Find the quadratic function that is the best fit for f(x) defined by the table below
Answers
We have to calculate a, b and c from the given table
1st Calculate c:
for x = o, y = -1.55
- 1.55 = a(0)² + b(0) + c → then c = -1.55
and the equation becomes: y = ax² + b.x - 1.55
2nd Calculate a and b:
for x = 2 , y = 17.29
17.29 =a(2)² + b(2) - 1.55 → 4a + 2b - 1.55 = 17.29 or 4a + 2b = 18.84 (1)
for x = 4 , y = 54.93
54.93=a(4)² + b(4) - 1.55 → 16a + 4b - 1.55 = 54.93 or 16a + 4b = 56.48 (2)
Now solve the system of 2 equations:
4a + 2b = 18.84 (1)
16a + 4b = 56.48 (2)
And you will find :
a= 2.35 and b = 4.72 . And the final equation is:
y = 2.35.x² + 4.72x - 1.55
The quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55
How to determine the function?A quadratic function is represented as:
f(x) = ax^2 + bx + c
Using the table of values, we have:
a(0)^2 + b(0) + c = -1.55
This gives
c = -1.55
Also, we have:
a(2)^2 + b(2) + c = 17.29
4a + 2b -1.55 = 17.29
This gives
4a + 2b = 18.84
Divide through by 2
2a + b = 9.42 --- (2)
Also, we have:
a(4)^2 + b(4) + c = 54.93
16a + 4b -1.55 = 54.93
This gives
16a + 4b = 56.48
Divide through by 4
4a + b = 14.12 ---- (3)
Subtract (2) from (3)
2a = 4.7
Divide by 2
a = 2.35
Substitute a = 2.35 in 4a + b = 14.12
4*2.35 + b = 14.12
Evaluate
b = 4.72
Substitute values for a, b and c in f(x) = ax^2 + bx + c
f(x) = 2.35x^2 + 4.72x -1.55
Hence, the quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55
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Related Questions
After a lesson on exponents,Tia went home and said to her mom,"I learned that 10 to the power of 4 is the same as 40,000." She has made a mistake in her thinking. Use words,numbers, or a place value chart to help Tia correct her mistake. Please show the actual solution
Answers
A seller has a house that is 1700 ft^2. The neighborhood comps show the line of best fit to be y=0.074x + 50.48. What is a fair price for this house?
Answers
Using the line of best fit, it is found that a fair price for the house is of $176,280.
What does the line of best fit states?It states that the fair price for a house of x square feet, in thousands of dollars, is given by:
y = 0.074x + 50.48.
In this problem, we have a house of 1700 ft^2, hence the fair price in thousands of dollars is given by:
y = 0.074(1700) + 50.48 = 176.28.
Which is a fair price of $176,280.
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Answer:199,000
Step-by-step explanation:
A baseball player went up to bat 250 times in a season. He hit the ball 100 times. Find the rate of balls hit to times at bat. Express as a simplified fraction.
a. 2/5 b.5/2 c. 2/3 d. 3/5
Answers
250/50=5
100/50=2
5/2
Final answer:
To find the rate of balls hit to times at bat, divide 100 hits by 250 at bats, simplifying the fraction by dividing both numerator and denominator by 50, resulting in a simplified fraction of 2/5.
Explanation:
The rate of balls hit to times at bat can be found by dividing the number of hits by the number of times at bat. In this case, the baseball player hit the ball 100 times out of 250 times at bat.
To find the simplified fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 50:
100 ÷ 50 = 2 and 250 ÷ 50 = 5.
Thus, the simplified fraction of the rate of balls hit to times at bat is 2/5.
Marty is selling her 2,950 square foot house and wants to list it for the average price per square foot for houses stills in her area. Based on the table that shows the last five houses sold, at what price will Marty list her house? (Round to nearest hundreds)
Answers
The total price is
548,000 + 480,200 + 650,500 +,488,000 +,578,000 = $2,744,700
The total area is
3200 + 3100 + 3350 + 3225 + 2800 = 15,675 ft²
The price per square feet is
2744700/15675 = $175.1005 per sq. ft.
Marty's house 2950 ft².
On the basis of area, Marty's house should sell for
(2950 ft²)*(175.1005 $/ft²) = $516,546.41 = $516,500 (nearest hundredth)
Answer: $516,500 (nearest hundredth)
Answer:
516
Step-by-step explanation:
the length of the kitchen counter of Sal's house is 9 times the length of a book. The length of a book is 8 inches. What is the length, /, of the kitchen counter? Draw a picture and write an equation to solve
Answers
The perimeter of a trapezoid is 39 – 7. Three sides have the following
lengths: 9, 5 + 1, and 17 – 6.
