11xy , 1x1y , 1xy1 ,
Because the number must have exactly two identical digits, x ≠ y, x ≠ 1, and y ≠ 1.
Hence, Of this form there are 3 × 9 × 8 = 216 numbers .
Now suppose that two identical digits are not 1 , we will have the following possibilities:
1xxy , 1xyx , 1yxx
Again, x ≠ y , x ≠ 1 , and y ≠ 1 .
Of this form there are 3 × 9 × 8 = 216 numbers .
So , the total numbers are 216 + 216 = 432 .
Therefore , the total numbers are 432 .
Learn more about Numbers here
https://brainly.com/question/13220269
#SPJ4
The value of expression when 5x²- 2 when x=3 is
Answers
Answer:
43
Step-by-step explanation:
Substitute x = 3 into the expression, that is
5(3)² - 2 = 5(9) - 2 = 45 - 2 = 43
Let's solve your equation step-by-step.
5x2−2x=3 Step 1: Subtract 3 from both sides. 5x2−2x−3=3−35x2−2x−3=0 Step 2: Factor left side of equation. (5x+3)(x-1)=0 Step 3: Set factors equal to 0. 5x+3=0 or x−1=0x=−35 or x=1
Answer: x=−35 or x=1
Membership in the Anime club went from 35 members last year to 49 members this year. What is the percent of increase in membership? Round your answer to the nearest percent.
please explain how you got your answer.
Answers
Answer:
Percent increase is 40%
Step-by-step explanation:
btw this is my answer so it mayor may not be right so check other resources and find out whether my answer is right or wrong
~Jamie
what measurement is equal to 6 kilometers
Answers
Answer:
where is the options? or is any given.
Step-by-step explanation:
Complete each box with the missing operation or missing equation. use linear combination to solve {7x+2y=7 11x+5y=2
Answers
Answer: A: -35x-10y=35
B: multiply equation 2 by 2
C: add equation 1 and equation 2
D: x=-3
E: (-3,7)
Step-by-step explanation:
See the image................
Nate walks 25 meters in 13.7 seconds. If he walks at this same rate, which of the following is closest to the distance he will walk in 4 minutes? A) 150 meters B) 450 meters C) 700 meters D) 1,400 meters
Answers
Answer:
450 meters
Step-by-step explanation:
4 minutes = 240 seconds
\(\frac{x}{240} =\frac{25}{13.7}\)
solve for x
x = 438m
Noah entered a 100-mile bike race. he knows he can ride 32 miles in 32 minutes, At this rate, how long will it take him to finish the race? Use each table to find the answer
Answers
Which expression represents the following calculation?
Add the product of 7 and 5 to the quotient of 288 and 18
Answers
TRY 5814
:]
please mark brainliest! <3
Which of the following lists of ordered pairs is a function?
A. (1,1),(2,3)(1,5),(4,7)
B. (2,4),(-2,4), (3,9), (-2,-4)
C. (2,4), (3,9),(4,16), (5,25)
D. (0,2), (4,2), (0, -4), (4.-2)
Answers
The function below has at least one rational root. Find the y-intercept and use the rational roots theorem to find all rational roots. Fill in the sign table and sketch a graph below. Your graph must accurately cross all known intercepts. y f(x)=2x 3 −x 2 −4x+3
Answers
Answer:
Step-by-step explanation:
1/5 de los animales en el zoológico son monos 5/7 de los monos son machos
¿Qué fracción de los animales en el zoológico son monos machos?
Answers
1/7 of the animals in the zoo are male monkeys.
What fraction of the animals in the zoo are male monkeys? Explain with workings.
To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.
Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:
= 1/5
= 5/25.
And 5/7 of the monkeys are male which is written as 5/7.
To get fraction of male monkeys, we will multiply these two fractions:
= (5/25) * (5/7)
= 25/175
= 1/7.
Full question:
1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?
Read more about fraction
brainly.com/question/17220365
#SPJ1
perimeter of a ground is 6m. Find the cost of fencing it at the rate of rs 250per meter
Answers
Answer:
to find the rate of fencing, you should find the perimeter of the rectangle.
2(l+b)
2(155+125)
2*180
360m
cost of fencing = 360*10
= Rs 3600
now to find the cost of fielding, find the area
(l*b)
155*125
19375 square mtr
cost of fielding = 19375*15
= Rs 290625
Step-by-step explanation:
Evaluate the expression.
4(11 + 7) – 9.8
Answers
Answer:
4(11+7) - 9.8
4 (18) - 9.8
72 - 9.8
= 62.2
Brenda wants to make scrapbooks with old family photos. An online scrapbooking company charges $12 for a basic book and $2 per page. Meanwhile, a family friend is willing to make a scrapbook for $47 plus $1 per page. For a certain number of pages, the price would be equal. How many pages would that be? How much would that cost?
