2x3 + 8x2 + 10x + 4 all potential roots and actual roots
Answers
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.
Related Questions
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
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
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 SchoolStep 1: Add the ratios
=> 3 + 5=> 8Step 2: Divide 160 by 8.
=> 160 ÷ 8=> 20Step 3: Multiply.
=> Total students of boys: 20 x 3 = 60 students=> Total students of girls: 20 x 5 = 100 studentsTherefore, there are 60 boys and 100 girls at Rotterdam High School
Hoped this helped.
[tex]BrainiacUser1357[/tex]
HELP ASAP PLEASEEEEEEEEEEE HELP MEEE
Answers
Answer:
5x 24 = 120 pulus degreece so that = a 120 digree angle
Step-by-step explanation:
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
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.
Can you explain how you got the answe
Answers
Answer:
3
Step-by-step explanation:
she put 4 stickers on each car
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 :)
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 milesReasons:
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
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
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
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
help pls, i will give brainliest :)
Answers
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.
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:
$6347.26Step-by-step explanation:
Given:
Initial amount P = 5483Interest rate r = 5% or 0.05Compound number n = 1Time t = 3 yearsFind 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]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]
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:
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
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.
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
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
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.
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
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
I need some help :(
A)4
B)2.9
C)3.8
Answers
Answer: C
Step-by-step explanation:
last one… someone help please.
Answers
Answer:
32 degrees
a triangle is = to 180 degrees
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.
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
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!!!
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
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
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: