What are the zeros of the polynomial function: f(x) = x3 + x2 – 6x ? ...?

Answers

Answer 1
The solution to the problem is as follows:

  
x³ + x² − 6x = 0 
x (x² + x − 6) = 0 
x (x − 2) (x + 3) = 0 
x = 0, 2, −3 


f(x) = 2x³ + 5x² + 6x − 4 
f(−x) = −2x³ + 5x² − 6x − 4 

Let's look at signs only and how many sign changes there are: 
f(x) = + + + − 
1 sign change ----> 1 positive root 
f(−x) = − + − − 
2 sign changes ----> 2 or 0 negative roots 

Min. number of real roots = 1 ----> max. number of complex roots = 2 
Max. number of real roots = 3 ----> min. number of complex roots = 0

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Related Questions

If M(-8, 12) is the midpoint of segment PQ, and P(8, 0), find the coordinates of Q.

Answers

P(x1,y1)= (8,0)
Q(x2,y2)=(a,b)
M(x,y)=(-8,12)
x1+x2/2=-8;y1+y2/2=12
8+x2=-16;0+y2=24
x2=-24;y2=24
Q(x2,y2)=(-24,24)

If you subtract the death rate from the birth rate of a population, you will calculate what?

A. the arithmetic growth rate.
B. the expansion rate.
C. the carrying capacity.
D. the intrinsic growth rate.


Answers

The best and most correct answer among the choices provided by your question is the third choice or letter C.

If you subtract the death rate from the birth rate of a population, you will calculate the carrying capacity.


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Subtracting the death rate from the birth rate of a population calculates its intrinsic growth rate, expressed as dN = (b - d)N, where 'r' is the intrinsic rate of increase.

When you subtract the death rate (D) from the birth rate (B) of a population, you calculate the intrinsic growth rate of the population. The birth rate is typically expressed on a per capita basis, shown as B = bN, where 'b' represents the per capita birth rate and 'N' is the number of individuals in the population. Similarly, the death rate is expressed as D = dN, where 'd' is the per capita death rate. To find the population growth rate at a specific point in time, differential calculus is used to obtain an instant-specific measurement:

dN = (b - d)N

This formula simplifies the relationship between the birth and death rates, where 'b - d' is substituted with 'r', representing the intrinsic rate of increase. Therefore, the correct answer to the student's question is D. the intrinsic growth rate.

Find the area of the regular polygon. Give the answer to the nearest tenth.

dodecagon with a perimeter of 108 cm ...?

Answers

A regular dodecagon is a polygon with 12 equal sides.
Length of each side = 108/12 = 9 cm.

Length of the apothem = (9/2)/tan 15 = 9/2tan 15 = 16.79 cm

Area of each triangle = 9/2(16.79) = 75.57 cm^2

Therefore, area of the dodecagon = 12(75.57) = 906.9 cm^2
Each side is 9 cm long 


a 12 sided regular polygon is composed of 24 right triangles with one side

half the length of a side = 4.5 cm 

the other side is 4.5 / tan (360/24) = 4.5 / tan(15) 


A = 24 (1/2) 4.5^2 / tan(15) = 906.9 cm^2 


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A jug of juice holds 8 cups. convert 8 cups to pints

Answers

8 cups convert to pints = 4 pints

Further explanation

7 main quantities have been determined based on international standards, namely:

1. Length, meters (m)2. Time, second (s)3. Mass, kilograms (kg)4. Temperature, kelvin (K)5. Light intensity, candela (cd)6. Electric current, ampere (A)7. Amount of substance, mol (m)

Volume is a derivative quantity derived from the length

The unit of volume can be expressed in liters or milliliters or cubic meters

The conversion is

1 cc = 1 cm³

1 dm = 1 Liter

1 mL = 1 cm³

1 L = 1 dm³

The other common units for US standart volume are :

Fluid OuncesCupsPintsQuartsGallons

The conversion for all those units :

1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces

The conversion for pints and cups :

[tex]\large{\boxed{1\:pints=2\:cups}}}[/tex]

A jug of juice holds 8 cups

so 8 cups = 8 : 2 pints

8 cups = 4 pints

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A city that uses ten billion BTUs of energy

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what is the total mass in micrograms of cofactor

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A vineyard has 145 acres of Chardonnay grapes.