Answers
For a 35 number of pages, the price would be equal. & it would cost $82.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
An online scrapbooking company charges $12 for a basic book and $2 per page.
Meanwhile, a family friend is willing to make a scrapbook for $47 plus $1 per page.
let, the number of page = x, the price would be equal.
so, we get,
12 + 2x = 47+x
i.e. x = 35
Hence, For a 35 number of pages, the price would be equal. & it would cost $82.
To learn more on equation click:
brainly.com/question/24169758
#SPJ1
a nuber to be multiplied is called
Answers
Answer:
7×5 4×5 777⁷7777777777×7
Answer:
it is called factors
Step-by-step explanation:
Determine the third velocity component v such that all the components satisfy the continuity equation. The two components are as follows: u = 2xt-3xyz + 4xy w = 3x-5yzt+yz Also find the velocity and acceleration of a fluid particle at (1, 0, 1) at time, t= last digit.
Answers
The given velocity components are:
u = 2xt - 3xyz + 4xyw = 3x - 5yzt + yz
To satisfy the continuity equation, the third velocity component must be of the form
v = -ux - wy
Thus,v = -2xt + 3xyz - 4xy (from u)v = -3x + 5yz t - yz (from w)
The third velocity component
v = -2xt + 3xyz - 4xy - 3x + 5yz t - yz
= -2xt + 3xyz - 4xy - 3x + 5yz (t - 1)
The velocity of the fluid particle is given by,
v = (u, v, w) = (2t, -2t + 3z, 3 - 5zt + y)at (1, 0, 1) and t = 1 (last digit),v = (2, -2, -2)
The acceleration of the fluid particle is given by,
a = (at, av, aw)
= (∂u/∂t, ∂v/∂t, ∂w/∂t)at (1, 0, 1) and t = 1 (last digit),a = (2, 3, -5)
To know more about particle visit:
https://brainly.com/question/13874021
#SPJ11
jamal is attending a university where fitr tuition one year costs 11,800. he has a scholarship worth 1,500 per year he earns 2,500 per year at his part time job. he plans to take out a loan to cover the remaining tuition costs. Tuition will increase by 100 each year. If he completes collage in 4 years , how much money will jamal need to borrow
Answers
Answer:
Jamal will have to borrow 31,800.
Step-by-step explanation:
Total tuition for the full four years = 11,800 + 11,900 + 12,000 + 12,100 = 47,800
Total money from scholarship = 1,500 × 4 = 6,000
Total income received = 2,500 × 4 = 10,000
Total money to borrow = 47,800 - 6,000 - 10,000 = 31,800
If you answer this correctly, you are very cool guy. :)
Answers
-1.5 A
3^2 G
0.5^3 B
30 E
The real-life scenarios below represent the importance of using basic arithmetic and algebra to solve real-world quantitative problems.
Choosing a gym membership that fits my budget and lifestyle.
Gym A has a monthly payment of $50.
Gym B has a cost of $10 per visit.
Explain how you would calculate the result. You can infer and add any additional details you feel you might need to create the calculation.
Answers
To determine which gym membership is more cost-effective, you would need to compare the total cost for a given period. Let's consider a time frame of one month.
For Gym A, the monthly payment is $50. This means that regardless of how many times you visit the gym, you will pay a fixed amount of $50 each month.
For Gym B, the cost is $10 per visit. To calculate the total cost for a month, you need to estimate the number of times you plan to visit the gym in that period. Let's assume you plan to visit the gym 10 times in a month.
The total cost for Gym B would then be calculated as:
Total Cost for Gym B = Number of Visits * Cost per Visit
Total Cost for Gym B = 10 visits * $10 per visit
Total Cost for Gym B = $100
Comparing the total costs, we find that for Gym A, the monthly payment is $50, and for Gym B, the estimated cost for 10 visits is $100. In this case, Gym A would be the more cost-effective option if you plan to visit the gym at least 10 times in a month. However, if you anticipate visiting the gym less than 10 times in a month, Gym B might be the more affordable choice.
By using basic arithmetic to calculate the total costs based on the given pricing structures, you can make an informed decision regarding the gym membership that fits your budget and lifestyle.
Learn more about Budget here -: brainly.com/question/8647699
#SPJ11
Which of the following is a true statement about the angles in the
figure below?
22
21
24
43°
56
23
them is 99
Answers
Answer:
6ix9ine..69. ..
