consider the following. quadratic x y −2 5 −1 −3.5 0 −8 1 −8.5 2 −5 3 2.5 4 14 find the equation of the function of the specified type that is the best fit for the given data. y(x)
Answers
The quadratic function that best fit the given data is y = 2x² - 5/2x - 8.
In algebra, quadratic function is defined as a function in the second degree or power. It can be expressed as y = f(x) = ax² + b x + c, where a, b, and c are constants.
Using only three points from the given data, we can determine the quadratic equation that fits the data.
Let P1 = (-2 , 5)
P2 = (0 , -8)
P3 = (2 , -5)
Substitute the points in the expression f(x) = y = ax² + b x + c.
5 = a(-2)² + b(-2) + c ⇒ 5 = 4a - 2b + c (equation 1)
-8 = a(0)² + b(0) + c ⇒ -8 = c (equation 2)
-5 = a(2)² + b(2) + c ⇒ -5 = 4a + 2b + c (equation 3)
Substitute equation 2 in equation 1 and 3.
5 = 4a - 2b + -8 ⇒ 13 = 4a - 2b (equation 4)
-5 = 4a + 2b + -8 ⇒ 3 = 4a + 2b (equation 5)
13 = 4a - 2b (equation 4)
-(3 = 4a + 2b) (equation 5)
10 = -4b
b = -5/2
Substitute the value of b in equation 4.
13 = 4a - 2(-5/2)
4a = 13 - 5
a = 2
If a = 2, b = -5/2 and c = -8, then the quadratic equation should be y = 2x² - 5/2x - 8.
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Related Questions
if i had 5 divided by 1 + 5 on evaluating expressions......what would the answer be?
Answers
Answer:
[tex]\frac{5}{1+5}[/tex]
Step-by-step explanation:
Hope this helps :))
g(n)=2n
h(n)=n^2-4
Find g(-9) + h(-9)
A) 4
B) 59
C) 20
D) 95
Answers
Answer:
g(-9)+h(-9)=59
the answer is B
At the beginning of a month, your account balance was $738. During the month,
you withdrew $550, deposited $189, and paid a fee of $10. What was your balance
at the end of the n month?
Answers
Answer:
$367
Step-by-step explanation:
738-550+189-10=367
A rectangular carpet measures 10m by 6m. part of the carpet is covered by a square rug of length 2m. what fraction of the carpet is covered by the rug?
Answers
Answer: 1/15
Step-by-step explanation:
The area of the entire carpet is [tex](10)(6)=60[/tex] square meters.
The area of the square rug is [tex]2^2=4[/tex] square meters.
So, [tex]\frac{4}{60}=\frac{1}{15}[/tex] of the carpet is covered by the rug.
Answer: 1/15
Step-by-step explanation: The area of the entire carpet is square meters.
The area of the square rug is square meters.
So, of the carpet is covered by the rug.
Vote me for the president of America here’s why -I would be the first female president of u.s -I will Ban all pick me’s who whisper about you when you’re right in front of them and try’s to be better than you -Give all homeless animals good shelter -ban emos - less money for gas -overall better Vote me
Answers
Answer:
Lmafo
Step-by-step explanation:
The table shows interest owed for a home improvement loan based on how long it takes to pay off the loan.
a. How much more interest is owed on $900 for 9 months than 6 months?
b. Does the interest rate increase at a constant rate?
Can you give a long good explanation please? Thank you <3
Answers
The $8.78 more interest is owed on $900 for 9 months than 6 months.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
(a)
The formula for simple interest:
I = Prt
I(for 9 months) = 900x(2.9/100)(9/12)
I(for 9 months) = $19.575 = $19.58
I(for 6 months) = 900x(2.4/100)(6/12)
I(for 6 months) = $10.8
Difference = $19.58 - $10.8 = $8.78
(b)
From the table: the interest rate from 6 months to 9 months increases by 0.5% after that it increases constantly.
Thus, the $8.78 more interest is owed on $900 for 9 months than 6 months.
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1. A percent is found by dividing the percentage by the base. True
or false
Answers
It is true but incomplete, a percent is found by dividing the percentage by the base and multiplying it with 100.
What is percentage?
Percentage is a relative value that represents hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Divide the percentage by the quantity to get the percent of a number, then multiply the result by 100. Put the word "percent" (%) after the finished item.
