2x3 + 8x2 + 10x + 4 all potential roots and actual roots

Answers

Answer 1

Answer:

potential: {±1/2, ±1, ±2, ±4}actual: [-2, -1, -1}

Step-by-step explanation:

The Rational Root Theorem tells you that potential rational roots are ...

  ±(divisor of constant term)/(divisor of leading coefficient)

Ignoring the fact that all of the coefficients can be reduced by a factor of 2, straightforward application of this theorem suggests possible rational roots might be ...

  ±{1, 2, 4}/{1, 2} = {±1/2, ±1, ±2, ±4} . . . potential roots

Examination of the graph of the function shows the actual roots are ...

  x = -2, -1 (multiplicity 2)

_____

Additional comment

Descartes' rule of signs eliminates positive real roots from the list. (There are no coefficient sign changes, hence no positive real roots.)

Division of the polynomial by 2 gives x³ +4x² +5x +2 = 0, which only suggests rational roots of -2 or -1. The answer to the question of potential roots depends on the extent to which you refine the list above.

2x3 + 8x2 + 10x + 4 All Potential Roots And Actual Roots

Related Questions

Pablo has $5,483 in a savings account. The interest rate is 5%, compounded annually.

To the nearest cent, how much will he have in 3 years?

(compound interest formu)

Answers

Answer:

$6347.26

Step-by-step explanation:

Given:

Initial amount P = 5483Interest rate r = 5% or 0.05Compound number n = 1Time t = 3 years

Find the total amount in 3 years:

[tex]A = P(1+r/n)^{nt}[/tex][tex]A = 5483*(1+0.05/1)^{1*3}=5483*(1.05)^3 = 6347.26[/tex]

[tex]\tt\red{\overbrace{\underbrace{\tt\color{orange}{ANSWER}}}}[/tex]

Here we've been given,

Principal amount (p) = $5843

Compound number (n) = 1

Rate of Interest (r) = 5% = 5 × 1/100 = 0.05

Time (t) = 3 years

A = ?

The standard formula for Compound interest (C.P) is given by,

[tex]:\implies\tt{A = p( { \frac{1 + r}{n} )}^{n \times t} } \\ \\ \\ :\implies\tt{A = 5483( { \frac{1 + 0.05}{1}) }^{1 \times 3} } \\ \\ \\ :\implies\tt{A = 5483 \times {1.05}^{3} } \\ \\ \\ :\implies\tt{A = 6347.26}[/tex]

You are selling candy for $2 each and burgers for $5 each. You have a budget for $150. The equation for this situation can be written as 2x+5y=150

Find the x intercept and y intercept. Show all work.

If you are selling 0 burgers, how many candies did you sell? Show your work.







If you are selling 0 burgers, how many candies did you sell? Show your work.



Answers

30 burgers because 5 x 30=$150

I need some help :(
A)4
B)2.9
C)3.8

Answers

Answer: C

Step-by-step explanation:

Four times a number decreased by 5 is 67. Find
the number…

Answers

Answer:

288

Step-by-step explanation:

Do the reverse.

67+5= 72

72*4= 288.

hope this helped :)

PLEASE ANSWER ASAP
Please give an answer i can copy paste into the answer box, please nothing extra


Using the following 3 equations, answer the questions:

11x + y = 4x + y = -2x - 2y = 18


How can you determine which equations can be graphed more easily using x- and y-intercepts, rewriting in slope-intercept form, or using a table of values?

Which method works best for you personally? When does it not work as well?

