here is a graph of a polynomial function with degree 4 what statements are true about the function?

Here Is A Graph Of A Polynomial Function With Degree 4 What Statements Are True About The Function?

Answers

Answer 1
The leading coefficient is positive (starts and ends positive given an even degree polynomial)

It has 4 linear factors (the graph crosses the x-axis at 4 places)

One of the zeroes is x=2 (the graph crosses the x-axis at x=2)
Answer 2

The statements that are true about the functions are:

The leading coefficient is positive.

It has two relative maximums

It has four linear factors.

One of the zeroes is x = 2.

What is a polynomial?

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

From the graph,

The graph passes through the following points on the graph.

x = -4

x = -2

x = 2

x = 6

This means the polynomial function is:

P(x) = (x + 4)(x + 2)(x - 2)(x - 6)

If we simplify the polynomial we get,

P(x) = (x² + 2x + 4x + 8) (x² + 6x - 2x + 12)

P(x) = [tex]x^{4}[/tex] + 6x³ - 2x³ + 12x² + 2x³ + 12x² - 4x² + 24x + 4x³ + 24x² - 8x² + 48x + 8x² + 48x - 16x + 96

P(x) =[tex]x^{4}[/tex] + 10x³ + 44x² + 104x + 96

The leading coefficient is positive 1 so it is positive.

The constant term is a positive number (96).

The relative maximum is a point on the graph where the function changes from increasing to decreasing.

So,

From the graph, there is only one point.

So only one relative maximum.

The relative minimum is a point on the graph where the function changes from decreasing to increasing.

So,

From the graph, there are two relative maximums.

The function has four linear factors

(x + 4), (x + 2), (x - 2), and (x - 6).

x = -4, x = -2, x = 2, and x = 6

Thus,

The statements that are true about the functions are:

The leading coefficient is positive.

It has two relative maximums

It has four linear factors.

One of the zeroes is x = 2.

Learn more about polynomials here:

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Related Questions

1
2 kg de plátanos cuesta $400 ¿ Cuál será el valor de 5,5 kg de esa fruta?

Answers

Answer:

Gfd 600

Step-by-step explanation:

A recipe calls for 2/3 a cup of butter. Georgia wants to cut the recipe in half. How much butter would she need?

Answers

Answer: 1/3

Step-by-step explanation: 2/3 - 1/3 = 1/3

Question 9 (1 point) Which of the following does NOT describe mass?
a remains constant
b a measure of matter
C a measure of gravitational force
d measured in kilograms ​

Answers

C. A measure of gravitational force

The answer is a measure of gravitational force

commission expense is budgeted to be $16,000 at a planned sales level of 4,000 units. if only 2,900 units are sold, how much commission expense will appear on the flexible budget, and is the activity variance favorable or unfavorable?

Answers

The amount of commission expense that will appear on the flexible budget if 2900 units were sold is; $11600

The activity variance is favourable.

According to the question;

The budgeted commission expenses is to be $16,000 at a planned sales level of 4,000 units.However, only 2900 units are sold.

To solve this;

We must be aware that the commission expense is directly proportional to the number of units sold.

In essence;

$16,000 is expected at 4,000 units of sale.Therefore, $x is expected at 2,900 units of sale.

By cross product;

x = (2900 × 16000)/4000

x = $11,600

Ultimately, the activity variance is favourable bas less commission expense is recorded for less sale.

Read more;

https://brainly.com/question/24487497

If the logarithmic regression model for a set of data is y = 2 + In x. What is the residual for the data value (2,4)?​

Answers

Answer: 4,2
Explanation: 4 is opposite

In a survey of 2,600 people who owned a certain type of​ car, 1,430 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Answers

Answer:

55%

Step-by-step explanation:

1430 divided by 2600 is 0.55

0.55 is 55%

!!!!!!PLEASE I NEED HELP!!!!!! I WILL GIVE YOU BRAINLIEST!!!!!

1.The product of two consecutive negative integers is 10506. Write a quadratic equation that you could solve to find the integers.