Example of calculation of percentage:
What percent of 10 is 7?
here, 7 is percentage and 10 is quantity, On dividing we get,
7/10 = 0.7
Now multiplying by 100, we get
70 %
This is the answer
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Simplify 9x^2-3x+7/x-2
Answers
Answer:
9x³−3x²−2x+7
Step-by-step explanation:
f(x)=x^2
g(x)=−x^2+7
h(x)=(x−6)2
p(x)=(x−2)2−9
q(x)=x^2+12
Answers
Answer:
Step-by-step explanation:
interval notation is (-∞,∞)
set-builder notation is {x|x ∈ R}
What 685,203 rounded to the nearest ten , hundred , thousand, ten ten thousand and, hundred thousand
Answers
Answer:
685200 is ten and hundred 685000 thousand 690000 ten thousand 700000 hundred thousand
Please answer the question in the photo
Answers
Answer:
i got
Step-by-step explanation:
seventy-nine
so
you now know
42° + b + 22° + b - 42° = 180 °
you can simplify this to
64° + 2b - 42° = 180°
you can then take away 64 from both sides
2b - 42° = 116°
then you add the - 42 to both sides
which leaves you with
2b = 158
you divide it by two on both sides
which makes
b = 79
you can check this by doing
79 + 22 = 101
79 - 42 = 37
and then adding it
101 + 37 + 42 = 180
you’re welcome
Please help me with this pls
Answers
Answer:
thw answer is 67.910
Step-by-step explanation:
the second one
Answer:
#2
Step-by-step explanation:
the four answers start with 67. So if you focus on the digits that come after the decimal, which ever digits are higher than the original decimal will be your answer
The marked of a jacket at a dealer's shop is Rs. 2400 The dealer allows a discount of 15% to the retailer. As the company's policy the marked price of the retailer should be the same as decler's marked price. What SP should the retailer fix for the Jacket ? What would it's final price beif 10% VAT is imposed? What would be the actual gain of retailer ? If 10% discount is allowed.
Answers
Answer:
Step-by-step explanation:
Given,
The marked price of a jacket at dealer shop is Rs. 2400
The dealer allows a discount of 15% to the retailer.
The marked price of the retailer should be same as the dealer's marked price.
To find,
1. SP the retailer should fix for the jacket
2. Its final price if 10% VAT is imposed
3. The actual gain of the retailer if 10% discount is allowed
Solution,
The SP rate for the jacket without VAT 2400
Let 10% VAT on jacket price 2400 be x
x= 2400÷10
x= 240
So, the final price including 10% VAT = 2640 (2400+240)
As the dealer allowed discount of 15% to the retailer, the retailer gain profit is 15% on the jacket price i.e., 2400
Let y be the gain of the retailer
y= 15/100 × 2400
y= 360
Therefore,
SP the retailer should fix for the jacket is 2400
final price if 10% VAT is imposed is 2640
the actual gain of the retailer is 360
Thanks for all the help
Answers
Answer:
x=4.4
Step-by-step explanation:
To get from 4 to 10 what happens?
Well, we multiply 4 by 2.5.
That should be the same for x.
Thus, 2.5x=11
x=4.4
Sergio Is asked to write one million in scientific notation. He writes 106 and gets it wrong.
Why was he wrong?
O He should have written 106.
O He should have written 10 5.
O He should have written 1 x 10 6.
He should have written 1 × 10 5.
Answers
In scientific notation, it should be written as 1 × 10⁶
What is notation?In mathematical notation, operations, unnamed numbers, relations, and any other mathematical objects are represented by symbols that are combined into expressions and formulae. Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 ×10⁸ in scientific notation.
Given Data
Sergio Is asked to write one million in scientific notation. He writes 106 and gets it wrong.
He should have written as 1 × 10⁶
A power of 10 and a number in the range of 1 to 10 are required for standard form.
In scientific notation, it should be written as 1 × 10⁶
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steven had $5 that his mom gave him to buy lunch at school he spent $5 on his lunch. plot a point on the number line to show how much money steven has after he spent $5 on food
Answers
If Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, then he will have $0 remaining, as plotted on the number line in the reference attachment hereby.
As per the question statement, Steven had $5 that his mom gave him to buy lunch at school and he spent all of the $5 on his lunch.
We are required to plot a point on the number line to depict how many dollars Steven has left with himself after spending on his lunch.
To solve this question, we simply need to subtract the amount Steven spent for his lunch, from the amount, his mother gave him to spend on lunch, and then plot the result of the said subtraction on the number line to obtain our desired answer.
Since, Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, he has $(5 - 5) = $0 left with himself after spending on his lunch.
That is, we will have to plot 0 on the number line, which is shown in the reference attachment hereby.
Number Line: In elementary Mathematics, a number line is a graduated straight line that serves as visual representation of real numbers, marked at regular, equal intervals.To learn more about Number Line, click on the link below.