Answers

Answer:

Step-by-step explanation:

I'll assume these are the equations:

11x + y =  18

4x + y  = 18

-2x - 2y = 18

=======

The easiest approach to graphing, for me, is to rearrange each to y=mx+b (slope-intercept) format:

y = -11x+18      y-intercept of 18      (0,18)y = -4x + 18     y-intercept of 18      (0,18)y =   - x -9       y-intercept of -9      (0,-9)

It seems to me that all three can be graphed easily from simply reading the slope and y-intercept values.  Since these are straight lines, all we need is two points for each line, and one is standing out in plain view, the y-intercept:  (0,y-intercept).  The second point can be determined by using whatever value of x makes the calculation easy

An example:  y =  - x -9.  Plot (0,-9) for the y intercept, and then calculate one additional point (e.g., for x = - 9).  (-9,0)  Then connect a straight line between these two points and presto (metric term for magic), a graph. For the first equation, I picked 20 for x.  For x = 20, y = -29.  That was easy, and we have the second point:  (1,-10)

See the attachment for how this was done.  The first points are all for the y-intercept (0,[18 or 9]).  All of the second points were calculated in my head by using a convenient value for x.

This approach doesn't work well for non-linear equations.  There, I find it easier to set up a table of values - a spreadsheet such as Excel is my tool for the calculations.

The attachment also demonstrates the Really Easy Way to graph functions.  DESMOS, a free, and excellent, online calculator.

find 3 solutions that satisfy the equation -5x=10+2y

Answers

Answer:

(2, -10)

(4, -15)

(6, -20)

Step-by-step explanation:

First you should simplify the equation.

-5x=10+2y

-5x-10=2y

-2.5x-5=y

Then put in any number in for x. since we have a decimal I'll make the numbers I put in even the keep the solution whole numbers.

Putting in 2 gives you -10 so (2, -10) is a solution.

Putting in 4 gives you -15 so (4, -15) is a solution.

Putting in 6 gives you -20 so (6, -20) is a solution.

Yaniq has these two spinners
Answer it all right NO wrong​

Answers

Answer:

b should be 2/11

c should be 2/11 as well

Step-by-step explanation:

Used The Graph info

total spins 11

both are 2over9

Step-by-step explanation:

9 results 2 only

A farmer has 419 rows of corn. If he can get 573 ears of corn from each row, how many ears of corn would he have in total

Answers

Answer:

419x573=240,087 ears of corn

Step-by-step explanation:

HELP ASAP PLEASEEEEEEEEEEE HELP MEEE​

Answers

Answer:

5x 24 = 120 pulus degreece so that = a 120 digree angle

Step-by-step explanation:

Need help Please due soon help I beg

Answers

Answer:

the variables mean (1)

Step-by-step explanation:

you need to divide

Answer:

equals y<5?

Step-by-step explanation:

i dont think this will help but i hope it does help

Find an equivalent ratio in simplest terms:
64 : 24
Submit Answer

Answers

Answer:

64/24

32/12

16/6

8/3

8:3

Hope This Helps!!!

Which number is greater than 555,621,000? A. 5.0 x 10 B. 6.2 x 10 C. 5.55621 x 10 D. 9.99 x 10

Answers

Answer:

None of these

Step-by-step explanation:

None of these are correct because you would need to multiply 5 x 10 to a certain power. 5.55621 x 10 to the 8th power would do it.

Answer: I believe D is correct

Step-by-step explanation:

The map shows two biking trails that meet at a park, located at the coordinate (1, 9). Each unit on the map represents 0.5 mile.How many miles longer is Trail A than Trail B?

Answers

The length of the trails can be determined be using a formula related to

Pythagorean theorem, which makes use of the rise and run of a trail.

The number of miles longer Trail A is than Trail B is 4 miles

Reasons:

The location of the park = (1, 9)

The stating point of Trail A = (-7, -6)

Starting point of Trail B = (6, -3)

The length of a trail is adapted from the formula for the distance between points which is a form of Pythagorean theorem as follows;

[tex]Length \ of \ a \ trail, \ L = \mathbf{\sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}}[/tex]

Therefore;

[tex]Length \ of \ trail, \ A = \sqrt{\left (1-(-7) \right )^{2}+\left (9-(-6) \right )^{2}} = \mathbf{17}[/tex]

[tex]Length \ of \ trail, \ B = \sqrt{\left (1-6 \right )^{2}+\left (9-(-3) \right )^{2}} = \mathbf{13}[/tex]

The difference between the lengths of the trails = 17 mi - 13 mi = 4 miles

Therefore;

Trail A is 4 miles longer than Trail B

Learn more about finding the distance between two points on a graph here:

https://brainly.com/question/9917504

Two​ trains, Train A and Train​ B, weigh a total of 378 tons. Train A is heavier than Train B. The difference of their weights is 210 tons. What is the weight of each​ train?

