WILL GIVE BRAINLIEST PLEASE HELP FAST!! Write the function f(x)= 2x3+1+x2 x2−9 as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function.
Answers
f(x) = (2x³ + 1 + x²)/(x² + 9) as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function is f(x) = 2x³/(x² + 9) + (1 + x²)/(x² + 9).
To answer the questions, we need to know what functions are
What are functions?A function is a mathematical expression that shows the relationship between two variables.
Types of functionOdd functions - These are functions in which f(-x) = -f(x)Even functions - These are functions in which f(-x) = f(x)Neither - When the function is neither even nor odd.Since f(x) = (2x³ + 1 + x²)/(x² + 9).
The odd part of f(x)Its odd part g(x) = [f(x) - f(-x)]/2
So, g(x) = [f(x) - f(-x)]/2
= [(2x³ + 1 + x²)/(x² + 9) - (2(-x)³ + 1 + (-x)²)/((-x)² + 9)]/2
= [(2x³ + 1 + x²)/(x² + 9) - (-2x³ + 1 + x²)/(x² + 9)]/2
= (2x³ + 1 + x² + 2x³ - 1 - x²)/2(x² + 9)
= 4x³/2(x² + 9)
g(x) = 2x³/(x² + 9)
The even part of f(x)
Its even part h(x) = [f(x) + f(-x)]/2
So, h(x) = [f(x) + f(-x)]/2
= [(2x³ + 1 + x²)/(x² + 9) + (2(-x)³ + 1 + (-x)²)/((-x)² + 9)]/2
= [(2x³ + 1 + x²)/(x² + 9) + (-2x³ + 1 + x²)/(x² + 9)]/2
= (2x³ + 1 + x² - 2x³ + 1 + x²)/2(x² + 9)
= 2(1 + x²)/2(x² + 9)
h(x) = (1 + x²)/(x² + 9)
So, f(x) = g(x) + h(x)
f(x) = 2x³/(x² + 9) + (1 + x²)/(x² + 9)
So, f(x) = (2x³ + 1 + x²)/(x² + 9) as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function is f(x) = 2x³/(x² + 9) + (1 + x²)/(x² + 9).
Learn more about odd and even functions here:
https://brainly.com/question/26322830
Answer:
[tex]g(x)=\frac{2x^{3} }{x^{2} -9}[/tex]
[tex]h(x)=\frac{x^{2}+1 }{x^{2} -9}[/tex]
Step-by-step explanation:
'x² - 9' is an even.
Break up the numerator into odd an even parts to get your answer.
'2x³' is odd and 'x² + 1' is even.
[tex]g(x)=\frac{2x^{3} }{x^{2} -9}[/tex]
[tex]h(x)=\frac{x^{2}+1 }{x^{2} -9}[/tex]
Related Questions
a
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$250 and $300.
Answer using the 68 - 95 - 99.7 rule.
[ ? ]%
Answers
Answer:
2 Answers By Expert Tutors
Since 400 is the mean and the standard deviation is 50, $400-$450 is +1 standard deviation. One standard deviation is 34.1% probability that the worker's wages would fall in this range.
Given the cost function C(x) = 0.81x + 60, 420 and the revenue function R(x) = 1.87x, find the break-even point
Answers
Answer:
x = 57,542.8571
Step-by-step explanation:
C(x) = 0.81x + 60,420
R(x) = 1.87x
At break even point, Cost function and revenue function becomes equal.
-> C(x) = R(x)
-> 0.81x + 60,420 = 1.87x
-> 60420 = 1.87x - 0.82x
-> 60420 = 1.05x
-> x = 60420/1.05
-> x = 57,542.8571
Thus, at break even point x = 57,542.8571
.
Ben deposits $1,750 into each of two savings accounts.
Account I earns 2.75% annual simple interest
Account II earns 2.75% interest compounded annually
Ben does not make any additional deposits or withdrawals. Which amount is closest to the difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years?
Answers
The difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years is $1.32.
What is the differnce in the interest?Simple interest is when only the amount deposited increases in value.
Simple interest = deposit x interest rate x time
1750 x 0.0275 x 2 = $96.25
Interest earned with compounding = future value - amount deposited.