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Find the difference of the polynomials. Write the result in standard form.
(33r3s3-16rt7+72s5t2) - (24rt7 - 18s5+2 – 47r³s3)
A 8rt7+90s5t2 +80r3s3
B-40rt7 +54s5t2 -14r3s3
C 8rt7+54s5t2 -14r3s3
D-40rt7+90s5t2 +80r3s3
Answers
The difference of the polynomial is -40rt⁷+90s⁵t² +80r³s³. the correct option is D.
What are polynomials?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The given expression is (33r³s³-16rt⁷+72s⁵t²) - (24rt⁷ - 18s⁵t² – 47r³s³). The difference will be calculated as follows:-
Difference = (33r³s³-16rt⁷+72s⁵t²) - (24rt⁷ - 18s⁵t² – 47r³s³).
Separate the like terms in the polynomial and solve accordingly.
Difference = (33r³s³+ 47r³s³-16rt⁷- 24rt⁷+72s⁵t²+ 18s⁵t² ).
Difference = 80r³s³- 40rt⁷+ 90s⁵t²
Therefore, the difference of the polynomial is -40rt⁷+90s⁵t² +80r³s³. the correct option is D.
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Here is some information about a heating oil tank.
Top Outlet Tank
Height (h): 2550 mm
Diameter (d): 2100mm
Mass: 650kg
(b) Work out the volume, in cubic metres, of the tank.
Answers
The volume of the tank is 15315.35
What is volume?Volume is a measurement of three-dimensional space that is occupied. [1] Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.
Given that,
Top Outlet Tank
Height (h): 2550 mm
Diameter (d): 2100mm
radius (r) : 2.1/2
Mass: 650kg
The volume, in cubic metres, of the tank is
volume of tank = 2π + π[tex]r^{2} h[/tex]
= 2π(1100) + π(2.1/2)(2550)
= 2(3.14)1100+ (3.14)(2.1/2)(2550)
= 6908+ 8407.35
= 15315.35
Therefore, the volume of the tank is 15315.35
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Evaluate c/2 -3 + 6/d when c=14 and d=3
with an explanation if possible :))
Answers
Answer:
c/2-3+6/d
=
14/2-3+6/3
= (Order of Operations)
7-3+2
=
6
Step-by-step explanation:
See explanation above
Fifth graders at a school write a paper about a historical person for a contest. There are $5$ classes of $25$ students and $1$ class of $28$ students participating in the contest. Use the expression $5\times25+28$ to find how many students participate in the contest.
Answers
A school's fifth graders prepare a paper about a historical figure for a contest. The total number of students who participated in the contest is 153.
Given that,
A school's fifth graders prepare a paper about a historical figure for a contest.
The contest is being competed in by $5 classes of $25 students and $1 classes of $28 students.
We have to calculate the number of students who enter the contest.
We get
=5×25+1×28
Multiply the terms
=125+28
Adding the terms
=153
Therefore, the total number of students who participated in the contest is 153.
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Given the function f(x) = 3x + 1 and the linear function g(x), which function has a greater slope?
Answers
The function that has the greater slope is the function g(x) that is represented by the graph.
How to Determine the Slope of a Function?The slope (m) of a function using two points on a graph can be calculated as:
Slope of the line (m) = change in y/change in x
If we are given the equation of the line using function notation as .f(x) = mx + b, the slope of the function is represented in the equation as "m". The value of "m" is the slope of the function given.
Given the function, .f(x) = 3x + 1, the value that represents "m" which is 3. Therefore, the slope of the function .f(x) = 3x + 1 is: 3.
Find the slope of the function of the graph using two points on the line, say (2, 3) and (3, 7):
Slope of the function (m) = change in y / change in x = (7 - 3)/(3 - 2)
Slope of the function (m) = 4/1
Slope of the function (m) = 4
The larger the value of the slope, the greater the slope of the function.
Therefore, the function g(x) that is represented by the graph has a greater slope.
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Answer: B
Step-by-step explanation:
Simple
How do I work it out?
Answers
Answer:
13/42
Step-by-step explanation:
The directions probably say "Evaluate" or "Substitute and simplify"
They give us values for x and y.
x = 7 and y = 6
Fill in 7 and 6 for x and y.
(x + y) / xy
= (7 + 6) / 7•6
= 13/42
13/42 cannot be simplified.
when determining the maximum and minimum, why must the test point be in the feasible region
Answers
The constraints of a linear programming issue must all be concurrently satisfied for a solution to be viable. We are aware that the ideal solution must maximize the value of the goal function and be located at one of the corners of the feasible region.