Answers

Answer:

Train A is 294 tons and Train B is 84 tons

Step-by-step explanation:

You can create a system of equations

A+B=378

A-B=210

Adding both would get

2A=588

2A/2=588/2

A=294

Now plug that in to the second equation (either is fine)

294-B=210

B=84

Check

294+84=378

Step-by-step explanation:

Let,

Weight of train A = x

Weight of train B = y

x + y = 378 (1)

x - y = 210 (2)

Now,

On adding 1 and 2

x + y + x - y = 378 + 210

2x = 588

x = 588/2

x = 294 tons

From 1

294 + y = 378

y = 378 - 294

y = 84 tons

Which of the following ordered pairs is the solution to the following system of equations?
X + y = 11
x - 4y = -14
(5,6)
(5-6)
(6,5)
(6,-5)

Answers

(6,5)
To cancel a term from both equations you have to multiple the top one by 4 so
4x + 4y = 44
x - 4y = -14
cancel out the y’s from both equations and add the terms from both so you’ll have
5x = 30
divide by 5
x = 6

substitute 6 for x in the first equation
6+y=11
subtract 6 from both sides
y = 5

Find the area of the shaded rectangle by multiplying its length and width. Fill in the equation.

Answers

Answer:

5

Step-by-step explanation:

6/7 x 5/7 = 35/7

35/7 = 5

Can you explain how you got the answe

Answers

Answer:

3

Step-by-step explanation:

she put 4 stickers on each car

last one… someone help please.

Answers

Answer:

32 degrees

a triangle is = to 180 degrees

Peter has 100$. The price of a watch is 60$. If Peter gets 25% discount,can he buy 2 watches?

Answers

yes.

25 percent discount means that the price of one watch is 45 dollars.

45 plus 45 is less than 100.

Answer:

The answer is yes.

Step-by-step explanation:

25% = divide by 4

25% of 60$ = 60$ divided by 4 = 25$

So then we need to do 60$ - 25$ which equals to 45$.

45$ + 45$ = $90.

Hope that helps. x

What is the equation of the line that passes through the point (-4,-3)(−4,−3) and has a slope of \frac{3}{4}

Answers

Answer:

y = 3/4x

Step-by-step explanation:

Given:

x1 = -4

y1 = -3

slope (m) = 3/4

Solution:

y - y1 = m ( x - x1 )

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

y + 3 = 3/4 ( x + 4 )

y + 3 = 3/4x + 3

y = 3/4x + 3 - 3

y = 3/4x

What do the following two equations represent?
9-3 = 2(x – 3)
y+5 2(+ 1)
Choose 1 answer:
The same line
ons
Distinct parallel lines
Perpendicular lines
Intersecting, but not perpendicular lines
HELP

Answers

Answer:

Intersecting but not perpendicular

Step-by-step explanation:

Assuming you forgot to add the = between y+5 and 2(1)

Since there is a opposite single variable in either equation the lines will intersect but not be perpendicular

what is the 78th term of the arithmetic sequence -4, -2, 0,

Answers

Answer:

T78=150

Step-by-step explanation:

Tn=a+(n-1)d

T78=-4+(78-1)2

T78 =-4+(77)2

T78 =-4+154

T78=150

Solve the system by graphing. Y=2x-9 y=-2x-1

Answers

Answer:

(2,-5)

Step-by-step explanation:

See attachment

One can also solve this by calculation:

y=2x-9

y=-2x-1

-

Rearrange either equation to find x.  I'll use the first:

y=2x-9

2x = y+9

x = (y+9)/2

Now use this value of x in the second equation:

y =  -2x-1

y =-2((y+9)/2)-1

y = (-2y-18)/2)-1

y = -y -9 - 1

2y = -10

y = -5

Now use -5 for y in the rearranged equation:

y =  -2x-1

-5 =  -2x-1

-2x = -4

x = 2

Solution is (2,-5)

But the question wants a graph solution, which is also fun when you use DESMOS.

help pls, i will give brainliest :)

Answers

I think the answer should be -3

If the circumference of a circle is 13 pi, what is the diameter of the circle.