Answers

[tex] {x}^{2} + x - 10506 = 0[/tex]

Step-by-step explanation:

-x, -(x+1)

-x-(x+1)=10506

x^2+x-10506=0

what has the same value as 0.45

Answers

Answer:

9/20 or 45%

Step-by-step explanation:

Step-by-step explanation:

WHY IT IS SAYING YO WRITE AT LEAST 20 CHARACTERS

OHH, IT IS ALREADY 20 CHARACTERS

How much will it cost to fill a
13-gallon gas tank at $2.30 per gallon?

Answers

Answer:

$29.90

Step-by-step explanation:

Just multiply gallons by price:

13 gallons x [tex]\frac{2.30 dollars}{1 gallon}[/tex] = 29.9

29.90 of course u just multiply 2.30 to 13

Make my life easier and do 5-7 please.

Answers

Answer: 5. -64 6. 81 7. 144

Step-by-step explanation:

5. -4 x -4 = +16. +16 x -4 = -64

6. -3 x -3 = 9. 9 x -3 = -27. -27 x -3 = 81

7. kiera + 11 of her friends = 12 people total if 12 people each give fliers to 12 people, its 12 x 12 which is 144

Answer:

(-4)³; (-3)⁴; 12²

Step-by-step explanation:

Q5-4 * - 4* - 4 = (-4)³Q6-3 * -3 * -3 * - 3 = (-3)⁴Q7

Each 12 people gives 12 fliers to others. The number of people who gets fliers is:

12 * 12 = 12²

please answer!! will give a thanks and brainliest! :)))

Answers

8.

Since they have twice as many games won as lost there are 3 parts.

The losing part and the two winning parts.

The winning part is [tex]\frac{2}{3}[/tex] the games while the losing part is [tex]\frac{1}{3}[/tex] the games.

Just multiply [tex]\frac{2}{3}[/tex] by the games played to find the games won.

[tex]\frac{2}{3} (96)=\frac{192}{3} =64[/tex]

The ravens won 64 games.

10.

Make a system of equations.

Let s be the number of skips interviews and w be the number of woodys interviews.

s=w-8

s+w=20

Then just use algebra to rearrange and find each persons interviews.

For this one we can rearrange the second equation to get s=20-w.

Since we have two solutions for s we can set them equal.

w-8=20-w

2w-8=20

2w=28

w=14

Now that we have the number of woodys interviews substitute it into the first equation to get skips interviews.

s=w-8

s=14-8

s=6

So skip had 6 interviews and woody had 14 interviews.

12.

Make a system of equations

y-x=7

x+y=33

Then just use algebra to rearrange and find each amount of items.

Start by solving with substitution. (Elimination could work too im just going to use substitution.)

y-x=7

y=7+x

Substitute into the second equation

x+(7+x)=33

2x+7=33

2x=26

x=13

Now plug this x value back into the first equation

y-13=7

y=20

The number of items on one list is 13 and the number of items on the second list is 20.

I only need help with the circled ones

Answers

Answer:

9. ⅓

12. 1/12

15. 4/25

bye

Step-by-step explanation:

9. ⅔×½=⅓ ( the 2 in the numerator cancel out with the 2 in the denominator).

12. ⅓×¼=¹/(3×4) = ¹/12. (multiply the denominators 3 & 4)

15. ⁴/10×⅖= 4/25. (divide 2 in the numerator with the 10 in the denominator which gives the quoetiont 5) .

hope this helps you.

answer the question with clear explanation !!

Answers

[tex]food = \frac{1}{3} \times 48000 = 16000 \\ rent = \frac{1}{5} \times 48000 = 9600 \\ clothes = \frac{1}{4} \times 48000 = 12000 \\ food + rent + clothes = x \\ 16000 + 9600 + 12000 = 37600 \\ ndagune \: income - what \: he \: spends = what \: he \: saves \\ 48000 - 37600 = 10400 \\ ndagune \: saves \: 10400[/tex]

What is the slope of a line perpendicular to the line whose equation is 6x+4y=72 Fully simplify your answer.

Answers

Answer:

m = 2/3

Step-by-step explanation:

4y = -6x + 72

y = -3/2x + 18

Negative reciprocal = 2/3

what is 8f to the 4th power/2f to the third power in parentheses squared

Answers

The parenthesis squared mean it is the 4th power to the 8th

simplify the expression
SCREEN SHOT ATTACHED​

Answers

Answer:

c

Step-by-step explanation:

The correct answer is D.

