Show that f(x) = 3x
4 − 2x
2 + 5 is an even function.

Answers

Answer 1
Answer:
Step-by-step explanation:
This f(x) is an even function.
Explanation:
An even function is one where f(−x)=f(x) for all x in the domain.
An odd function is one where f(−x)=−f(x) for all x in the domain.
In the case of f(x)=3x4−x2+2 we find:
f(−x)=3(−x)4−(−x)2+2=3x4−x2+2=f(x)
So f(x) is an even function.
Actually, there is a shortcut with polynomial functions:
If all of the terms have even degree then the function is even.
If all of the terms have odd degree then the function is odd.
Otherwise the function is neither odd nor even.
in our example, 3x4 has degree 4, −x2 has degree 2 and 2 has degree 0. So all of the terms are of even degree and the function is even

Related Questions

Represent the number 144 in four different ways using repeated multiplication.

example: 4 x 4 x 3 x 3

Answers

2x36x2
4x9x2x2
Here’s 2

I need help on this question

Answers

Answer:

wow that is a tough one             the answer is 438654

Step-by-step explanation:

all that is to it

6. Roughly what percent of the US
flag is red?

Answers

Answer:

about 14 percent but the exact is 14 3

the red part takes up exactly 41.5% of the US flag. so roughly 41 percent?

extra info: the white is 40.9% and the blue is 17.6%

i hope this helps you!:)

The field trip to the science museum will cost $22 per student. If Mrs. Robertson has 24 students, how much money will she collect in all?

Answers

Answer:

528

Step-by-step explanation:

22x24=528

Answer:528$

Step-by-step explanation: you have to do 22 dollars times 24 students which would be 528

PLEASE HELP
The graph of g(x)=3x^2+bx-24 has the same x-intercepts. what is the value of b?

(A) -6

(B) 14

(C) -2

(D) 1

Answers

The value of b so that 3 · x² + b · x - 24 has the same x-intercepts (only one x-intercept) is 12 √2.

How to determine a missing coefficient in a second order polynomial

Second order polynomials are represented graphically by parabolae and it may have two, one or no x-intercepts. The quantity of x-intercepts can be deducted from the discriminant of the quadratic formula, which is defined below:

For a · x² + b · x + c = 0, the discriminant is defined by:

d = b² - 4 · a · c   (1)

There are three rules to determine the number of possible intercepts:

If d < 0, then there are no x-intercepts.If d = 0, then there is only one x-intercept.If d > 0, then there are two x-intercepts.

Then, we have to find a value of b so that (1) has the following form:

b² - 4 · 3 · (-24) = 0

b² - 288 = 0

b = 12√ 2

The value of b so that 3 · x² + b · x - 24 has the same x-intercepts (only one x-intercept) is 12 √2. [tex]\blacksquare[/tex]

Remark

The answer choices do not correspond with the given statement, the phrase "same x-intercepts" may lead to confusion and possible graph cannot be found. A possible corrected statement is shown below:

The graph of g(x) = 3 · x² + b · x - 24 has only one x-intercept. What is the value of b?

To learn more on parabolae, we kindly invite to check this verified question: https://brainly.com/question/10572747

Answer:

Step-by-step explanation:

How many square meters are there in a floor that is 9 meters long by 12 meters wide?

99
108
109
117

Answers

Answer:

108

9×12

Step-by-step explanation:

please mark me as brainlest

What is the area of the figure shown delow?

Answers

Answer:

160mm2 is the correct answer

Step-by-step explanation:

the box plot shoes the lengths of the songs on two digital music players

Answers

Hello, it seems your questions didn't upload correctly. Are you able to resend it?

A ball follows a path described by the function h(x) = -3x^2 +12x +14 where h(x) is the height of the ball after x seconds. After how many seconds will the ball be at its
highest point?

A. 1 second
B. 2 seconds
C. 3 seconds
D. 4 seconds

Answers

Answer:

3

Step-by-step explanation:

A school's principal wanted to give a special 'Good Luck' pencil for each student in the fifth grade. If there are 105 kids in the fifth grade, and there are 12 pencils in each box, how many boxes will he need to buy?