Answers

Answer:  13 units

Explanation:

Use the formula [tex]C = \pi d[/tex] where C is the circumference and d is the diameter.

the ratio of boys and girs at rotterdam high school is 3:5. there are 160 students at the school calculate the number of boys and the number of girls at rotterdam high school

Answers

Answer:

There are 60 boys and 100 girls at Rotterdam High School

Step 1: Add the ratios

=> 3 + 5=> 8

Step 2: Divide 160 by 8.

=> 160 ÷ 8=> 20

Step 3: Multiply.

=> Total students of boys: 20 x 3 = 60 students=> Total students of girls: 20 x 5 = 100 students

Therefore, there are 60 boys and 100 girls at Rotterdam High School

Hoped this helped.

[tex]BrainiacUser1357[/tex]

PLEASE HELP WILL MARK BRAINLIEST

Answers

Answer:

S (2, - 15 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Using (x₁, y₁ ) = T (0, 3 ) and (x₂, y₂ ) = S (x, y )

Calculate the midpoint using above and equate to coordinates of (1, - 6 )

[tex]\frac{x+0}{2}[/tex] = 1 ( multiply both sides by 2 )

x = 2

[tex]\frac{y+3}{2}[/tex] = - 6 ( multiply both sides by 2 )

y + 3 = - 12 ( subtract 3 from both sides )

y = - 15

S has coordinates (x, y ) = (2, - 15 )

Answer:

Point S is at the ordered pair (2,-15)

Step-by-step explanation:

midpoint formula : midpoint ordered pair (x,y) = ( [tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])

midpoint x = [tex]\frac{x1+x2}{2}[/tex] ; midpoint y = [tex]\frac{y1+y2}{2}[/tex]

midpoint x = 1 x1 = 0 midpoint y = -6 y1=3

Solve each equation for x2 and y2 to get the points for S.

x = [tex]\frac{x1+x2}{2}[/tex]

1 = (0) +x2 / 2

2 = x2

y = [tex]\frac{y1+y2}{2}[/tex]

-6 = 3 + y2 / 2

-12 = 3 + y2

-15 = y2

(2,-15) are the coordinates to point S.

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal? 0 34 units 0 39 units 0 41 units o 49 units Mark ihis and return Save and Exit​

Answers

Answer:

41

Step-by-step explanation:

a² + b² = c²

9² + 40² = c²

81 + 1,600 = c²

√1681 = √c²

41 = c

Gerry purchases 12 hamburgers at a fast food restaurant for $2.25 each. For half the amount of money, he could purchase 5 buffalo chicken sandwiches. What is the “half” amount?

Answers

The answer is 18 dollars. 2.25 x 12=36.00 or 36, 36/2 =18

Use the GCF and the Distributive Property to find the sum. 26+39

Answers

Answer:

65--but the method is the important part that the directions indicated.

Step-by-step explanation:

26 + 39

(2 × 13) + (3 × 13)

The GCF is 13.

Factor the 13 out; it's like Distributive Property in reverse.

13 (2 + 3)

13 (5)

65

26+39= 65, so we obtain the same answer as just adding, by using GCF and Distributive Property.

Answer:

  13(2 +3)

Step-by-step explanation:

26 = 2·13

39 = 3·13

The greatest common factor is 13, so the sum can be written ...

  26 +39 = 13(2 +3)

_____

Additional comment

Of course, the value of the sum is ...

  13(2+3) = 13(5) = 65

Alternatively, the sum can be evaluated as ...

  26 +39 = 26 -1 +1 +39 = (26 -1) +(1 +39) = 25 +40 = 65

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