The formula for calculating future value:
FV = P (1 + r) nm
FV = Future value P = Present value R = interest rate N = number of years1750 x (1/0275)^2 = $1847.57
$1847.57 - $1750 = $97.57
Difference in interest; $97.57 - $96.25 = $1.32
To learn more about future value, please check: https://brainly.com/question/18760477
Ben and Carson went to the movies with friends. Ben purchased 3 popcorn and 2 boxes of candy for $41. Carson purchased 1 popcorn and 2 boxes of candy for $29. How much did the popcorn cost?
Answers
Answer:
$6
Step-by-step explanation:
B- 3P+2C=$41
C-1P+2C=$29
since they both bought at least 1 popcorn and 2 candy you can just subtract 29 from 41. you get 12 which equals the other 2 popcorns that ben bought
12/2=6
since you need to find the price of 1 popcorn you have to divide 12 by 2
X/5= 7
X/2= 6.5
Find x
Answers
Answer:
1. Answer is 35
2. Answer is 13
Step-by-step explanation:
All you have to do is multiply 5 on both sides for number 1 and multiply by 2 on both sides for number 2.
Tickets for a carnival cost $8 for children and $12 for adults. The carnival sold a total of 233 tickets and collected $2,156. How many children’s tickets were sold?
A.
180
B.
160
C.
73
D.
108
Answers
A quilt is made of 12 squares of equal size. Each square measures 15 cm by 15 cm.
What is the area of the quilt?
Answers
Answer: 12 x 15= 180 cuadrados
juas juas juas 180 + 180 = 360
15 x 15 cm = 360
Step-by-step explanation:
Answer:
Its [tex]2,700cm^{2}[/tex]
Ste,p-by-step explanation:
Charles decided that his old car could not make a 1200 mile trip; it might break down. Rather than take a chance on a big repair bill, and breaking down on the road, he decided to rent a car. The rental is $99 for a special three day weekend rate, with unlimited miles. If the rental car gets 30 miles per gallon and Charles has to pay $3.85 per gallon for gas, what is the total cost of gasoline and rental for the trip
Answers
Using proportions, it is found that the total cost of gasoline and rental for the trip is of $253.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, the total cost is composed by:
The rental fee of $99.The gasoline cost, of $3.85 per gallon, considering that 1200/30 = 40 gallons were used.Hence, the total cost is given by:
C = $3.85 x 40 + $99 = $253.
More can be learned about proportions at https://brainly.com/question/24372153
Answer:
C = $3.85 x 40 + $99 = $253.
Step-by-step explanation:
I took the test
A. 28/12
B. 12/28
C. 7/3
D. 3/7
Answers
Answer:
28/12 Samsung felo tee Samsung felo tee Samsung felo tee
A rectangular prism is a
Choose...
two-dimensional, three dimensional or one dimensional.
Answers
Answer: Three dimensional
Step-by-step explanation:
A rectangular prism is a three-dimensional shape.
[] A one-dimensional shape is a line
[] A two-dimensional shape is a rectangle, circle, etc
[] This means that a rectangular prism is a three-dimensional shape
A rectangular prism is a
Two dimensionalThree dimensional Four dimensional Explanation -:A rectangular prism is three dimensional.
One dimensional -:
Lines that have length in at least one direction.Two dimensional -:
Shapes that are flat and have two dimensions i.e. length and breadthThree dimensional -:
A solid figure that has three dimensions i.e. length, breadth and height.[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tiny \rm{spbankingandsscseries}[/tex]
[tex] \rule{75mm}{6pt}[/tex]
What answer is this I can’t find it
Answers
Yes Or No
Mr. Rainey is a new depositor at your institution. He complains that charges for funds transfers are too
expensive
Should his complaint be logged and handled by the Reg E Department?
O Yes
Ο Νο
Answers
Answer:Yes
Step-by-step explanation:His complaint is valid.
Question 5
Thank you
Answers
mC= 45
Because the triangle has total 180
So 12x+12+15+3x+18=180
So x=9
Subtitute for equation
12x9+12=120
3x9+18=45
CAN SOMEBODY SOLVE THE EQUATION
Answers
Answer:
s = 38.1 billion
Step-by-step explanation:
x = 22 (2020-1998)
s = 1.5 x 22 +5.1
s = 38.1 billion
Juan measured the thickness of the books in his bookcase. This line plot shows his results. Juan stacked the thinnest books and thickest book in one pile. How thick was his pile of books?