Answers

To find the number of boxes divide the total kids by number of pencils in each box. Here 105/12 leaves remainder. It means still kids are left over. So add 1 to the quotient
105/12= 8 and remainder is 9.
So add 1 to the quotient 8 which is 9
Total pencil boxes = 9

Area of the figure .

Answers

Answer: the answer is not in the multiple choice.

area = 60 in^2

Step-by-step explanation:

Choose the set of numbers with an average of 8.
A) 3, 5, 7, 8, 12
B) 2, 3, 6, 13, 16
C) 2, 4, 8, 11, 20

Answers

The correct answer is B

To find the average we add all the given numbers together then divide by how many numbers there are.

A is 7

B is 8

C is 9

Answer:

B

Step-by-step explanation:

A) (3+5+7+8+12)/5 = 35/5 = 7 => Incorrect

B) (2+3+6+13+16)/5 = 40/5 = 8 => Correct

C) (2+4+8+11+20)/5 = 45/5 = 9 => Incorrect

Problem
* Henry has many different screwdrivers. Each screwdriver is 6 inches long. He wants to make a line of
screwdrivers that is 1 yard long. How many screwdrivers will Henry need?

Answers

Answer:

Henry will need 6 screwdrivers.

Answer:

Henry will need 6 screwdrivers.

Step-by-step explanation:

[tex]1yard = 36inches\\\frac{36inches}{6inches/screwdriver} = 6screwdrivers[/tex]

Estimate f(4.04) for f as in the figure

Answers

Answer:

2.013  to 3 DP's.

Step-by-step explanation:

f(4.04)  will be very close to the tangent line.

Equation of tangent line

is y - 4 = m(x - 10)

m = (4-2) / (10-4) = 1/3

y - 4 = 1/3(x - 10)

y = 1/3x - 10/3 + 4

y = 1/3x + 2/3

So the require estimate of f(4.04)

= 1/3(4.04) + 2/3

= 2.013333

Solve the two-step equation.

3
4
(x) − 1.72 = −6.82

1. The first step is to
✔ add 1.72
on both sides.
2. The second step is to
on both sides.


The solution is x =
.

Answers

Answer:

[tex]\boxed{\sf{x=-0.15}}[/tex]

Step-by-step explanation:

Isolate the term of x from one side of the equation.

34(x)-1.72=-6.82

Rewrite the problem down.

⇒ 34x-1.72=-6.82

First, add by 1.72 from both sides.

⇒ 34x-1.72+1.72=-6.82+1.72

Solve.

⇒ -6.82+1.72=-5.1

Rewrite the problem down.

⇒ 34x=-5.1

Divide by 34 from both sides.

⇒34x/34=-5.1/34

Solve.

Divide the numbers from left to right.

⇒ -5.1/34=-0.15

⇒ x=-0.15

Therefore, the solution is x=-0.15, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.

Here is the correct answer is this

Step-by-step explanation:

20.
19. Make Sense and Persevere Use the Distributive
Property to expand 7(7x - 3y) - 6.
HELP PLEASE

Answers

Answer:

49x-21y-6

Step-by-step explanation:

7(7x) 7(-3y) -6

49x-21y-6=0

Given g(x)
-2 – 2, find g(-3).
Answer:

Answers

The calculation of the function given shows that since g(x) = -2x² - 9, the value of g(3) will be -27.

How to calculate the function?

From the complete function, it should be noted that the value of g(x) = -2x² - 9.

Therefore, the value of g(3) will be calculated thus:

= -2(3)² - 9

= -2(9) - 9.

= -18 - 9

= -27

In conclusion, g(3) is -27.

