Give an example of an odd function and explain algebraically why it is odd.

Answers

Answer 1

An odd function is a function of a form [tex]y=x^n[/tex] where n is an odd number.

Some examples would be functions:

[tex]y=x,y=x^3,\dots[/tex].

A formal definition of odd function is the following.

(Algebraic proof).

Let [tex]f:\mathbb{R}\to\mathbb{R}[/tex] (real function).

The function is odd if the below equation is true for all x and -x for which the function is defined:

[tex]f(x)=-f(-x)[/tex].

Hope this helps.


Related Questions

Question 3
1 pts
Tim has 74 socks, all in pairs. He has 1 more pair of white socks than black socks. How many individual socks of
each color does he have?

Answers

Answer:

36 individual white socks

38 individual black socks

Step-by-step explanation:

Pairs of socks = 74

He has 1 more pair of white socks than black socks.

Take the colors of the socks to be white and black

Let

Black pairs of socks = x

White pairs of socks = x + 1

Individual socks of each color

A pair of white socks = 2 Individual white socks

= 2white

A pair of black socks = 2 individual black socks

= 2black

Total pairs of socks = black pairs of socks + white pairs of socks

74 = 2white + 2black

74 = 2(x) + 2(x +1)

74 = 2x + 2x + 2

74 = 4x + 2

Subtract 2 from both sides

74 - 2 = 4x

72 = 4x

Divide both sides by 4

x = 72/4

= 18

x = 18

Pairs of white socks = x = 18

A pair of white socks = 2whites

= 2(18)

= 36 individual white socks

Pairs of black socks = x + 1

= 18 + 1

= 19 pairs

A pair of black socks = 2black

= 2(19)

= 38 individual black socks

simplify 4/9 to the second power

Answers

Answer:

(2/3)^2

Step-by-step explanation:

A simplification of the expression 4/9 to the second power is [tex](\frac{2}{3} )^2[/tex]

What is an exponent?

In Mathematics and Geometry, an exponent is a mathematical operation that is commonly used in conjunction with an expression, so as to raise a given quantity to the power of another.

Mathematically, an exponent can be modeled by this mathematical expression;

[tex]b^n[/tex]

Where:

the variables b and n are numerical values, letters, or an expression.

n is known as a power.

By applying the law of indices for powers (division) to the given equation, we would have the following simplified expression:

[tex]\frac{4}{9} =\frac{2^2}{3^2} \\\\\frac{4}{9} =(\frac{2}{3} )^2[/tex]

Read more on exponent here: brainly.com/question/27858496

#SPJ6

A ray lies on the line MN←→−. It starts at point Q and passes through the points P and R. Which of the following is a correct name for this ray?

Answers

Answer:

please mark my answer brainliest

Step-by-step explanation:

the correct name will be QP...or QR

please help!!
Given the sets A and B expressed in interval notation, find A∩B A = (−∞,91) ∪ [93,+∞) B = (28,94) B = (28,94)

Answers

Answer: [tex](28, 91) \cup (93, 94)[/tex]

======================================================

Explanation:

Check out the diagram below.

I have drawn out two number lines with the key points 28,91,93,94 marked on them. The diagram isn't to scale, but that doesn't matter. All that matters is that the numbers line up (eg: we have the two 28's line up vertically).

The first number line drawing on top shows the shading for set A. Everything in the shaded region is either smaller than 91, or larger than 93, or 93 itself. We exclude 91 due to the curved parenthesis. The square bracket says to include the 93.

For the second graph, you have two endpoints as open holes (to exclude both endpoints) and you shade everything between.

-----------

After you draw the two number line regions, you would then mark off the interval(s) that they share in common.

The notation [tex]A \cap B[/tex] means "A intersect B" which means we want to find the stuff that is in both sets at the same time.

So we'll have two pieces here. The portion from 28 to 91 is the first interval, and then the second portion runs from 93 to 94. For each interval sub-piece, the endpoints are excluded

So that leads to the final answer [tex](28, 91) \cup (93, 94)[/tex]

Answer in simplest form -4/15 + 1/6 =

Answers

Answer:

The answer is -0.1

Step-by-step explanation:

You just need to calculate it in a calculator

Hope it helps :)

Answer : -1/9

Steps :

Melinda poured herself 20 ounces of orange juice for breakfast. By the end of her meal, she only has 4 ounces left. What scale factor represents the amount of orange juice she has left ?

Answers

Answer:my profile pic is a throwing dart not a ding dong dirty

Step-by-step explanation:

Suppose that you are a teacher with a total of 100 students 10 among them come from a disadvantaged and their average in year 1 is 80/100. All of the other students are not considered disadvantaged and have an average of 90/100. What is the overall average for your students in year 1?