Answers
The thickness of the pile of books measured by Juan and the information in the line plot is 5.
What is the thickness of the pile of books?Based on the information in the line plot, the thinnest book has a thickess of 1 1/4 and the thickest book has a thickess of 2 1/2.
The thickness of the pile of books = (1 1/4 x 2) + 21/2
(5/4 x 2) + 2 1/4 = 5
Please find attached the complete question. To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498
help please and ty lol
Answers
Answer:
A=35.5 degrees
Step-by-step explanation:
Check out the photo. Leave a comment if anything's not clear.
Which figure is not a prism?
Α.
B.
С.
D.
Answers
D is not a prism because it is a cylinder - A and C are rectangular prisms and B is a triangular prism
Answer:
D
Step-by-step explanation:
Prisms all have flat sides. The last image has curved sides so it is a cylinder and not a prism.
The length of a rectangle is 4 times its width.
The perimeter is 36.
Find the length and width of the rectangle.
Answers
Answer:
Length=14.4
Width=3.6
Step-by-step explanation:
l=4w
2l+2w=36
2(4w)+2w=36
8w+2w=36
10w=36
w=3.6
l=4w
4(3.6)
l=14.4
*check by plugging in answers into 2l+2w=36*
Answer:
[tex]L=\frac{72}{5}[/tex] or 14.4
[tex]W=\frac{18}{5}[/tex] or 3.6
Step-by-step explanation:
Please take note this probably not the easiest way to do the problem.
Formula for the Perimeter of Rectangle
[tex]P=2L+2W[/tex]
We are given the perimter.
[tex]36=2L+2W[/tex]
[tex]L=4*W[/tex]
To solve I would use the Gauss-Jordan method. (it is advanced, but it makes sense to me)
[tex]36=2L+2W[/tex]
[tex]L=4*W[/tex]
Write the coefficients of each eqaution as rows in the matrix.
[tex]\left[\begin{array}{ccc}2&2&36\\1&-4&0\\\end{array}\right][/tex]
Divide the first row by 2.
[tex]\left[\begin{array}{ccc}1&1&18\\1&-4&0\\\end{array}\right][/tex]
Multiply row 1 by -1 and add it to row 2.
[tex]\left[\begin{array}{ccc}1&1&18\\0&-5&-18\\\end{array}\right][/tex]
Divide the second row by -5.
[tex]\left[\begin{array}{ccc}1&1&18\\0&1&\frac{18}{5} \\\end{array}\right][/tex]
Multiply row 2 by -1 and add it to row 1.
[tex]\left[\begin{array}{ccc}1&0&\frac{72}{5} \\0&1&\frac{18}{5} \\\end{array}\right][/tex]
We now have an augmented matrix.
[tex]L=\frac{72}{5}[/tex]
[tex]W=\frac{18}{5}[/tex]
Landry is going to wrap a birthday present for his mom. He needs to know how much wrapping paper he needs to wrap the present with no overlap.
volume
or
surface area
Answers
Answer:
surface area
Step-by-step explanation:
Wrapping paper covers the surface of an object.
To know how much paper he needs, Landry will need to determine the surface area of the present.
What is the sum of the solutions to the equation below?
8x^2 + 2x - 3 = 0
A) 3/8 B) 1/4 C) -1/4 D - 3/8
Answers
Answer:
(x−1)43x3−8x2+10 can be resolved into partial fraction as x−1A+(x−1)2B+(x−1)3C+(x−1)4D
So , 3x3−8x2+10=A(x−1)3+B(x−1)2+C(x−1)+D
Put x=1 , we get 3−8+10=D
D=5
Comparing the coefficient of x3 on both sides we get , A=3 .
So equation reduces to 3x3−8x2+10=3(x−1)3+B(x−1)2+C(x−1)+5
Now compare the constant on both sides , 10=−3+B−C+5
=>8=B−C - (1)
Comparing the coefficent of x2 we get −8=−9+B
=>B=1
So , put B=1 in (1) , we get C=−7
Therefore , (x−1)43x3−8x2+10=x−13+(x−1)21−(x−1)37+(x−1)45
Step-by-step explanation:
hope it helps
49
Jerrelle spent $0.60 on five stickers. Each sticker costs the same amount. How much
did each sticker cost?
