Determine algebraically whether f(x) = x2(x2 + 9)(x3 + 2x) is even or odd.

Answers

Answer 1

Answer:

[tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex] is an odd function.

Step-by-step explanation:

Let be [tex]f(x) = x^{2}\cdot (x^{2}+9)\cdot (x^{3}+2\cdot x)[/tex], by Algebra this expression can be rewritten as:

[tex]f(x) = x^{3}\cdot (x^{2}+9)\cdot (x^{2}+2)[/tex]

Where [tex]x^{2} + 9[/tex] and [tex]x^{2}+ 2[/tex] are even functions, because they satisfy the condition that [tex]g(x) = g(-x)[/tex], whereas [tex]x^{3}[/tex] is an odd function, as the condition of [tex]h(-x) = - h(x)[/tex] is observed. Then, the overall function is odd.


Related Questions

A man bought a car for 15000GH cedis . He later sold it at a profit of 25% .What was his selling price.

Answers

Answer:

3750 GH cedis

Step-by-step explanation:

Step-by-step explanation:

100%=15000GH cedis

125%=?

125×15000/100

18750GH cedis

Plz Help I Will Mark Brainliest If Right!!!!!!!!!!!!!!!!!!!!!!!
Determine the domain of the function.

f as a function of x is equal to the square root of one minus x.

A). All real numbers
B). x > 1
C). x ≤ 1
D). All real numbers except 1

Answers

Hey There!!~

Your best answer choice is B). x > 1.

Good Luck!!

The length of the major axis of the ellipse below is 10 What is the sum of the lengths of the red and blue line segments? A. 10 B. 5 C. 15 D. 20

Answers

Answer:

A. 10

Step-by-step explanation:

As we know that

The length of the major axis of the ellipse is 10

i.e

2 a = 10

Also, the ellipse is the curve that consists of 2 focal points  in order that the total of the distance to the 2 focal points would remain constant for each and every point displayed in the curve

Now we assume that P is the curve point

So,

PF1 + PF2

i.e

2 a (blue line) + (red line)

2 a = 10

Therefore the sum of the length is 10

Answer:

10

Step-by-step explanation:

Match each statement with its corresponding value for the system below:

y = -2(3)x and y = 9x - 2

1. The number of points of intersection.
2. The x-coordinate of the solution.
3. The y-coordinate of the solution.

Answers

Answer:

1. 1 point

2. The x-coordinate of the solution = 2/17

3. The y-coordinate of the solution = -16/17

Step-by-step explanation:

Given that the equation is of the form;

y = -2³×x and y = 9·x - 2, we have;

y = -8·x and y = 9·x - 2

1. Given that the two lines are straight lines, the number of points of intersection is one.

2. The x-coordinate of the solution

To find a solution to the system of equations, we equate both expression of the functions and solve for the independent variable x as follows;

-8·x = 9·x - 2

-8·x - 9·x=  - 2

-17·x = -2

x = 2/17

The x-coordinate of the solution = 2/17

3. The y-coordinate of the solution

y = 9·x - 2 = 9×2/17 - 2 = -16/17

y = -16/17

The y-coordinate of the solution = -16/17.

6=m/8 whats does m equal?

Answers

Answer:

m=48

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

m = 48

▹ Step-by-Step Explanation

Rewrite:

m/8 = 6

Use the inverse operation:

8 * 6 = 48

m = 48

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

The triangle is a right triangle with the right angle marked. Which equation correctly expresses The Pythagorean Theorem for this triangle?​

Answers

Answer: Choice B

r^2 + s^2 = t^2

The legs are length r and s. Square them and add the squares to get the square of the hypotenuse t. The hypotenuse is always opposite the 90 degree angle.

Answer:

Hey there!

The pythagorean theorem states that the square of one leg plus the square of another leg is equal to the square of the hypotenuse.

Thus, r^2+s^2=t^2.

This can be a challenging topic, and if you need a further explanation, let me know. Hope this helps :)

Zula has a conical bird feeder with a volume of 64.3 cubic centimeters and a height of 7 centimeters. Which equation can be used to find the area of the circular lid needed to cover the bird feeder?