Answers

Answer:

  89/100

Step-by-step explanation:

The average weighted by the number of students is ...

  (90(0.90) +10(0.80))/100 = (81 +8)/100 = 89/100

All of the following should be included in the results section of a t test except:
a. dependent measure.
b. levene confidence intervals.
c. effect size.
d. homogeneity of variance test.

Answers

Answer:

Levene confidence intervals ( b )

Step-by-step explanation:

T- test should include all of the following in the results section except the  Levene confidence intervals.The confidence intervals may be constructed for various power values using the binomial distribution.

The dependent measure , the size and the Homogeneity of variance test are all included in the results section of a t-test

Please Help ASAP it's my Math HW

Answers

Step-by-step explanation:

Use segment addition/subtraction:

GK = GJ − HJ + HK

GK = 2x + 5 − x + 4x − 1

GK = 5x + 4

If GK = 39, then the value of x is:

39 = 5x + 4

5x = 35

x = 7

Use segment subtraction to find GH and JK.

GH = GJ − HJ

GH = 2x + 5 − x

GH = x + 5

GH = 12

JK = HK − HJ

JK = 4x − 1 − x

JK = 3x − 1

JK = 20

what is 0.7x in fraction form​

Answers

Answer:

7/10x hope it helps

The smallest 4-digit number with different digits is ---------. (Don’t use same digit)

Answers

Answer:

The smallest 4-digit number with different digits is 1023.

help pls !!!!!!!!!!!!!!

Answers

Answer:

h(1) = 1, h(2) = 3, h(3) = 4

Step-by-step explanation:

Given function h(x)

Need to find :

h(1), h(2), h(4)

h(1) falls under the second condition as -2 ≤1<2:

h(1) = - (x-1)² + 1 = -( 1 - 1)² + 1 = 1

h(2) and h(4) fall under the third condition as x=2,4 ≥ 2:

h(2) = 1/2x + 2 = 1/2*2 + 2 = 1 + 2 = 3h(4) = 1/2x + 2 = 1/2 * 4 + 2 = 2 + 2 = 4

( -8v + 6v 4 - 8 ) + ( 3v - 7 ) simplified

Answers

Answer:

6v⁴ - 5v - 15

Step-by-step explanation:

Step 1: Write out expression

-8v + 6v⁴ - 8 + 3v - 7

Step 2: Combine like terms (v)

6v⁴ - 5v - 8 - 7

Step 3: Combine like terms (constants)

6v⁴ - 5v - 15

What is greater than 1.45? A. 0.009 B. 0.019 C. 0.0032 D. 0.0177

Answers

All of these answer choices are less than 1.45

No option is greater than the value of 1.45.

What are decimal numbers?

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values.

Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples.

The given number is 1.45. The given options are:-

A. 0.009

B. 0.019

C. 0.0032

D. 0.0177

All the options are less than the value of 1.45. Therefore, No option is greater than the value of 1.45.

To know more about decimal numbers follow

brainly.com/question/1827193

#SPJ2

10x=15 find value of x

Answers

Answer:

x= 1.5

Step-by-step explanation:

According to the question

10x = 15

x = 15 / 10

x = 1.5

Answer:

x=1.5

Step-by-step explanation:

Isolate x on one side of the equation by dividing both sides by the factor 10:

[tex]10x=15\\\frac{10\,x}{10} =\frac{15}{10}\\x=1.5[/tex]

Ben and Sam are diving in a lake at 14 feet below the surface been spot Sam 9 feet directly below him find sams depth

Answers

Answer:

23

Step-by-step explanation:

1

14

+ 9

--------

2 3

hope this helps

The depth of Sam's from the surface is 23 feet.

We are given that Ben and Sam are diving in a lake.

Ben and Sam are 14 feet below the surface.

But after a while, Ben spots Sam 9 feet directly below him.

We have to find sam's depth from the surface.

Let the depth at which both Ben and Sam were diving in the lake be X.

i.e X = 14 feet.

Let the depth of Sam from Ben be Y.

i.e Y = 9 feet.

Now Sam's depth from the surface would be:

= X + Y

= 14 + 9

= 23 feet.

Thus, the depth of Sam's from the surface is 23 feet.

Learn more about addition word problems here:

https://brainly.com/question/24207827

#SPJ2

Find all complex solutions of 3x^2+4x+5=0 please guide!

Answers

Answer:

Step-by-step explanation:

The area of a rectangle is the product of its length and width. Both length and width are whole numbers. A rectangular poster has an area of 204 square inches. The width of the poster is greater than 10 inches and is prime. What is the width of the poster?

Answers

Answer:

17 inches.