A
$0.06
B
$0.12
с
$1.20
D $5
Answers
Answer:
A. $0.60
Step-by-step explanation:
there are 5 strikers that cost $0.60 each, so the answer is letter A.
A group of friends were working on a student film that had a budget of $1400. They used $168 of their budget on costumes. What percentage of their total budget did they spend on costumes?
Answers
Answer:
12%
Step-by-step explanation:
$ spent / total budget
168 / 1400 = 0.12
0.12 = 12%
find the value of x 115 [5x+30]
Answers
Answer:
i assume the question is 115-5x=10
Step-by-step explanation:
if yes then the answer will be
-5x=125
-5x/-5=125/-5
x=25
Sientific notation (please help!)
Answers
√5
You know that √4 = 2
so √5 > 2
2.5 * 2.5 = 6.25,
√6.25 = 2.5
so √5 in between 2 & 2.5
2 < n < 2.5
π/3
π/3 ≈ 3.14/3
3/3 = 1
4.5/3 = 1.5
π is in between 3 & 4.5
1 < n < 1.5
√3
√2.25 = 1.5
√4 = 2
√3 is in between
1.5 < n < 2
Hope this helped!
Convert 1/5 to the neatest tenth
Answers
Answer:
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
1 / 5 = 0.20
There are two parts to the decimal number above:
Integer Part: 0
Fractional Part: 20
Now, we will make the Fractional Part just one digit (nearest tenth) by using our rounding rules.*
In this case, Rule I applies, so 1/5 (or 0.20) rounded to the nearest tenth in decimal format is:
0.2Answer:
1.1
Step-by-step explanation:
If the digit after tenth is greater then or equal to 5, add 1 to the tenth.
Will give brainliest pls answer!!
Find the volume of the rectangular
prism.
A)29 cm³
B) 87 cm³
C)288 cm³
D)576 cm³
Answers
Answer:
D) 576 cubic cm
Step-by-step explanation:
[tex]16 \times 9 \times 4 = 576[/tex]
Answer:
the answer is D
Step-by-step explanation:
volume =height × length × width
so 9×4×16= 576
Joann has 3 green marbles, 5 blue marbles, and 9 yellow marbles. what is the ratio of green marbles to blue marbles?
Answers
3:5
The question asks for the ratio of green marbles to blue marbles. As stated in the question itself, Joann has 3 green marbles and 5 blue marbles. We can ignore the yellow marbles, while we're at it.
Blue:green
3:5
How to simplify in laws of exponents
Answers
Answer:
You multiply the exponents and or to keep the base the same.
Step-by-step explanation:
I apologize if it is incorrect-
I hope it helps! Have a great day!
Anygays-
A scientist is studying bacterial growth over time. Her research is conducted by placing 10 strep bacteria in a petri dish containing enough food for the bacteria to live and thrive for the course of the research. She records the number of bacteria present every two hours for 6 hours. The collected data is shown in the table below and on the given graph.
a. What function, linear or exponential, do you think would be the best choice to model this data? Explain why you think your choice is the best-fit.
b. Explain how to determine which function is the best choice mathematically, without using a graph. Demonstrate your method.
c. Think of an example of at least 4 data points that would be best modeled by the function you did NOT choose in part a. Explain how you set up the data so that it worked with this type of function.
Answers
Answer:
whatch pH bro......,.......
Answer:
the number of bacteria present every two hours for 6 hours. The collected data is shown in the table below and on the given graph.A scientist is studying bacterial growth over time. Her research is conducted by placing 10 strep bacteria in a petri dish containing enough food for the bacteria to live and thrive for the course
Step-by-step explanation:
What is the surface area of the cylinder with height 8 ft and radius 3 ft? Round your
answer to the nearest thousandth.
A: 186.885
B: 195.004
C: 205.132
D: 207.345
Answers
We know that,
The surface of a cylinder is given by,
2πr(r + h)h= heightr= radiusso,
the surface area of the given cylinder would be,
⇢2π*3(3+8)⇢6π*11⇢66π⇢207.345OPTION D
[tex]\bold{EXPLANATIONS:}[/tex]