Answers

Answer: [tex]64.3=\frac{1}{3}(B)(7)[/tex]

Step-by-step explanation:

[tex]V=\frac{1}{3} Bh[/tex]

B is the area of the base

h is the height of the cone

[tex]V=64.3 cm^3[/tex]

[tex]h=7cm[/tex]

[tex]64.3=\frac{1}{3}(B)(7)[/tex]

[tex]192.9=(B)(7)[/tex]

[tex]B=192.9/(7)[/tex]

[tex]=27.56cm^2[/tex]

Triangle P Q R is shown. The length of P Q is 17, the length of Q R is 15, and the length of P R is 14. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of AngleP to the nearest whole degree? 35° 52° 57° 72°

Answers

Answer:

P = 57°

Step-by-step explanation:

Given the following :

PQ = 17

QR = 15

PR = 14

Using the cosine formula since the length of the three sides are given:

a2 = b2 + c2 – 2bccos(A)

To find P:

QR^2 = PQ^2 + PR^2 – 2(PQ)(PR)cos(P)

15^2 = 17^2 + 14^2 – 2(17)(14)cos(P)

225 = 289 + 196 - 476 cosP

476*CosP = 485 - 225

476*CosP = 260

CosP = 260/476

CosP = 0.5462184

P = Cos^-1(0.5462184)

P = 56.892029

P = 57°

Answer:

57 degrees

Step-by-step explanation:

just took the test on edg2020

one day shahed was playing with numbers.He wrote 15 fractions using all natural numbers from 1 to 30 exactly once-either as numerator or as denominator.How many of these fractions are most is integers.

Answers

Answer:

15

Step-by-step explanation:

half of 30 is 15

he used all the numbers upto 30 once

all the numbers in between arent integers but decimals

John used 1 3/4 kg os salt to melt the ice on the sidewalk. He then used another 3 4/5 kg on the driveway. How much salt did he use in all? PLEASE SHOW YOUR WORK I WILL MARK YOU BRAINIEST AND PLEASE EXPLAIN HOW YOU GOT YOUR WORK.

Answers

Answer:

111/20 = 5.55

Step-by-step explanation:

He used a total of 1  3/4 and  3  4/5 salt.

Convert both these mixed numbers into fractions.

=> 7/4 + 19/5

Take the LCM of the denominators

=> 35/20 + 76/20

Add the numerators

=> 111/20 = 5.55

He used a total of 111/20 or 5.55 kgs of salt.

Please give me the correct answer

Answers

Answer:

Height = 15

Step-by-step explanation:

[tex]Volume = 392.5\\r = 5\\h =?\\\\V= \frac{1}{3} \pi r^2 h\\\\392.5 = \frac{1}{3} \times 3.14 \times 5^2 \times h\\\\392.5 = \frac{78.5h}{3} \\\\392.5 = 26.16h\\\\\frac{392.5}{26.16} =\frac{26.16h}{26.16} \\\\h = 15.00[/tex]

Answer:

h=15 in

Step-by-step explanation:

V=πr²(h/3)

h=3v/πr²

h=[3(392.5)]/[3.14(5)²]

h= 15 in

i need help with this question ​

Answers

Answer:

1000ml

Step-by-step explanation:

4 days she drank ½ of the bottle

so she drank ⅛ l of juice everyday

so

1000ml is the answer

A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 6 gallons.

Answers

Answer:

3.625 gpm

Step-by-step explanation:

The minimal passing score for a test is 80%. There are 12 exercises on the test. What is the minimum number of correct exercises needed to earn a passing score?

Answers

Getting each exercise correct gets you 8.3(recurring)%. Therefore if you answer 10 exercises correctly you get 83.3%, and if you answer 9 exercises correctly you get 75%, this means that the minimal exercises you need to get correct is 10.

E
What is the value of x in the equation 3x.. by y 18, when y27

Answers

Answer:

x = 15

Step-by-step explanation:

We need to find the value of x in the equation 3x – y = 18 when y = 27.

To find the value of x, put y = 27 in the above equation.

So,

3x - 27 = 18

3x = 45

x = 15

So, the value of x is 15.

Please help! Algebra 1.

Answers

Answer:

The correct answer is B.

Step-by-step explanation:The entrance fee ($18) and the cost per ball ($0.08B) added together should equal greater or equal to $75 in order to receive $10 off.