Learn more about function on:

https://brainly.com/question/25638609

Solve the inequality 4i−4(i+2)≥6(8i−8) and write the solution in interval notation

Answers

Answer:

[tex](-\infty,\frac{25}{24}][/tex]

Step-by-step explanation:

Assuming [tex]i[/tex] is a variable:

[tex]4i-4(i+2)\geq6(8i-8)\\\\4i-4i+2\geq48i-48\\\\2\geq48i-48\\\\50\geq48i\\\\\frac{50}{48}\geq i\\ \\\frac{25}{24}\geq i\\ \\i\leq\frac{25}{24}\\ \\(-\infty,\frac{25}{24}][/tex]

What is 1 + 1 x 3 Whoever answers it to

Answers

Answer:

It equals 4

Step-by-step explanation:

1 + 1 x 3=4

Answer:

I think it equals 4

Step-by-step explanation:

1 + 1 x 3=4

Ted needs 2500 metres of lighting cable for a job. What is this length in kilometres?

Answers

Answer:

2.5km

Step-by-step explanation:

1000m=1km

We have 2500m

2500m=2.5km

2500 m because 1000 metre=1km.

The distance between the points (1,2) and (x,-1) is 5 units. Find the possible values of x​

Answers

Answer:

-3,5

Step-by-step explanation:

[tex]d = \sqrt{(x _{2} - x _1) {}^{2} + (y _{2} - y _{1} {} ) {}^{2} } [/tex]

[tex]5 = \sqrt{(x - 1) {}^{2} + ( - 1 - 2) {}^{2} } [/tex]

[tex]5 = \sqrt{(x - 1) {}^{2} + ( - 3) {}^{2} } [/tex]

[tex]25 = (x - 1) {}^{2} + 9[/tex]

[tex]16 = (x - 1) {}^{2} [/tex]

[tex]4 = x - 1[/tex]

[tex]x = 5[/tex]

Or

[tex] - 4 = x - 1[/tex]

[tex]x = - 3[/tex]

Can someone help me!

Answers

Answer:

Top left.

Step-by-step explanation:

can someone help me answer this question?

Answers

check picture uploaded to see steps

children = 201

adults = 277

Giving brainliest to people who get this right

Answers

Answer:

A

Step-by-step explanation:

If y is a function of x, then the equation for y would be y=Ix(+or-or*or%) to nI

For this specific event, the proper equation would be y=Ix-0.5I

Breaking down this equation, y equals the absolute value of x-0.5.

So if x was 2, it would go as y=I2-0.5I where y equals 1.5.

Solve the equation, 3x – 6 = 12, for x. Which of the following properties did you apply? Question 2 options: A) Addition property of equality and multiplication property of equality B) Addition property of equality and division property of equality C) Distributive property, subtraction property of equality, and multiplication property of equality D) Distributive property, addition property of equality, and division property of equality

Answers

Add -6 to 12 that anwser is b

Which pair shows equivalent expressions?
2x + 10 = -2(x-5)
-2(x+5) = 2x-10
-2x-10 = -2(x+5)
-2(x-5) = -2x-10

Answers

Answer:

The 3rd equation, -2x-10 = -2(x+5)

Step-by-step explanation:

Equivalent expressions means both sides of the equal sign equal the same thing

To find which ones are equivalent expressions, we must solve/simplify both sides of each equation to see if they're actually equal to each other

We will use PEMDAS for this

1. 2x + 10 = -2(x - 5)

Start with Parentheses, and distribute the -2 to what's inside said parentheses

2x + 10 = -2x + 10

Not equal

2. -2(x+5) = 2x-10

Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses

-2x - 10 = 2x - 10

Not equal

3. -2x-10 = -2(x+5)

Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses

-2x - 10 = -2x - 10

Equal

4. -2(x-5) = -2x-10

Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses

-2x + 10 = -2x - 10

Not equal

Which of the binomials below is a factor of this expression?

49x^2 + 28xy + 4y^2

A. 7x + 4y

B. 7x + 2y

C. 7x - 2y

D. 7x - 4y

Answers

Answer:

B. 7x+2y

Step-by-step explanation:

[tex]49x^2+28xy+4y^2\\\\=(7x)^2+2\cdot 7x \cdot 2y + (2y)^2\\\\=(7x+2y)^2\\\\=(7x+2y)(7x+2y)[/tex]

A boat, which moves at 29 miles per hour in water without a current , goes 825 miles upstream and 825 miles back again in 58 hours. Find the speed of the current to the nearest the the place.