Step-by-step explanation:
m...vgcty
Bret bought his family lunch. Before tax, the bill came to $42. The sales tax was 6% and Bret tipped the waitress 20% before tax was added. How much money did Bret spend?
Answers
Answer: Bret spent $52.92 on the lunch, including tax and tip.
Step-by-step explanation:
Given:
The bill before tax = $42
Sales tax = 6%
Tip = 20% before tax
To find:The total amount of money Bret spent
Solution: Calculate the sales tax:
Sales tax = 0.06 * $42 = $2.52
Calculate the total bill, including tax:
Total bill = $42 + $2.52 = $44.52
Calculate the bill before tax, based on which the tip is calculated:
Bill before tax = $44.52 - $2.52 = $42
Calculate the tip amount:
Tip = 0.2 * $42 = $8.40
Calculate the total amount spent by Bret:
Total spent = $44.52 + $8.40 = $52.92
Therefore, Bret spent $52.92 on the lunch, including tax and tip.
In one month 382 adults and 65 children stayed in a hotel. How many people stayed at the hotel altogether?
Answers
Answer:
447 people
Step-by-step explanation:
382 plus 65 is 447.
Sam is earning some money picking apples. She gets paid $10 plus $2 per kilogram of apples that she picks. If Sam earns $C for n kg of apples picked, complete the following.
a) Write a rule for C in terms of n.
b) Use your rule to find:
(i) the amount Sam earned after picking 9kg of apples.
(ii) the number of kilograms of apples Sam picked if she earned $57.
Answers
Answer: BUY THEM
Step-by-step explanation:
Which statement is true about the relationship between the height of the plant and the number of days?
A. This relationship is a function because the plant can be more than one height at a time.
B. This relationship is not a function because the plant can be more than one height at a time.
C. This relationship is not a function because the plant can only be one height at a time.
D. This relationship is a function because the plant can only be one height at a time.
Answers
This relationship is a function because the plant body can be of only one particular height at a time.
A function can be defined as a relationship between a set of inputs having only one output each. In other words, a function is basically a relationship between inputs and outputs; where each input is related to only one output at a time. Functions are said to occur when the recorded value of x is varied each time. Since we know that the height of the plant (the x-value) varies by each day, Therefore it is a function.
thus we can conclude that the correct option for the relationship between the height of the plant and the number of days is option D, which tells that this relationship is a function because the plant body can only be of one particular height at a time.
To learn more about functions
visit; https://brainly.com/question/12431044
#SPJ1
It rained 4/5 inches on Monday.
On Tuesday, it rained 7/10 inches less than it did on Monday.
How much did it rain on Tuesday?
Answer:
inches.
Write your answer as a decimal.
Answers
Three of these turtles weight 1,050 pounds. How much does one Pinta Island Tortoise weight?
Answers
Answer:
350 pounds
Step-by-step explanation:
Assuming three of the turtles are Pinta Island Tortoise, then:
3 turtles -- 1050
1 turtle -- 1050/3 = 350
Thenks and mark me brainliest :))
Answer:
the answer is 350
Step-by-step explanation:
1050 divided by 3 equals 350!!! hope this helps
1. Find the surface area of the pyramid. SHOW YOUR WORK.
5 cm
9cm...
5 cm
5 cm
9 cm
a. Find the area of all 4 triangles. SHOW YOUR WORK including formula and final units.
b. Find the area of the square. SHOW YOUR WORK hhxgincluding formula and final units.
c. Find the total surface area of the pyramid. SHOW YOUR WORK and include the units.
I need the answer fast !!!
Answers
The surface area of the square pyramid is 115 square meters
Finding the surface area of the prismFrom the question, we have the following parameters that can be used in our computation:
The square based pyramid
The formula for the surface area of a square pyramid is:
S = a² + 2al
where a is the length of one side of the square base and l is the slant height.
Area of 4 triangles
This is calculated as
A = 1/2 * 5 * 9 * 4 = 90
Area of the square
This is calculated as
A = 5 * 5 = 25
So, we have
Area = 90 + 25
Area = 115
Hence, the surface area of the square pyramid is 115 square meters.
Learn about surface area here
brainly.com/question/16519513
#SPJ1
please help I dont understand
Answers
Answer:
I dont know The answer sorry
Step-by-step explanation:
Answer: 2
Step-by-step explanation: The average rate of change is calculated as the slope of the line between the two points on the graph. Since at x = 1, y = -3, and at x = 3, y = 1, these are the two points which we calculate the slope from. Using the formula
m = (y2 - y1)/(x2 - x1)
m = (1 - (-3))/(3 - 1)
m = 4/2
m = 2