The mean number of people per day visiting an art show in July was 110. If
20 more people each day visited the museum in August, what was the mean
number of people per day visiting in August?
A. 130
B. 620
C. 640
D. 110

Answers

Answer:

I believe the answer is A. 130

Answer:

A 130

Step-by-step explanation:

It says to find the area of the shaded square, but I not sure how to get the answer. ​

Answers

Answer:

68 square cm

Step-by-step explanation:

Interior square WXYZ is making four right triangles of equal bases (8 cm) and heights (2 cm) inside the square ABCD. Therefore,

Area of shaded Square = Area of square ABCD - 4 times area of one right triangle.

[tex] = {10}^{2} - 4 \times \frac{1}{2} \times 8 \times 2 \\ = 100 - 32 \\ = 68 \: {cm}^{2} [/tex]

Answer ASAP, Will give brainliest!!

Answers

Answer:

First. 115°

Second. 65°

Third. 65°

Fourth. 7

Fifth. 425.25

First

angle DAB = angle ADC (since this is an isosceles trapezoid)

Second

In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)

180-115 is 65°

Third

(Same reason as second)

Fourth

The side 3x+4 is same as the opposite side

So 3x + 4 = 25

on solving you get x = 7 in

Fifth

[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]

area = 1/2 × 13.5 (20+43)

area = 1/2 × 13.5 × 63

Thus area is 425.25

Answer:

Step-by-step explanation:

1)As ABCD is isosceles trapezium,

∠ADC= ∠DAB

∠ADC = 115°

2) AD //BC

∠ADC + ∠DCB = 180°   {co interior angles}

115 + ∠DCB = 180

 ∠DCB = 180 - 115

 ∠DCB = 65°

3) As ABCD is isosceles trapezium,

∠CBA = ∠DCB

∠CBA = 65°

4) As ABCD is isosceles trapezium, non parallel sides are congruent.

AB = DC

3x + 4 = 25 in

3x = 25 - 4

3x = 21

x = 21/3

x = 7 in

5) height = 13.5 in

a= 43 in

b= 20 in

Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]

                   [tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]

1. At the end of one school day a teacher had 17 crayons left. The teacher remembered
giving out 14 crayons in the morning, getting 12 crayons back at recess, and giving out
11 crayons after lunch. How many crayons did the teacher have at the start of the
day?

Answers

Answer:

30 crayons

Step-by-step explanation:

Let x be the number of crayons he started with

gave out 14 crayons

x-14

Got 12 back

x-14+12

Gave out 11 after lunch

x-14+12 -11

This equals 17

x-14+12 -11 =17

Combine like terms

x-13 = 17

Add 13 to each side

x -13+13 =17+13

x = 30

Answer: 30

Step-by-step explanation:

For this problem work backwards. Start from 17 and add 14. You should get 31. Then subtract 12, which equals 19. Finally add 11 to 19, which equals 30. Basically you are doing the inverse operation to get your answer. Hope this helps!

anyone know how to solve a functions equation such as x^2-x-x <0

Answers

Answer:

Step-by-step explanation:

[tex]x^{2} -x-x<[/tex] 0

[tex]x^{2} -2x[/tex] < 0

x^2-2x+1<1

(x-1)^2<1

-1<x-1<1

0<x<2

[tex](x-1)^{2}[/tex][tex](x-1)^{2}[/tex]

A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number.

Answers

A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.

Answer:

at 95% Confidence interval level: 0.501776   < p < 0.558224

Step-by-step explanation:

sample size n = 1200

population proportion [tex]\hat p[/tex]= 53% - 0.53

At 95% confidence interval level;

level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

The critical value for [tex]z_{\alpha/2} = z _{0.05/2}[/tex]

the critical value [tex]z _{0.025}= 1.96[/tex] from the standard normal z tables

The standard error S.E for the population proportion can be computed as follows:

[tex]S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.2491}{1200}}[/tex]

[tex]S,E = 0.0144[/tex]

Margin of Error E= [tex]z_{\alpha/2} \times S.E[/tex]

Margin of Error E= 1.96 × 0.0144

Margin of Error E= 0.028224

Given that the confidence interval for the proportion  is  95%

The lower and the upper limit for this study is as follows:

Lower limit: [tex]\hat p - E[/tex]

Lower limit: 0.53 - 0.028224

Lower limit: 0.501776

Upper limit: [tex]\hat p + E[/tex]

Upper limit: 0.53 + 0.028224

Upper limit: 0.558224

Therefore at 95% Confidence interval level: 0.501776   < p < 0.558224

Se repartió una suma de dinero entre tres personas; la segunda recibió x pesos mas que la primera, la tercera b pesos más que la segunda. Expresa la suma repartida, siendo t la parte de la primera.