Answers

Answer:

  4 mph

Step-by-step explanation:

Travel time is proportional to distance and inversely proportional to speed. If c represents the speed of the current in miles per hour, an equation for the total trip time is ...

  825/(29 -c) +825/(29 +c) = 58 . . . . . . hours travel time

  825(29 +c) +825(29 -c) = 58(29 -c)(29 +c)

  58c² -928 = 0 . . . . . . . rearrange to standard form

  58(c -4)(c +4) = 0 . . . . factor

Values of c that satisfy this equation are 4 and -4. For the purpose here, we'll choose the positive solution.

The speed of the current is 4 miles per hour.

Can the sides of a triangle have lengths 2, 6, and 7?

Answers

Answer:

Yes

Step-by-step explanation:

The third largest side is 7 and the other two sides added are bigger than seven.

2 + 6 = 8

Is this answer accurate?

least to greatest 52, 63, 55, 56, 62, 54, 59, 60, 53, 61, 88

Answers

Answer:

52, 53, 54, 55, 56, 59, 60, 61, 62, 88

Step-by-step explanation:

You need to start from 52 to 88 (least to greatest) and then you will get answer.

Other Questions
After several years of working, Katy has saved $125,000. If she invests that $125,000 in a savings fund that adds 4% eachyear, about how much will her savings account have after15 years? For this question, ignore compounding and taxes, andassume Katy does not put additional money into savings. A $185,000(B) $200,000C $190,000(D) $175,000Question 1610 Points A+restaurant+bill+before+tax+is+$15. 50. +if+the+sales+tax+is+8%+and+a+15%+tip+is+added,+what+is+the+total+cost+of+the+meal? The ratio 216 : x is equivalent to x^2 : 216. What is the value of x? When he goes on a date, Jack gets bored easily and tends to be misunderstood, even though he frequently and loudly voices his opinions. His friend advises that _______________ would make him more attractive to potential partners Should a student have to redo work even though it was the teacher's fault for losing the assignment(s)?My biology teacher lost TWO of my assignments. He KNOWS that I gave the assignments to him. We both came to a conclusion that either he had misplaced it or it was stolen. What influences the reconstruction of past events?. Point P(5.15, 7.05) is a reflection across the x-axis of which of the following points? (5.15, 7.05) (7.05, 5.15) (5.15, 7.05) (7.05, 5.15) How does Sumner try to make Butler and his position on slavery seem ridiculous? PLEASE HELP!!! I WILL MARK BRAINLIEST!!!! TRUE OT FALSE!! The International Banking System is "Decentralized" meaning that there is not a coordinating bank with power over the entire international banking system and there is NOT a single set of rules that governs this. Question 1 options: True FalseQuestion 2 (2 points) Currency exchange is the trade of different kinds of money.Question 2 options: True False why language is an important of communication tools? Identificar. Complete the following statements by conjugating the verb tener in the blanks provided. fill in the blanks. 1. Mi padre ( )mucho xito. 2. T( ) prisa cada maana. 3. Yo no tengo un suter por eso( ) fro. 4. Ellos quieren un refresco porque( ) sed 5. Nosotros( ) mucha hambre. Vamos a comer! hi, please answer the question, show your work PLS HELP :How is energy causing motion or creating a change in this image? (2 points)(leaves of a plant in the sunlight)1.Energy from fuel allows the plant to grow and make its own food.2.Energy from the sun allows the plant to grow and make its own food.3.Energy from the wind allows the plant to grow and make its own food.4.Energy from the water allows the plant to grow and make its own food 2. Describe asteroids and their orbits in the solar system. The __________ requires that healthcare providers refrain from acts of omissions that would foreseeably result in harm to others, especially in cases in which the individuals are particularly vulnerable to the risk. what do we learn about Esperanza through the chapters chanclas,hips,the first job. for house on mango street Find the area of the figure two red triangles This is a semi-question that I know the answer too. Do yall know what pepperoni rolls are if so please leave your state. I already halfway did this but I still feel like imma get some answers wrong so can someone help me (also this is not history this is Science but brainly don't have a Science subject) A quarter is tossed three times. What is the probability that it will landon tails three times in a row?