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Keywords: volume,pints, cups, a jug, juice

daniel team scored 40 points at the game danielscored 50% of the teams points how many poits did daniel scored

Answers

he scored 20 of the points

What is the greatest common factor of 20, 45x?

Answers

The greatest common factor of 20 and 45x is 5

How to know if true or false?? HELP ASAP thank you!

picture added.

Answers

True
Because a negative square root is an i

Compare 0.409 and 0.490 with >,<,=

Answers

0.409 < 0.490

hope this helps you

If arc AXC = 235°, what is m∠ABC?

117.5°
60°
55°
125°

Answers

The answer is 55°. Hope this helps.

The measure of the exterior angle of the circle ∠ABC = 55°

What is the Area of the Sector?

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

A = θ/360 x πr²

where;

θ is the central angle of the sector

r is radius

Given data ,

Let the measure of the arc be represented as A = 235°

So , the difference of the measures of arc = 235 - 125°

Now , the measure of the external angle ∠ABC = ( 235 - 125 ) / 2

So , the external angle ∠ABC = 55°

Hence , the measure of angle ∠ABC = 55°

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What are the 2 types of unbiased samples?

Answers

Systematic Random Sample, Stratified Random Sample, and Simple Random Sample.

solve for x. round to nearest tenth if needed.


1. 7r-7=2r+18

a.r=-5
b.r=5
c.r=2.2
d.r=1.2


2. 2x+12=18-x

a.x=3
b.x=10
c.x=6
d.x=2



3. 8x-3=15x+18

a.x=-3
b.x=3
c.x=2.1
d.x=0.9



4. 6y-6=4y+16

a.y=2.2
b.y=-2.2
c.y=11
d.y=5


5. 3(x-4)=5(x+2)

a.x=11
b.x=-11
c.x=1
d.x=-1

Answers

7r-2r=18+7→5r=25→r=5
-----------------
2x+x=18-12→3x=6→x=2
---------------
8x-15x=18+3→-7x=21→x=-3
----------------
6y-4y=16+6→2y=22→y=11
--------------
3x-12=5x+10→3x-5x=10+12→-2x=22→x=-11

On solving the linear equations given, we get the values as 5, 2, -3, 11 and -11 for the equations  7r - 7 = 2r + 18, 2x + 12 = 18 - x, 8x - 3 = 15x + 18, 6y - 6 = 4y + 16 and 3(x - 4) = 5(x + 2) respectively.

What is Linear Equation?

Linear equations are equations which includes one or more variables and constants with the highest degree of the variable being 1.

1. 7r - 7 = 2r + 18

  Taking the variables on one side and constants on the other side,

  7r - 2r = 18 + 7

  5r = 25

  r = 5

2. 2x + 12 = 18 - x

   2x + x = 18 - 12

   3x = 6

   x = 2

3. 8x - 3 = 15x + 18

   8x - 15x = 18 + 3

   -7x = 21

   x = -3

4. 6y - 6 = 4y + 16

   6y - 4y = 16 + 6

   2y = 22

   y = 11

5. 3(x - 4) = 5(x + 2)

   Multiplying each term inside the bracket by the term outside,

   3x - 12 = 5x + 10

   3x - 5x = 10 + 12

   -2x = 22

   x = -11

Hence we got the values of the unknowns as 5, 2, -3, 11 and -11 for the equations  7r - 7 = 2r + 18, 2x + 12 = 18 - x, 8x - 3 = 15x + 18, 6y - 6 = 4y + 16 and 3(x - 4) = 5(x + 2) respectively.

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The distance a spring will stretch varies directly with how much weight is attached to the spring. if a spring stretches 9 inches with 100 pounds attached, how far will it stretch with 90 pounds attached? round to the nearest tenth of an inch.