Simplify the radical by breaking the radicand up into a product of known factors, assuming the real numbers. This is very hard to explain on a keyboard because there is no square root symbols lol

solve 3(b-5) = 27
solve 2x/3 = 6
solve 2(n + 5) = 15
solve a + a + a + a = 24
solve 4c + 6 = 18

please answer with an explanation
50 points given with explanation

Answers

Step-by-step explanation:

3(b-5) = 27

=> 3b - 15 = 27

=> 3b = 27 + 15 = 42

=> b = 42/3

=> b = 14 (Ans)

2x/3 = 6

=> 2x = 6 × 3 = 18

=> x = 18/2

=> x = 9 (Ans)

2(n + 5) = 15

=> 2n + 10 = 15

=> 2n = 15 - 10 = 5

=> n = 5/2

=> n = 2.5 (Ans)

a + a + a + a = 24

=> 4a = 24

=> a = 24/4

=> a = 6 (Ans)

4c + 6 = 18

=> 4c = 18 - 6 = 12

=> c = 12/4

=> c = 3 (Ans)

HELP ASAP BRAINLIEST!
One pump can fill a tank of water in 4 hours. A second pump can fill the same tank in 3 hours. If both pumps are used together, how long will it take to fill the tank?
1.7 hours
6.7 hours
.5 hours
2.3 hours

Answers

Answer:

1.7

Step-by-step explanation:

in one hour, the first pump can fill the tank 1/4 of the way

in one hour, the other can fill it 1/3 of the way.

get them to the same denominator.

3/12+4/12=7/12 of the tank in one hour

1÷7/12=12/7=1 5/7=1.7

Manuel wants 30 liters of a mixture of water and 10% lemon juice. He has a mixture of 8% lemon juice and a mixture of 20% lemon juice. How many liters of the 8% and 20% mixtures should he mix to get what he wants?

Answers

Manuel needs 20 liters of the 8% and 5 liters of 20% mixtures to be mixed so as to get 30 liters of a mixture of water and 10% lemon juice.

Let x represent the amount of 8% lemon juice in liters and y represent the amount of 20% lemon juice in liters.

Since Manuel wants to produce a 30 liters mixture from 8% lemon juice and 20% lemon juice, hence:

x + y = 30      (1)

Also, Manuel wants 30 liters of a mixture of water and 10% lemon juice, hence:

8% of x + 20% of y = 10% of 30 liters

0.08x + 0.2y = 3         (2)

Solving equation 1 and 2 simultaneously; multiply equation 1 by 0.2 and subtract equation 2 from the result:

0.12x = 3

x = 25 liters

x + y = 30

25 + y = 30

y = 5 liters

Manuel needs 20 liters of the 8% and 5 liters of 20% mixture

Find out more at: https://brainly.com/question/15024774

Pls do 5 and 2 also explain

20pts plus BRAINLIST

Answers

So for any shape that has 4 sides to find the area multiply the width by the length so for question 2 the answer is 10x10 which is 20
And for 5 the answer is 6x6 which is 36

Hope this helped

Please help!
Solve for x
3(x - 4) - 2x = 6

Answers

Answer:

Step-by-step explanation:

first open the bracket

3x-12-2x=6

collect like terms

3x-2x-12=6

x-12=6

x=12+6

x=18

This is your answer

Help please! Will give brainlist for correct answer with steps. If you’re a troll I will report!

Answers

Answer:

x²-10x+34=0. here u go I'm 12

Bobby and his brother had 3 over 4 of a pizza leftover after dinner. Their father came home and ate 1 over 2 of the leftover pizza. How much pizza did their father eat?

