Stanley analyzes the table of values for a polynomial function. He has determined through applying Descartes’ rule of sign that there is 1 negative real zero, and either 1 or 3 positive real zeros. He has also determined that the upper bound of the function is 3.
X , f(x)
-2, -105
-1, 0
0, 5
1, -2
2, 3
3, -20
4, -175

a. What is the degree of the polynomial function? How can you tell?

b. How many positive real zeros does the function have? How can you tell?



Stanley Analyzes The Table Of Values For A Polynomial Function. He Has Determined Through Applying Descartes

Answers

Answer 1

9514 1404 393

Answer:

  a) 4

  b) 3

Step-by-step explanation:

a. The total number of real and complex zeros is equal to the degree of the polynomial. That total is (1 negative real) + (3 positive real/complex) = 4 total zeros. The degree of the polynomial is 4.

The even degree is confirmed by the answer to part b, and by the end-behavior shown in the table, which has a tendency to -∞ for |x|→∞.

__

b. The intermediate value theorem tells you there will be zeros in the intervals (0, 1), (1, 2), and (2, 3) according to the values in the table. (The function changes sign in those intervals.) Thus there are 3 positive real zeros.

_____

Additional comment

Stanley cannot tell anything about Descartes' rule of signs by analyzing the table of function values. To use that rule, he must have terms of the polynomial. If he has those terms, he already knows the degree of the polynomial.


Related Questions

The elevation of Lake Baikal is about 1,494 feet below sea level. Which integer represents this elevation?

Answers

Answer:

-1,494

Step-by-step explanation:

If sea level is 0, the on a scale below sea level would be a negative integer.

HELP ME!!!

Steve goes on a road trip. He travels a total of 835 miles, and the trip takes 10 hours from start to finish.

What is his average rate of change of distance? Please include units in your answer.

Answers

835/ 10 is 83.5
So his average rate of change is 83.5 miles per hour

Can someone help me?? 3+3

Answers

Answer:

6

Step-by-step explanation:

count your fingers

The answer is 6 . I hope this helped you

This is a 100 point question. Please get it right. The image below is the question. Please completely show your work and get it correct.

Answers

hi <3

multiply the coefficient of x^2 with the last value:

2 x 3 = 6

you need to find a value that multiplies to give 6 and adds to give 5

this would be 3 and 2

now you have:

(x + 3)(x + 2)

we need to incorporate the 2 into it

you can divide the 2 by 2 so that part is fine. however, as 3 cant be divided by 2, you have to carry the 2 up as a coefficient for x

your final answer works out to be:

(2x + 3)(x + 1)

hope this helps :)

Need this worked out please so I can understand it
a) Find the slope of the curve y= x^3 + 3 at the point P(-2, -5)

b) Find an equation of the tangent line to the curve at P(-2, -5)

Answers

9514 1404 393

Answer:

  a)  12

  b)  y +5 = 12(x +2)

Step-by-step explanation:

The slope of a function is its derivative.

a) The slope of y = x^3 +3 at any point is y' = 3x^2. So, at the point where x=-2, the slope of the curve is ...

  m = 3(-2)^2 = 12 . . . . slope at (-2, -5)

__

b) The equation of the tangent line is most easily written using the point-slope form of the equation of a line.

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y +5 = 12(x +2) . . . . line with slope 12 through point (-2, -5)

Sorry for asking more questions

Answers

[tex]\text{CJ}=3\text{x}+6\\\\\text{CT}=37\\\\\text{JT}=3\text{x}+7\\\\\text{CJ}+\text{JT}=\text{CT}\\\\3\text{x}+6+3\text{x}+7=37\\\\6\text{x}+13=37 \ \ /-13\\\\6\text{x}=24 \ \ /:6\\\\\text{x}=4\\\\\text{JT}=3\cdot4+7=12+7=\boxed{19}[/tex]

Find the slope and y-intercept of the following line.
- 10x - 8y = 8
Find the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The slope of the line is (Simplify your answer. Type an integer or a fraction)
O B. The slope of the line is undefined
(Answer quickly)

Answers

Answer:

Slope: - 5/4

y-intercept: - 1

Step-by-step explanation:

- 10x - 8y = 8

- 8y = 10x + 8

y = - 10x/8 -8/8

y = - 5/4x - 1

Which is the best estimate of 90 square root

Answers

Answer:

9.486

Step-by-step explanation:

the best estimate of 90 square root is 9.486

HELPPP PLSSSSS!!!!!!!!!

Answers

Answer:

3x³+10x²-8x-2

Step-by-step explanation:

(-3x³+7x²-8x+11)-(-3x²+13)

remove unnecessary parentheses

-3x³+7x²-8x+11-(-3x²+13)

collect like terms

-3x³+10x²-8x+11-13

ans=

-3x³+10x²-8x-2

Choose all expressions that are equal to 5.
31÷6.2
27.6÷5.2
18.6÷4
6÷2.1
20.1÷4.1

Answers

Answer:

without rounding, only the 1st one would be equal to 5

Step-by-step explanation:

31÷6.2=5

27.6÷5.2=5.307...

18.6÷4=4.65

6÷2.1=2.8

20.1÷4.1=4.9

BUT HEY, I HAVE PARANOIA AND THIS TIME I DIDNT CHECK LIKE A DOZEN TIMES SO MAYBE IM WRONG

oh and i forgot to say have a nice day or night or etc and good luck!

Answer:

31 / 6.2 = 5

Step-by-step explanation:

31/6.2 = 5

27.6/5.2 = 5.3

18.6/4 = 4.65

6/2.1 = 2.86

20.1/4.1 = 4.90

Can someone please help and explain

Answers

Answer:

[tex]c = 300000 {(1.05)}^{50} [/tex]

Step-by-step explanation:

The future value formula is FV=PV(1+i)^n, where the present value PV increases for each period into the future by a factor of 1 + i.  value PV increases for each period into the future by a factor of 1 + i. 

[tex]fv = pv {(1 + r)}^{n} [/tex]

fv = future value

pv = present value

r = annual interest rate ( decimal number)

n= period

Error Analysis jeremy incorrectly says that 2 1/8 is the same as 2.18 Convert 2 1/8 to a decimal correctly. Then explain ​'s likely error.

Answers

Answer:

1 divided by 8 = 0.125 let's replace the 0 with a 2 since 2 is the whole number = 2.125 is correct

Step-by-step explanation:

Jeremy has mistaken 2 1/8 as 2.18 probably because he thought 1/8 was 0.18

The correct decimal value is 2.13.

We have Jeremy who incorrectly said that [tex]2\frac{1}{8}[/tex] is the same as 2.18.

We have Convert [tex]2\frac{1}{8}[/tex] to a decimal correctly.

How will you convert the mixed fraction -  [tex]5\frac{2}{3}[/tex] to normal fraction?

The method to convert the mixed fraction to normal fraction is -

[tex]5\frac{2}{3}\\[/tex] = [tex]\frac{3\times 5 +2}{3} = \frac{17}{3}[/tex]

According to question, we have -

Mixed fraction = [tex]2\frac{1}{8}=\frac{17}{8}[/tex] = 2.125 = 2.13

Hence, the correct decimal value is 2.13.

To solve more questions on Error analysis, visit the link below -

https://brainly.com/question/11152559

#SPJ2

Evaluate the function at each specified value of the independent variable and simplify. (If an answer is undefined, enter UNDEFINED.) g(y) = 3 − 2y

(a) g(0) =

(b) g(3over2)=

(c) g(s + 1) =

Answers

Answer:

UNDEFINED

Step-by-step explanation:

Can't further simplify the function

The table below shows a linear relationship between x and y.
х
-4-2
0
6
у
8
5
2
-7
Which graph below represents the relationship in the table?

Answers

The only graph with the point (6,-7) on it is Graph D.

What is mean median mode range?

Answers

Answer:

Mean- the average of data, meaning you add up all the numbers, and then divide the sum of the numbers by how many numbers there are. For example:

2, 2, 3, 4, 6, 6, 9.

7 numbers total.

2 + 2 + 3 + 4 + 6 + 6 + 9 = 32

32 ÷ 7 = 4.57

The mean would be 4.57.

Median- the middle point of the numbers. You cross off each of the numbers until you have one last number standing. If you have an even number of numbers, you find the middle of the last two numbers you crossed off. For example:

2, 2, 3, 4, 6, 6, 9

2, 3, 4, 6, 6

3, 4, 6

4

4 would be the median.

Mode- the largest number on the data.

Range- subtract the mode (largest number) from the smallest number to get range. For example:

2, 2, 3, 4, 6, 6, 9

9 - 2 = 7

7 would be the range.

Step-by-step explanation:

Question question question question helppppppppp
Thanks!