What is a feasible and optimal solution?All of the constraints on the problem are met by a feasible solution. A feasible answer that, when maximized, yields the highest possible value for the objective function is known as an optimum solution (or smallest when minimizing). A linear program with two variables can be solved using a visual solution method.
A fundamental feasible solution (BFS), according to the theory of linear programming, is a solution with a small number of non-zero variables. Each viable solution polyhedron's corner correlates geometrically to a BFS. There must be an optimal BFS if there is an optimal solution. Therefore, taking into account the BFS-s is adequate to arrive at an ideal solution. The simplex algorithm, which effectively moves from one BFS to another until one is found that is optimal, makes use of this property.
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When an integer is subtracted from 5 times the next consecutive odd integer,the difference is 22.find the value of the greater integer
Answers
The value of the greatest integers will be 5.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
'' An integer is subtracted from 5 times the next consecutive odd integer, the difference is 22''.
Now,
Write the mathematical expression for an algebraic expression as;
Let an integer = 2x + 1
Then, The next consecutive odd integer = 2x + 3
So, We can formulate;
5 (2x + 3) - (2x + 1) = 22
Solve for x as;
5 (2x + 3) - (2x + 1) = 22
10x + 15 - 2x - 1 = 22
8x + 14 = 22
Subtract 14 both sides, we get;
8x + 14 - 14 = 22 - 14
8x = 8
Divide by 8,
x = 8/8
x = 1
Since, The greatest integers = 2x + 3
Substitute x = 1, we get;
The greatest integers = 2x + 3
The greatest integers = 2 × 1 + 3
The greatest integers = 2 + 3
The greatest integers = 5
Therefore, The value of the greatest integers will be 5.
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What is the temperature in the thermometer if it rises by 45°F (a) 65°F (b) - 65°F (c) 20°F (d) 0°F
Answers
Using the mathematical operation of addition, the temperature in the thermometer, if it rises by 45°F, is (d) 30°F.
What are mathematical operations?Mathematical operations use operands to combine with numbers and variables in a function so that they can produce results.
Some of the mathematical operations are addition, subtraction, division, and multiplication.
The temperature before the rise = -15°F
The temperature change = +45°F
The temperature after the rise = 30°F (-15°F + 45°F)
Thus, after adding the rise in temperature to the initial temperature, the new temperature in the thermometer is 30°F.
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i need help ASAP!!!!!!!!!!!!
Answers
Answer:
420 mark Brainliest
Step-by-step explanation:
distance is going up by 60 and the points are moving 2 for time so at 12 it will be 360 then 14 will be 420 so the answer is 420
Write an equation of the line passing through point P(-1,-4) that is parallel to
y = -6x + 8
Answers
The equation of the line passing through point P(-1,-4) that is parallel to y = -6x + 8 is y = -6x - 10.
What is a straight line?A straight line is made up of an infinite number of points connected at their ends.
Any straight line's slope, "m," is determined by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line y = -6x + 8
m = -6
The slope of the line passing point P (-1,-4)
M = -6
y - (-4) = -6(x - (-1))
y + 4 = -6(x + 1)
y = -6x - 10
Thus, the equation of the line passing through point P(-1,-4) that is parallel to y = -6x + 8 is y = -6x - 10.
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Solve the following expression when
k = 12 and v = 6
4 + 5 - 4v + 12
Answers
Divya and Miguel were asked to find an explicit formula for the sequence 80, 40, 20, 10,..... which one of them is right?
Answers
The explicit formula for the sequence is aₙ = 80 (0.5)ⁿ⁻¹
Given,
The sequence = 80, 40, 20, 10, ...
We have to find the explicit formula for the above sequence.
Explicit formula for a sequence: aₙ = a₁ (r)ⁿ⁻¹
That is,
a₁ = first term
r = common ratio
Lets check:
The sequence is 80, 40, 20, 10,....
a₁ = 80
a₂ = 40
a₃ = 20
a₄ = 10
Now, lets find the common ratio:
a₂/a₁ = 40/80 = 1/2
a₃/a₂ = 20/40 = 1/2
a₄/a₃ = 10/20 = 1/2
That is, the common ratio, r for the sequence is 1/2 which equals 0.5
Then, the explicit formula for the sequence is aₙ = 80 (0.5)ⁿ⁻¹
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1. Evaluate the expression. Give your answer as a mixed number in simplest form.
11/12 + 5/6
Answers
Answer: 1 3/4
Step-by-step explanation:
1. find common denominator
11/12+10/12=21/12
2. simplify
21/12=7/4= 1 3/4