Step-by-step explanation:

If the area of a rectangle is the product of its length and width, then;

Area of a rectangle = Length × Width

Given that the width of the poster is greater than 10 inches and is prime, this means and W>10

Area of the rectangle = 204in²

On substituting the values in the formula;

A = LW

204 = LW

Since W is greater than 10 and is prime, it can be between the prime numbers 11, 13 and 17. Note that L must be a whole number as well for any number to be the right answer we seek.

Let's test each values of the prime width that will give a length that is a whole number.

If W = 11

204 = 11×L

L = 204/11

L = 18.54

Since the length didn't give us a whole number, this means our width is not 11.

If W = 13

204 = L × 13

L = 204/13

L = 15.69

Also, we can see that the length is not also a whole number for the value of 13 as the prime width.

If W = 17

204 = L × 17

L = 204/17

L = 12

It can be seen that the length of the rectangle gave us a whole number when we used the prime width of 17, hence the width of the poster that is greater than 10 inches and is prime that makes both length and width to be a whole number is 17 inches.

Answer:17 inches

Step-by-step explanation:

Find the surface area of the following triangular prism. surface area=_________ ft²

Answers

Answer:

312 ft²

Step-by-step explanation:

3 rectangles

2 triangles

4 yd = 12 ft

A = 4ft×12ft + 8ft×12ft + 10ft×12ft + 2×6ft×8ft/2

= 48ft² + 96ft² + 120ft² + 48ft²

= 312 ft²

Answer:

336

Step-by-step explanation:

Got it right

You are welcome :)

I NEED HELP PLEASE HELP ME

Answers

Answer:

Step-by-step explanation:

y - 5 = 8

y = 13

Pleas helppppppppppp

Answers

Answer:

Line AB

Hope this helps!

Pounds gained by people in your class during the first month of the semester on example of which type of data? 1. Qualitative 2. Quantitative 3. Extreme 4. Statistic

Answers

Answer:

quantitative

Step-by-step explanation:

Weight is a continuous variable, and so the numbers of pounds gained by people in your class is quantitative.

Pounds gained by people in your class during the first month of the semester is 2. Quantitative type of data.

What are the types of statistical data?

In Statistics, Data Types play a very crucial and important role, which needs to be understood, to apply statistical measurements correctly to your data so that we can correctly conclude certain assumptions about the data.

They are Numerical data, Ordinal data, and Categorical data.

Given, Pounds gained by people in your class during the first month of the semester can be represented as numbers so it is a numerical or

Quantitative data.

learn more about data types in statistics here :

https://brainly.com/question/12685540

#SPJ2

what valúe of x solves the equation?
5+x-6x=-5​

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 2}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{5 + x - 6x = - 5}[/tex]

Collect like terms

⇒[tex] \sf{5 - 5x = - 5}[/tex]

Move 5 to right hand side and change it's sign

⇒[tex] \sf{ - 5x = - 5 - 5}[/tex]

Calculate

⇒[tex] \sf{ - 5x = - 10}[/tex]

Divide both sides of the equation by -5

⇒[tex] \sf{ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} }[/tex]

Calculate

⇒[tex] \sf{x = 2}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\Huge \boxed{x=2}[/tex]

Step-by-step explanation:

[tex]5+x-6x=-5[/tex]

Combining like terms.

[tex]5-5x=-5[/tex]

Subtracting 5 from both sides.

[tex]-5x=-10[/tex]

Dividing both sides by -5.

[tex]x=2[/tex]

How do you solve 6^14/(2^5)(3^7)?

Answers

Answer:

1119744

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

[tex]\frac{6^{14}}{(2^5)(3^7)}[/tex]

Step 2: Evaluate exponents

6¹⁴ = 78365164096

2⁵ = 32

3⁷ = 2187

Step 3: Replace

[tex]\frac{78364164096}{32(2187)}[/tex]

Step 4: Multiply

[tex]\frac{78364164096}{69984}[/tex]

Step 5: Divide

1119744

Volume of a cube is 5832 m². Fince the
cost of painting its total surface area
at the rate of Rs. 3.50 per m².​

Answers

a≈18

V Volume

5832=18

Pattern y: Starts at 0. Rule: Add 6. The values of Pattern x and Pattern y are graphed on a coordinate graph. Some of the ordered pairs for this pattern are (0,0), (3,6),(6,12), and (9,18). Which ordered pair also belongs to this pattern?

A.(12,24)
B. (15,24)
C.(12,36)
D.(1,6)

Answers

Answer:

A (12, 24)

Step-by-step explanation:

The pattern in the ordered pair is (Add 3, Times itself)

Mick earns $45,000 a year. This year, he had $2,700 of state taxes returned to him.
What percent of his income did he have returned to him?