What is the length of the fourth side?
Answers
9, 6, 11 are your other sides
9 + 6 + 11 = 26
32 - 26 = the fourth side
the fourth side = 6
hope this helps
Leon evaluated the expression (–4a – 6) + a2 for a = 8. (-4(8) - 6) + 82 (-32-6) + 82 (-38) + 82 (-38) + 16 –19 + 16 –3 Analyze Leon's work. Check all that apply. Leon should have subtracted inside the parentheses before he multiplied. The expression inside the parentheses should be simplified to –26 instead of –38. Leon multiplied 8 by 2 when he should have raised 8 to a power of 2. The multiplication of two negative values in step 4 should result in a positive value. The correct answer should be 35.
Answers
Answer:
c,d,e
Step-by-step explanation:
Final answer:
Leon should have simplified the expression inside the parentheses before adding -38 and 64.
Explanation:
Leon evaluated the expression (–4a – 6) + a2 for a = 8.
Substituting a = 8 into the expression, we get (-4(8) - 6) + 82.
Simplifying the expression, we have (-32 - 6) + 64.
Combining like terms, we get -38 + 64.
Finally, adding -38 and 64 gives us 26.
What is the greatest common factor of 28, 48, and 64?
Answers
28 = 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3
64 = 2 x 2 x 2 x 2 x 2 x 2
The only factor which appears in all lists is 2. It appears twice in the first number, so the greatest common factor in the group is 2 x 2 = 4
Please click 'thanks' for the answer :-)
The greatest common factor of 28, 48, and 64 is, 4
We have to given that,
To find the greatest common factor of 28, 48, and 64
Now, We can find prime factor all of the numbers.
Then, collect the factors which appear in all three lists:
28 = 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3
64 = 2 x 2 x 2 x 2 x 2 x 2
Here, The only factor which appears in all lists is 2.
It appears twice in the first number,
So, the greatest common factor of 28, 48, and 64 is 2 x 2 = 4
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Does this table represent a function?
Answers
Carl’s Cable Company charges $55 for monthly service plus $4 for each pay-per-view movie. Teleview Cable Company charges $110 per month with no fee for movies. For what number of movies is the cost of Carl’s Cable Company less than the cost of Teleview?
Answers
The number of movies for which the cost of Carl's Cable Company is less than the cost of Teleview is about 13.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given, Carl's Cable Company charges $55 for monthly service and $4 for each movie.
Let the number of movies be x, then the total charge for Carl's Cable Company is:
Carl's Cable = 55 + 4x
The cost of Teleview Cable Company is $110.
Therefore, the cost of Carl's Cable Company is less than the cost of Teleview if:
55 +4x < 110
4x < 110 - 55
4x < 55
x < 55/4
x < 13.75
Hence, the number of movies for which the cost of Carl's Cable Company is less than the cost of Teleview is about 13.
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Final answer:
Carl's Cable Company is cheaper than Teleview Cable Company when the number of pay-per-view movies watched is less than 14. As we can't watch a fraction of a movie, Carl's Cable is less expensive for up to 13 movies.
Explanation:
To determine for what number of movies is the cost of Carl's Cable Company less than the cost of Teleview, we set up an inequality based on the cost structures provided. Let m represent the number of pay-per-view movies.
Carl's Cable Company: $55 + $4m
Teleview Cable Company: $110
To find the number of movies where Carl's is cheaper, we want to find when:
$55 + $4m < $110
Now we solve for m:
Subtract $55 from both sides to isolate the variable term: $4m < $110 - $55
Simplify the right side: $4m < $55
Divide both sides by $4 to solve for m: m < $55 / $4
Simplify: m < 13.75
Since m must be a whole number (you can't watch a fraction of a movie), Carl's Cable is cheaper for up to 13 movies.
the scores on an exam are normally distributed with a mean of 74 and a standard deviation of 7. what percent of the score are less than 81?
A. 50%
B. 84%
C. 13.5%
D. 16%
Answers
Your answer is B. 84% :)
Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.
Megan solved a similar equation below. Is Megan's solution correct? Explain why or why not.
3(2x − 4) = 5x − 1
6x − 12 = 5x − 1
11x − 12 = –1
11x = 11
x = 1
can someone do it step by step?
Answers
When you use the Distributive Property, we will find...