Answers

9/100 = x/90
Cross multiply to get 810 = 100x
Divide both sides by 100 to get x = 81 inches

Let f(x) = 7x − 13. find f−1(x). (1 point)13x − 77 over quantity of x plus 13quantity of x plus 13 over 71 over quantity 7 x minus 13

Answers

I hope this helps you




f (x)+13=7x



x=f (x)+13/7



f^-1 (x)=x+13/7

Use the formula P = 2l + 2w to find the length of a rectangle whose perimeter is 57 inches and whose width is 13 inches.


Answers

P = 2L + 2w
57 = 2L + 2(13)
57 = 2L + 26
-26       -26
31 = 2L
2      2
15.5 = L

Temperature rose 9°f in 3 hours if the starting wad -5°f what was the final temperature

Answers

4F is the final temp.

is it possible for a line to pass through only one quadrant?
How about four quadrants? explain

Answers

Yes it is possible for a line to only start in one quadrant and never leave that quadrant and vice versa a line can start in one quadrant and pass into another quadrant but how will you know if you line will be in certain or multiple quadrants simple just look at your points given if you have the points (3,4) (4,5) you notice that your X's are positive and your Y's are positive there is only one quadrant were your X and Y are positive and that is quadrant 1 but lets say you have points (-4,5),(3,4) you see how one of the points have a negative X and a positive Y there is only one quadrant that has a negative X and a positive Y that is quadrant 2 and and for point (3,4) that is in quadrant 1 so your line will run through quadrant 2 and 1 

yes it is possible for a line to only be in one quadrant and it is also possible for a line to be in multiple quadrants basically it can be any place on a plane  

It is not possible for a line to pass through one quadrant. A line is a 2 dimensional shape and crosses through 2 quadrants, even if passing through the origin. If a line passes through the origin, it still only enters and exits 2 quadrants. there must be a curvature in order to cross 4 quadrants.

For a $1,000 loan at a rate of 16 3/4 % for 5 years, the simple interest is a. $83.75
b. $167.50
c. $500.00
d. $837.50

Answers

d 837.5 is the right answer

An electrician charges a $50 house call fee and $65 per hour for the work. Which algebraic expression represents this situation to represent the total cost for h hours of work?

Answers

$50 house call fee is a FIXED constant. There is no variable it multiplies to. $65 is attached to h because it represents how much you earn PER hour.

Thus:
$50+$65h
Final answer:

The algebraic expression is Total Cost = 65h + 50.

Explanation:

To represent the total cost for h hours of work, we need to consider the house call fee of $50 and the hourly rate of $65. The total cost will depend on the number of hours worked.

We can calculate the total cost using the expression: Total Cost = (Hourly Rate * Number of Hours) + House Call Fee.

Therefore, the algebraic expression that represents this situation is: Total Cost = 65h + 50.

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Use the stem and leaf plot shown to answer the following question.

What is the upper quartile median value?

37
40
41

Answers

(16,18,(23),25,26),34,(37,37,(40),41,46)
Q1 = 23
Q2 = 34
Q3 = 40 <== ur upper quartile median value

Answer:

The upper quartile median value is 40. Therefore second option is correct.

Step-by-step explanation:

Stem is first digit of a number and leaf is last digit of a number.

Stem 1 leaf 4 can be written as 14.

From the given table, the observations can be written as

[tex]16,18,23,25,26,34,37,37,40,41,46[/tex]

Total number of observations is 11, which is an odd number.

[tex]median=\frac{n+1}{2}\text{th term}[/tex]

[tex]median=\frac{11+1}{2}\text{th term}=6\text{th term}[/tex]

Therefore median is 34.

We have 5 terms before 34 and 5 terms after 34.

[tex]Q_1=\frac{n+1}{4}\text{th term}=3\text{th term}[/tex]

[tex]Q_1=23[/tex]

[tex]Q_3=\frac{3(n+1)}{4}\text{th term}=9\text{th term}[/tex]

[tex]Q_3=40[/tex]

Q₃ is also known as upper quartile median value. Therefore second option is correct.

Which ordered pair is a solution to this equation?

(x+3)y = 14

A. (3, 2)

B. (5, 2)

C. (11, 1)

D.(7, 2)

Answers

The answer to your question is C. (11,1)
Hope this helps and if you need any more help just ask!! :)

find the missing angle of the triangle.