Answers

Answer:

3t + 2x + b

Step-by-step explanation:

primera: t

segunda: t + x

tercera: t + x + b

suma: t + t + x + t + x + b = 3t + 2x + b

Based on the graph what are the solutions to ax^2 + bx+c=0 Select all that apply

A. X=-2

B. X=10

C. X=5

D. X=8

Answers

Answer:

x=-2 and x = 5

Step-by-step explanation:

The solutions to the equation are where the graph crosses the x axis

We can see that the graph crosses at x=-2 and x = 5

Answer:

x = -2

x = 5

Step-by-step explanation:

The answer is found when the graph crosses the x-axis

Hope this helps :D

for 0°<θ<-180° which of the primary trigonometric functions may have positive values?

Answers

sine and cosecant.

you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate

Eddies saving account has a balance of $140. He deposits $17 for each of the next five weeks. He withdraws $11 in the final week. He wants to use his savings to buy a game system for $210. Do he have enough money to buy the game system?

Answers

Answer:

No. he need 64 more

Step-by-step explanation:

yes he has enough money
140+85=225-11=214
17x5=85

For what real numbers x is x 2 − 10 x + 25 negative?

Answers

Answer:

no real numbers

Step-by-step explanation:

x^2 − 10 x + 25

Factor

What 2 numbers multiply to 25 and add to -10

-5*-5 = 25

-5+-5 = -10

( x-5) (x-5)

This touches the graph at x =5

The parabola is positive so there are no values where the graph is negative

Answer:

No real solutions

Step-by-step explanation:

Part 1: Factoring the quadratic

The equation is in quadratic form - ax² + bx + c = 0.

Therefore, we can use a factoring technique to solve for x. I will use the quadratic formula - [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac} }{2a}[/tex].

[tex]x=\frac{-(-10)\pm \sqrt{(-10)^{2}-4(1)(25)} }{2(1)}\\\\x=\frac{10\pm\sqrt{100-4(25)} }{2}\\\\x=\frac{10\pm\sqrt{100-100}}{2}\\\\x=\frac{10\pm\sqrt{0}}{2}\\\\x=\frac{10\pm0}{2}\\\\x=\frac{10}{2}\\\\\boxed{x=5}[/tex]

Part 2: Using discriminant to determine roots

Because the discriminant (square root portion of formula) was equivalent to zero, this is the only solution that proves the equation correctly. Therefore, there is no possible negative value that can be substituted for x  without altering the final value that the equation is equal to.

Evaluate without actual multiplication 1) 95x96 2)103x107

Answers

Answer:

:

"(100 + 3) (100 + 7)

Now, by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = 3 , b = 7

= (100)² + (3+7)*100 + (3*7)

= 10000 + 1000 + 21

= 11021

.

(110 - 7) (110 - 3)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = (-7) , b = (-3)

= (110)² + { (-7) + (-3) }*110 + {(-7)*(-3)}

= 12100 + (-10)*110 + 21

= 21200 - 1100 + 21

= 11021

.

➖➖➖➖➖➖➖➖➖➖

.

(90 + 5) (90 + 6)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 90 , a = 5 , b = 6

= (90)² + (5+6)*90 + (5*6)

= 8100 + 990 + 30

= 9120

.

(100 - 5) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = (-5) , b = (-4)

= (100)² + { (-5) + (-4) }*100 + 20

= 10000 + (-9)*100 + 20

= 10000 - 9000 + 20

= 10020 - 900

= 9120

.

➖➖➖➖➖➖➖➖➖➖

.