5x - 4 = -6x - 4
Eliminate 4 by adding it to both sides.
5x = -6x
Add 6x to both sides and we get 11x = 0.
11x = 0
Divide both sides by 11.
x=0
The only mistake Megan made was when adding 5x with Megan accidentally subtracting 5x from the other side.
For this problem:
3(2x − 4) = 5x − 1
Distribute
6x - 12 = 5x - 1
Add 1 to both sides
6x - 11 = 5x
Subtract 6x from both sides
-11 = -x
Divide both sides by -1.
x = 11.
Hope this helps! Like this answer? Give it a Brainiest reward if so.
Use the distributive property to calculate what's in the parentheses
5x - 4 = -6x - 4
Add 4 to both sides
5x = -6x
(From here you can say x = 0 but here's a few final steps if you want)
Add 6 x to both sides
11x = 0
Divide both sides by 11
X=0
---------------------------------------------
Problem 2: Megan's solution
Megan correctly distributed the parentheses in her first step
Megan errored when she ADDED 5x to the left side but SUBTRACTED 5x from the right side in her third line
From that error she correctly finished the problem, but due to her error she got the wrong answer
The correct answer is x=11
Charissa is eating out with friends, and it is her turn to pay the gratuity. The bill for the food is $26.50. If she plans to tip at 20%, what should she pay if she doesn’t want to leave pennies on the table?
Answers
So the total she’ll pay is $31.80
The drag force F on a boat varies jointly with the wet surface area A of the boat and the square of the speed s of the boat. A boat with a wet surface area of 50ft2 traveling at 7mph experiences a drag force of 98N . Find the wet surface area of a boat traveling 7.5mph and experiencing a drag force of 135N .
Answers
Final answer:
The wet surface area of the boat is approximately 69.7ft^2.
Explanation:
The drag force on a boat varies jointly with the wet surface area and the square of the speed of the boat. This can be represented by the equation:
F = k · A · s^2
where F is the drag force, A is the wet surface area, s is the speed, and k is a constant of variation.
To find the wet surface area of a boat traveling at 7.5mph and experiencing a drag force of 135N, we can set up the following proportion:
(98N) ÷ (50ft^2) = (135N) ÷ (x ft^2)
Cross-multiplying and solving for x, we find that the wet surface area of the boat is approximately 69.7ft^2.
Julia spends $2.25 on gas for her lawn mower. She earns $14.00 mowing her neighbor's yard. What is Julia's profit?
Answers
what is the LCM of 3 and 8
Answers
[tex]3^1 (2^3)= 24 [/tex]
That's how we found our answer was: [tex]24[/tex]
You can also go through your multiplication of [tex]3 [/tex] & [tex]8[/tex]
Good luck on your assignment and enjoy your day
~[tex]MeIsKaitlyn:)[/tex]
What is the value of 0 in 601,199
Answers
10,000.
A certain brand of coffee comes in two sizes. An 11.3 -ounce package costs $2.88 . A 27.8 -ounce package costs $6.48 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Answers
To calculate the unit price for each coffee package, you divide the total cost by the number of ounces. The 11.3-ounce package has a unit price of about $0.255 per ounce, and the 27.8-ounce package has a unit price of about $0.233 per ounce. The 27.8-ounce package is the better buy with a lower unit price.
Explanation:To find the unit price for each size of coffee package, you divide the cost by the number of ounces.
For the 11.3-ounce package:
Unit price = Total price / Number of ouncesUnit price = $2.88 / 11.3 ouncesUnit price ≈ $0.255 cents per ounce (rounded to the nearest cent)For the 27.8-ounce package:
Unit price = Total price / Number of ouncesUnit price = $6.48 / 27.8 ouncesUnit price ≈ $0.233 cents per ounce (rounded to the nearest cent)Comparing the unit prices, the 27.8-ounce package is the better buy based on the lower unit price.
To find the unit price, divide the cost by the number of ounces. The 27.8-ounce package is the better buy based on a lower unit price.
Explanation:To find the unit price for each size of the coffee, we divide the cost by the number of ounces. The unit price of the 11.3-ounce package is $2.88 divided by 11.3, which is approximately $0.255.
The unit price of the 27.8-ounce package is $6.48 divided by 27.8, which is approximately $0.233.
Based on the unit price, the 27.8-ounce package is the better buy as it has a lower unit price than the 11.3-ounce package.
State the ratio of 700 participants to 28 judges
Answers
Compute
$(\sqrt{3755}+\sqrt{3752})(-\sqrt{3755}-\sqrt{3752})(\sqrt{3755}-\sqrt{3752})(\sqrt{3752}-\sqrt{3755})$.