Answers

Answer:

5/6 5/7 5/8 5/12? im bad at fractions sorry hope it helped tho

Step-by-step explanation:

Answer:

5/12 5/8 5/7 5/6

Step-by-step explanation:

If we divide 5 by 12 we get 0,42

If we divide 5 by 6 we get 0.83

So we know 5/12 is less than 5/6, so we just need to order the numbers in between, and as result we get:

5/12 < 5/8 < 5/7 < 5/6

Does anyone know how to solve it?

Answers

Answer:

The right answer is the fourth ( 4/5)

lim ((x+3)(x-1) / (x+3)(x-2)) =lim( (x-1) / (x-2))=

(-3-1)/(-3-2)=4/5

PLS HELP i will mark brainliest

Give an example of the product of a rational number and an irrational number and explain whether the answer would result in a rational or irrational number. MATH

Answers

Answer:

Step-by-step explanation:

there doesn't exist an example of Rational and Irrational Numbers whose product is Rational, except when an Irrational Number is multiplied by 0, which results in 0, a Rational Number.

can someone tell me what the lcd is??​

Answers

I think it’s International Classification of Diseases but I’m not sure cause it doesn’t match anything with math good luck though.


Select two ratios that are equivalent to 27 : 9.

Answers

Answer:

the ratio are missing

Step-by-step explanation:

27 : 9 can be written as

3:1

54 :18

Answers:

3 : 1

54 : 16

How do I write five times the quantity of a number and 3 is 50

Answers

Answer:

[tex]{ \boxed{5(x+3) = 50}}[/tex]

Step-by-step explanation:

let the number be x :

[tex]5 \times (x+4) = 50 \\ 5(x+4) = 50[/tex]

further more :

[tex]x+4= 10 \\ x = 6[/tex]

Answer:

5x4x3=50

Step-by-step explanation:

simplify -5^2-2^4
and it just says to make it 20 words long

Answers

Answer:

9 because all you have to do is put number by number in the calculator

A circular blade turns through 589 revolutions. What is it angular displacement?

Answers

Step-by-step explanation:

One revolution is equivalent to an anuglar displacement of

[tex]2\pi\text{ rad}[/tex]

Therefore the total angular displacement is

[tex]589(2\pi)=1178\pi\text{ rad}[/tex]

If you spend ​$99.79​, in how many ways can you receive change from a one hundred​-dollar ​bill?

Answers

Answer:

3 different ways

Step-by-step explanation:

100 - 99.79 = 0.21

.21 = 2 dimes and 1 penny

.21 = 4 nickels and 1 penny

.21 = 1 dimes, 2 nickels and 1 penny

harold licorice company made 6,429.4 feet of licorice in 9 days. to the nearest hundredth of a foot how many feet of licorice on average did the company make per day​

Answers

Answer: 714.4

Step-by-step explanation: It says the company had made 6,429.4 feet of licorice in 9 days and you want to find the average amount made in 1 day. So what you would do is divide 6,429.4 by 9 and get 714.3777777 so on. Next its says by the nearest hundredths place meaning the 2nd placement after the dot, so what you would do is round it and you get 714.4.

Let A = {a, b, c, d}, B = {a, c, d, e}. Let f : A → R and g : B → R such that f = {(a, 1),(b, 2),(c, 2),(d, 4)} and g = {(a, 0),(c, 4),(d, 8),(e, 0)}. State the domain and find: f − g​

Answers

Answer:

b, but don't have translate into a great day. I name and phrase, angle of measurementhhvgz just don't have money in a sentence, and the king not sure how it was a great app that is

A garage sale has a total of 48 shirts
and 6 jackets for sale. Select the
answer that shows the ratio of shirts
compared to jackets in simplest form.

Answers

Answer:

d

Step-by-step explanation:

48/6=8

8/1

Which of the following is equal to the rational expression when x≠5

Answers

Answer:

the following is equal to the rational expressions when x5

Find the slope and y-intercept of the line.
- 6x + y = 8
-...
Find the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The slope of the line is (Simplify your answer. Type an integer or a fraction.)
OB. The slope of the line is undefined.
(Answer quickly)

Answers

[tex]\large \mathfrak{Solution : }[/tex]

let's write the given equation in its slope intercept form :

i.e y = 6x + 8

by comparing to the general equation : y = mx + c

we get, slope (m) = 6

Solve the exponential equation: 4 1/2x=256
A) x = 4
B) x = 2
C) x= 8
OD) x= 1/2

Answers

Hi there!

We are given:

[tex]4^{\frac{1}{2}x} = 256[/tex]

We can rearrange this into a logarithm:

[tex]log_4256 = \frac{1}{2}x[/tex]

Evaluate the left side:

4 = 1/2x

Multiply both sides by 2:

x = 8

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