Answers

Answer:9

Step-by-step explanation:

Find an equation of the sphere that passes through the point (7, 1, −3) and has center (5, 6, 5).

Answers

Answer:

The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is [tex](x-5)^{2}+(y-6)^{2}+(z-5)^{2} = 93[/tex].

Step-by-step explanation:

Any sphere centered at [tex](h,k,s)[/tex] in an Euclidean space with a radius [tex]r[/tex] is represented by the following formula:

[tex](x-h)^{2} +(y-k)^{2}+(z-s)^{2} =r^{2}[/tex]

If [tex](x,y,z) = (7,1,-3)[/tex] and [tex](h,k, s) = (5,6,5)[/tex], the radius of the sphere is obtained:

[tex](7-5)^{2}+(1-6)^{2}+(-3-5)^{2} = r^{2}[/tex]

[tex]r^{2} = 93[/tex]

[tex]r = \sqrt{93}[/tex]

The equation of the sphere that passes through the point (7,1,-3) and center at (5, 6, 5) is [tex](x-5)^{2}+(y-6)^{2}+(z-5)^{2} = 93[/tex].

A collection of points along a straight path that
extends endlessly in both directions is called a

Answers

Answer: line

In geometry, a line is completely straight and stretches in both directions infinitely. In contrast, a line segment is a line that doesn't go on forever but rather has a fixed set length. A line segment has two endpoints. A ray has only one endpoint and the other side extends forever.

George’s parents are going on a cruise and are concerned about paying their bills while they are gone because they will not have the usual means of communication. What is the best payment method for them to use while they are gone?
telephone
online payment
mail
automatic withdrawal

Answers

automatic withdrawal

D. Automatic withdrawal

May I have brainliest please? :)

Other Questions
What are two interesting things about a bow and arrow? The width of a rectangle measures (3.1s 1.6) centimeters, and its lengthmeasures (7.2s 4.6) centimeters. Which expression represents the perimeter, incentimeters, of the rectangle? Which of the following practices hurt farmers inthe late 1800s? Check all of the boxes that apply.Railroads opened new land for settlementand farmingRailroads used unfair business practices thatkept shipping rates high.Railroads charged higher shipping rates tosmaller businesses. Central Park in New York City is shaped like a rectangle. On a map of the park in the coordinate plane, three of the vertices are located at (-1.25,-0.25) (-1.25, 0.25), and (1.25, 0.25). Distances on the map are in miles. What is the perimeter of Central Park? Show your work. Isotopes of an element have the same number of protons but different numbers of what?I have no idea what subject to put this under qwq Share is 4 times as old as Marcos. If the sum of their age is 45, which equation could best be used to find their ages? People work:To earn money . To contribute to society. Because they like to be sociable. All of these are correct Which philosopher wanted to end torture and believed those accused of a crime have certain rights? Tell me what you think the word agriculture means and why is it important to you and the world around you. Do youthink agriculture is useful and do you use it daily? Explain why or why not.write at least a page What is the quotient of 8,592 24 Is 6p-8 monomial, binomial, or trinomial Which trigonometric inequality has no solution over the interval 00 c.cot(x)-1>0 d.tan(x)-1>0 Jane is having trouble sleeping. As she sits in bed looking around the darkened room, she notices that she does not see colors very well, this is because _______ are responsible for color What role does the brain play? A. Digests food to absorb nutrients into the body B. Removes toxins from the other systems C. Distributes oxygen to the other parts of the body D. Central command for the body Please help!!!!!Solve the equation 5(2y - 1) - 2(3y)= 1 Strategic Investments completed the following investment transactions during 2018: Read the requirementsRequirement 1. Joumalize Strategic's investment transactions. Explanations are not required.Requirement 2. Classify and prepare a partial balance sheet for Strategic's Phyflexon investment as of December 31. 2018. Jan. 14: Purchased 800 shares of Phyflexon stock, paying $50 per share. The investment represents 4% ownership in Phyflexon's voting stock. Strategic does not have significant influence over Phyflexon. Jan. 14. Purchased 800 shares of Phyflexon stock, paying $50 per share.Aug 22: Received a cash dividend of $0.24 per share on the Phyflexon stock. Dec. 31. Adjusted the investment to its current market value of $45 per share.Dec. 31: Phyflexon reported net income of $330,000 for the year ended 2018. is a toothpick a good model for showing the strength and brittleness of salt ? PLEASE HELP NEED ANSWERS NOW! Time-Distance GraphListed in the Item Bank are some important labels for sections of the image below. To find out more information about labels, some have more details available when you click on them. Drag and drop each label to the corresponding area it identifies in the image. arrange the events in the correct chronological order please explain to me CPJ and CRJ immediately I really need in depth explanation