Answers

Answer:

it could be 1/8

On Monday, 217 students went on a trip to the zoo. All 4 buses were filled and 9 students had to travel in cars. How many students were in each bus ?​

Answers

you need to divide so you you’ll divide 217 by 4

Write the equation of the line that passes through the points (0,0) and (7,8). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line

Answers

Answer:

PLS MARK BRAINLIEST

Step-by-step explanation:

m= y2 - y1/ x2 - x1( slope of a line)

m = 8 -0 / 7- 0

8/7 = m

m = 1.1

since m =y - y1/ x - x1

1.1 = y - 0/ x-0

1.1 = y/x(cross multiply)

y = 1.1 x

y -1.1 x = 0

or

y - 8/7 x = 0

1.5c - 6 = 7.5 i need help with this problem and i have no one to help me

Answers

Answer:

c=9

Step-by-step explanation:

Let's solve your equation step by step:

add 6 on both sidesdivide 1.5 from the product of 6 and 7.5 (aka 13.5)you will get Cput 9 in for C.[tex]1.5c-6=7.5[/tex]

1. [tex]1.5c-6+6=7.5+6[/tex]

1.5 [tex]1.5c=13.5[/tex]

2.[tex]\frac{1.5c}{1.5c}=\frac{13.5}{1.5c}[/tex]

3. C=9

1.5(9)-6=7.5

13.5-6=7.5

How to determine values of a,b and c

Answers

(i) The graph of f is symmetric about the y-axis - this is another way of saying f is an even function, which means

[tex]f(x) = f(-x) \iff \dfrac{ax+b}{x^2-c} = \dfrac{-ax+b}{x^2-c}[/tex]

The denominator remains unchanged, so

ax + b = -ax + b

Solve for a :

ax = -ax

2ax = 0

a = 0

(The alternative is that x = 0, but if that were the case then there would be infinitely many choices for a.)

So

[tex]f(x) = \dfrac{b}{x^2-c}[/tex]

(ii) Since

[tex]\displaystyle \lim_{x\to2^+}f(x) = +\infty[/tex]

it follows that x - 2 must be a factor of the denominator. If that's true, then

x ² - c = (x - 2) (x - r )

for some other root r of x ² - c. Expanding the right side gives

x ² - c = x ² - (2 + r )x + 2r

so that

-(2 + r ) = 0   ===>   r = -2

2r = -c   ===>   -c = -4   ===>   c = 4

and so

[tex]f(x) = \dfrac{b}{x^2-4}[/tex]

(iii) Finally, we're given that f ' (1) = -2. Differentiating f gives

[tex]f'(x) = -\dfrac{2bx}{(x^2-4)^2}[/tex]

so that

[tex]f'(1) = -\dfrac{2b}{(1^2-4)^2} = -\dfrac{2b}{9}[/tex]

Then

-2b/9 = -2   ===>   b = 9

and we find that

[tex]f(x) = \dfrac{9}{x^2-4}[/tex]

Find the slope of the line represented by each table of values

Answers

Answer:

slope is zero

Step-by-step explanation:

every y=9 then the line is parallel to x axiom

what is 5 * 4 + 6 - 5 * 5 * 7 / 8 * 6 - 8 + 2

Answers

The answer is -445/4 in improper fraction form, -111 1/4 as a mixed fraction, and -111.25 in decimal form.

Answer:

-111.25

Step-by-step explanation:

REPOST*
I NEED HELP ON THESE THREE QUESTIONS*
The number line compares the numbers –6, 3, and 5.

1. Write an inequality that compares –6 and 3. Justify your inequality using the number line.

2. Write an inequality that compares 3 and 5.

3. Write an inequality that compares –6, 3, and 5.

Answers

#1

-6-3-5

Hence inequality will be

[tex]\\ \sf\longmapsto -6\leqslant 5[/tex]

#2.

3<5

But we need inequality

[tex]\\ \sf\longmapsto 3\leqslant 5[/tex]

#3

The inequality given by

[tex]\\ \sf\longmapsto -6\leqslant 3\leqslant 5[/tex]

Answer:

See below

Step-by-step explanation:

Given numbers:

-6, 3 and 5

If we add these onto number line, we'll see them in same order from left to right.

We know the numbers increase from left to right on the number line, so the numbers to the left are smaller than the numbers to the right.

1.

-6 < 3, as -6 is to left from 3

2.

3 < 5, as 3 is to left from 5

3.

-6 < 3 < 5, as per above explanation
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