Answers

Is there a picture of the triangle?

Maggie was thinking of a number. If she multiply the number by 3 ,subtracted by 8 ,added by 2 times the 5 original number . the result was 48. write an equation that the number satisfies. Then answer it.

Answers

i hope this helps you



number is ?


3.?-8+2.5.?=48



13.?=56


?=56/13

To solve the word problem, we set up and solved an algebraic equation. Maggie's original number is approximately 4.31 after converting the written problem into the equation 3x - 8 + 10x = 48 and solving for 'x'.

The goal is to translate the word problem into an algebraic equation and solve for the unknown number. If Maggie is thinking of a number, let's use 'x' to represent this unknown number. According to the problem, she multiplies the number by 3, subtracts 8, and then adds 2 times the original number 5 times. The result of these operations is 48. Here's how you set up the equation:

3x - 8 + 10x = 48

The next step is to combine like terms:

13x - 8 = 48

Now we add 8 to both sides of the equation:

13x = 56

The last step is to divide both sides by 13 to solve for x:

x = 56 / 13

x = 4.3077 or approximately 4.31 if rounded to two decimal places.

Therefore, Maggie's number is approximately 4.31.

Which of the following is not an example of using the distributive property to multiply 12 times 22?
a. 12(20 + 2)
b. 22(10 + 2)
c. 10(2 · 22)

Answers

C does not mean 12 x 22 as you do what is inside the brackets first and this would mean it is 2.22 x 10
c 10 (2.22)

It doesn't have the correct format and is mixed up.

You are making a scale drawing out of your classroom using the scale 1 inch: 3 feet. The floor of your classroom is a rectangle with a length of 21 feet and a width of 18 feet. What should the length and width of the floor in your drawing be?

Answers

1 inch represents 3 feet

21 feet : 3 feet = 7 inches
18 feet : 3 feet = 6 inches

The dimensions of the floor in drawing are 7 inches × 6 inches

Use the graph below for this question:


graph of parabola going through 0, 3 and 2, negative 5.


What is the average rate of change from x = 0 to x = 2?

− 4
− 8
1
5
Can you please help me?

Answers

The average rate of change from x = 0 to x = 2 for the parabola described in the question is -4. Hence the correct option is 1.

The average rate of change of a function between two points is calculated by subtracting the y-values (function outputs) and dividing by the difference in x-values (inputs). In this case, to find the average rate of change of the parabola from x = 0 to x = 2, we use the points (0, 3) and (2, -5).

The average rate of change = (y2 - y1) / (x2 - x1)

Substitute in the given points: ( -5 - 3 ) / ( 2 - 0 )

Simplify the expression: -8 / 2 = -4

name all opisties of -12

Answers

One opposite of -12 I know is 12 because you just take away the -
The opposite of -12 is 12 

Clark Kent walks 3 miles west and then 4 miles north. How far is it for Superman to fly in a straight line back to his starting point? (It makes a right triangle.)

Answers

You can use the Pythagorean theorem to solve this problem. 3 miles west would be 3 units to the left on a graph, and 4 miles north would be four units up on a graph. The last line would be the hypotenuse. Now, if you know about special right triangles, then it can be recognized that the triangle is a 3-4-5 triangle, and the hypotenuse is 5 units. Otherwise, the Pythagorean theorem can be used.

a^2+b^2=c^2
3^2+4^2=c^2
9+16=c^2
25=c^2
sqr 25=sqr c^2
5=c 

You invest an initial $4,500 in an account that has an annual interest rate of 4.5%, compounded daily. How much money will you have in the account after 10 years? Round to the nearest whole number

Answers

4500(1+0.045/360)^360*10=??

in a parallelogram consecutive angles are _

Answers

In a parallelogram consecutive angles are supplementary.

the midpoint of a segment is (2,-5), and one of the endpoints is (3,6). where is the other endpoint?

Answers

(2, -5) is the mid point

(3, 6) is (2+1, -5+11) is an end point

therefor the other end point should be (2-1, -5-11) = (1, -16)

You could visualise this better if you draw it

Hope this helps, I don't really know a better way to explain it, sorry =P

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