Thanks!
Answers
[tex](a-b)(a+b)=a^2-b^2[/tex]
For the first and third factors there will be:
[tex](\sqrt{3755}+\sqrt{3752})(\sqrt{3755}-\sqrt{3752})=(\sqrt{3755})^2-(\sqrt{3752})^2=\\\\3755-3752=3[/tex]
and for the second and fourth:
[tex](-\sqrt{3755}-\sqrt{3752})(\sqrt{3752}-\sqrt{3755})=\\\\= (-\sqrt{3755}-\sqrt{3752})(-\sqrt{3755}+\sqrt{3752})=\\\\= (-\sqrt{3755})^2-(\sqrt{3752})^2=3755-3752=3[/tex]
So the answer is:
[tex]3\cdot 3=\boxed{9}[/tex]
Inverse Distributive property of 6x + 108
Answers
To do the inverse of the distributive property, we need to find the GCF. In this case, it's 6. then, we take the 6 common and divide each term by 6:
6(x + 18)
Hope this helps!
DIVIDING ALGEBRAIC FRACTIONS
a^2-7a-18/4a^3 divided by a^2-4a-45/2a^3-4a^2 multiplied by a^2+3a-10/a^2-4+4
Answers
Answer:
a+2/2a
Step-by-step explanation: this is the correct answer
If six different chips are to placed on the board, how many different layouts are possible?
Answers
Which is the graph of a logarithmic function?
A B C or D
Answers
Answer-
The D plot represents the logarithmic function.
Solution-
1st plot represents the rectangular hyperbola (with vertical asymptote at x=3 and horizontal asymptotes at y=0),
[tex]f(x) =\frac{1}{x-3}[/tex]
2nd plot represents the straight line (passing through origin and slope 1/5),
[tex]f(x)=\frac{x}{5}[/tex]
3rd plot represents the parabola (vertex at 3, 0),
[tex]f(x)=\frac{1}{c} (x-3)^{2}[/tex] (where c is a constant)
4th plot represents the logarithmic curve,
[tex]f(x)=c\log x[/tex] (where c is a constant)
∴ The 4th graph is a graph of a logarithmic function.
Solve the trigonometric equation on the interval 0 ≤ θ < 2π. (enter your answers as a comma-separated list.) 2 sin(θ) − 2 = 0
Answers
Final answer:
The solution to the trigonometric equation 2 sin(θ) − 2 = 0 on the interval 0 ≤ θ < 2π is θ = π/2.
Explanation:
The given trigonometric equation is 2 sin(θ) − 2 = 0. To solve this equation, we can isolate the sine function by adding 2 to both sides, resulting in 2 sin(θ) = 2. Then, dividing both sides by 2 gives us sin(θ) = 1. Since we are looking for solutions on the interval 0 ≤ θ < 2π, we know that the sine function is equal to 1 at π/2. Therefore, the solution to the equation is θ = π/2.
wildlife protection groups buld bat houses to help sve bate one bat house holds about 300 bats larry says 12 bat houses hold about 4500 bats do you agree
Answers
one bat hous holds about 3000 bats => 300 bats / house
So, to estimate the number of bats holded by 12 bat houses do>
300 bat / house * 12 house = 3600 bats
That is very far from the 4500 bats that Larry says.
You know that a number 8 less than 60 is the number 52. so, you could write your answer from the previous part as, "what number can you multiply by 4 to get 52
Answers
Currently, the area of Oak Park is represented by (9x2 + 6x + 9). The city will be expanding the park this summer. The area of the expansion is represented by 8x − 7. Which polynomial expression represents the total area of Oak Park after the expansion?
Answers
Answer:
9x2 + 14x + 2
Step-by-step explanation:
Combine like terms
(9x2 + 6x + 9) + (8x −7)
9x2 + 14x + 2
Find the zeros of the function
f(x)=2x^2-4x-2.9 to the nearest hundredth
Answers
The first recorded tempature is 109F. Four hours later the second tempature is 58F . What is the change in tempature
Answers
109-59=51. The temperature difference is 51 degrees
First temperature recorded = 109F
Second temperature recorded = 58F
Notice the change is temperature? Is the temperature increasing or decreasing?
Its decreasing! From 109 it has stepped down to 58F
Therefore, you will be subtracting ---
[tex]190-58=51[/tex]
The answer is 51F.
Hope I helped (:
have a great day!