(100 + 4) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = 4 , b = (-4)

= (100)² + { 4 + (-4) }*100 + 4*(-4)

= 10000 + (4 - 4)*100 - 16

= 10000 + 0*100 - 16

= 10000 - 16

= 9984

.

(90 + 14) (90 + 6)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 90 , a = 14 , b = 6

= (90)² + (14 + 6)*90 + (14*6)

= 8100 + 20*90 + 84

= 8100 + 1800 + 84

= 9984"

This answer was in another question

This answer was given by BloomingBud

Step-by-step explanation:

Answer:

1) 9120 2) 11021

Step-by-step explanation:

95 * 96 = (100-5)(100-4) = 10000 - 500 - 400 + 20 = 9120

103 * 107 = (100+3)(100+7) = 10000 + 300 + 700 + 21 = 11021

You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice. Write an equation for the number of minutes you swim, yyy, when your friend swims xxx number of minutes.

Answers

Answer:

y = x + 15

Step-by-step explanation:

My friend swims x minutes.

I swim 15 minutes more than my friends, so I swim x + 15 minutes.

I swim y minutes, so y equals x + 15

Answer: y = x + 15

The sum of 2 numbers is 250. One of them is greater than 150. Which of these is definitely true about the other number? a) It is equal to 100. b) It has to be less than 100. c) It has to be greater than 100. d) It has to be a number between 150 and 250. Please answer fast and do explain how you got the answer...

Answers

Answer:

b

Step-by-step explanation:

Answer:

d) it has to be greater than 150 and 250

Step-by-step explanation:

It  says in the question it is greater than 150. So the number will be between 150 and 250.

Mark it as Brainliest pls

Hope it helps!!!

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Which is/are possible genotypes for a person with straight little finger and brown eyes?a. bbrr b. bbRR c. BbRr d. bbRr Garfield Company has the following information for the current year: Beginning fixed manufacturing overhead in inventory $230,000 Fixed manufacturing overhead in production 850,000 Ending fixed manufacturing overhead in inventory 50,000 Beginning variable manufacturing overhead in inventory $40,000 Variable manufacturing overhead in production 140,000 Ending variable manufacturing overhead in inventory 30,000 What is the difference between operating incomes under absorption costing and variable costing? the 15 chihuahua puppies ate 63 cups of food last week if each puppy ate the same amount of food how many cups of puppy food did each puppy eat Mother wants to divide $36 between her daughters Ava and Charlotte in the ratio of their ages. If Ava is 15 years old and Charlotte is 12 years old, find how much Ava and Charlotte will get. Name one real-world object that suggests A. Points B. Lines and C. Planes It's nighttime, and you've dropped your goggles into a 3.2-m-deep swimming pool. If you hold a laser pointer 1.2 m above the edge of the pool, you can illuminate the goggles if the laser beam enters the water 2.0 m from the edge.How far are the goggles from the edge of the pool? Jared hiked a trail that is 12 miles long. He hiked the trail in section that were 1.5miles each. In how many sections did he complete the hike?A. 12B. 8 C. 10D. 4 Younique is writing an essay in favor of recycling to reduce garbage in the ocean. Which piece of evidence is least relevant to her argument? 1. Litter is not only ugly, but also harmful to animals in national parks 2. Millions of plastic water bottles end up in the ocean each year, adding to the millions already there and not decomposing. 3. Recycling has become easier with many public places including recycling bins right next to all garbage cans. 4. 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Jaime then writes out the contract, detailing only that he will sell Bronn his armor and the sword. He also lists the delivery date for next Wednesday. The next week on the day of performance, Jaime fails to deliver the armor and sword. Bronn sues him for breach of contract, but Jaime claims the contract is not enforceable because it was missing the price. When Bronn filed his lawsuit, which of the following needed to be included in the written contract for enforceability?a. signature of both partiesb. price subjectc. matterd. deliverye. performance -3 = k/12 help please A buoy floating in the sea is bobbing in simple harmonic motion with amplitude 13 in and period 0.25 seconds. Its displacement d from sea level at time t=0 seconds is 0in, and initially it moves downward. (Note that downward is the negative direction.)Required:Give the equation modeling the displacement d as a function of time t. What meaning is revealed through the use of an analogy in this cartoon? 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