Determine the rational zeros for the function f(x)=8x^(3)-6x^(2)-23x+6.
a. -(1)/(2),(1)/(4),2
c. -1(1)/(2),(1)/(4),2
b. 1(1)/(2),(1)/(4),-2
d. -1(1)/(2),-(1)/(4),2
Answers
Answer:
Step-by-step explanation:
Rational zeros of f(x) = 8x³-6x²-23x +6 is equals to [tex]2, \frac{-3}{2} , \frac{1}{4}[/tex].
What are rational zeros?"A rational zero of a polynomial P(x) is defined as when the variable x = p/q and P (p/q) = 0 where p and q are any integers."
According to the question,
Given,
f(x) = 8x³-6x²-23x +6
Factor of 6 'p' =±1, ±2, ±3, ±6
Factor of 8 'q' = ±1 , ±2, ±4 , ±8
Using trial and error method x=2 is a common factor
Substitute x=2 in f(x) we get,
f(2) = 8(2)³ -6(2)² -23(2) +6
= 64-24-46+6
=0
(x-2) is a factor of f(x).
Divide f(x) by (x-2)
[tex]\frac{8x^{3}-6x^{2} -23x+6 }{(x-2)}[/tex]
= 8x²+10x-3
Factorize it we get,
8x²+12x-2x-3
= 4x(2x+3) - 1(2x+3)
= (4x-1)(2x+3)
For rational zeros ,Substitute f(x=(p/q)) =0
x-2=0
⇒ x=2
2x+3=0
⇒x= -3/2
= [tex]-1\frac{1}{2}[/tex]
4x-1 =0
⇒x=1/4
Hence, Option (C) is the correct answer.
Learn more about rational zeros here
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Related Questions
5x – 3y < 12
x - 4y > 16
Identify 3 solutions to the system of inequalities .. hurry up please
Answers
Answer:
The solutions to this system of inequalities are included in this inequality:
5/3x - 4 < y < 1/4x - 4
Here are an example of 3 solutions:
(-1,-5), (-2,-6), (-4,-8)
The graph of y= -2x + 10 is:
A. a point that shows the yintercept. B. a line that shows only one solution to the equation.
C. a point that shows one solution to the equation.
D. a line that shows the set of all solutions to the equation,
Answers
Answer:
d is the right answer for your question
Triangle ABC has coordinates; A(4, 5), B(4,9)
and C(7,5). What is the perimeter of triangle
ABC?
Answers
Answer: I think it is 6.4 please don’t give a bad review if not
Step-by-step explanation: 4^2,5^2 and the square root that
1. Which situation represents a chemical change!
A. burning a pile of twigs
B. boiling water in a teakettle
C. washing the mud off a dirty car
Answers
Answer:
tbh i think all of them are but go with C
Step-by-step explanation:
Answer:
burning and cooking are 2 examples of chemical change
Step-by-step explanation:
so I think it's is A. B can't be the answer because it's just boiling water since there's nothing in it, it's not really cooking
Which of these is the algebraic expression for "some number to the power of 4?
Ο χ4
O 4
4x
Ox+4
X + 4
Answers
Hi!
In the given question, "some number to the power of 4" tells us that we are using exponents, because it states "to the power of".
Therefore, your answer is the first option, χ4.
The first option is the only option that uses exponents.
The other options would be said like such:
2.) "A number 4"
3.) "A number multiplied by 4"
4.) "A number added to 4"
For a similar question, see:
https://brainly.com/question/11818830
Would you classify 165 as a perfect square, perfect cube, both, or neither
Answers
Answer:
neither
Step-by-step explanation:
because the square root is not whole number and neither is the cube root of 165. so it is neither
Answer:
I would say neither
Step-by-step explanation:
It's not a perfect square. It's a bit close to say perfect cube. ∛165= ∛(5.485 x 5.485 x 5.485)
5 The taxi goes by your hotel at 8:00, 8:15 and 8:30. The bus goes by your hotel at 8:00, 8:12 and 8:24. If neither the taxi or bus change their rates of speed, at what time will the bus and taxi arrive at the same time other than 8:00?
Answers
If n = 440 and ^p(p-hat) = 0.1, construct a 99% confidence interval. Give your answers to three decimals. Please list formulas in excel used if possible
___ < p < ___
Answers
====================================================
Explanation:
The spreadsheet is shown below.
In cell B6, the formula used is the NORMINV function to get the z critical value. The name is the result of putting the words "NORM" and "INV" together, which refers to the inverse normal.
It's used to find the value of k in P(-k < Z < k) = 0.99, which in this case is roughly k = 2.576 so the z critical value is roughly z = 2.576
What you type in specifically is [tex]=\text{NORMINV}( (1-0.99)/2, 0, 1)[/tex]
The (1-0.99)/2 portion ensures that we get the alpha/2 value which in this case is 0.005
The 0,1 at the end refers to the mean and standard deviation respectively of the standard normal Z distribution.
The output of that NORMINV function is then made positive and then you'd round to 3 decimal places.
So that's how we can get excel to display z = 2.576
----------
The margin of error E formula is
E = z*sqrt(phat*(1-phat)/n)
which doesn't need an excel function to get the job done, though of course excel can handle it just fine. You'd type in the formula as shown, but be sure to reference the correct cells.
Once E is calculated, we compute the following
L = phat - EU = phat + Ewhich are the lower (L) and upper (U) bounds of the confidence interval.
The results are L = 0.063 and U = 0.137
That confidence interval can be written in the form (0.063, 0.137) which is equivalent to saying 0.063 < p < 0.137
If 3^x=8 what does 3^-2x equal
Answers
Answer:
0.01538
Step-by-step explanation:
A box is 13.5 inches long, 9.25 inches wide, and 4.5 inches high. What is the volume of the box? Enter your answer, rounded to the nearest whole number, in the box.
Answers
Step-by-step explanation:
1st Step:
Volume of a cuboid : Length * Breath * Height
2nd Step :
Volume : 13.5 * 9.25 * 4.5
Which is equal to 561.9375
3rd Step:
Rounded up : 562
Answer:
562
Step-by-step explanation:
A man earns rs 24000 per month and spends 70% of it find his monthly saving
Answers
Answer:
Savings=rs7200
Step-by-step explanation:
money spend=70% of 24000
=70/100*24000
=70*240
=rs 16800
savings=money earned-money spend
=24000-16800
=rs7200
Answer: rs 7200
Step-by-step explanation: So 70% of 24000 = 16800
24000-16800=7200
so he spends rs 16800 per month and has a saving of Rs 7200 per month from his monthly salary.
Which of the following is a radius of D?
A. AB
B. BD
C. BC
D. AC
Answers
Answer:
BD
Step-by-step explanation:
the radius of a circle is the line from the centre of the circle to a point on the circle, then
BD is the radius of the circle.
How do I put a picture of my problem on here. Thanks
Answers
Answer:
There is something that looks like a paper clip and you put your photos there.
In triangle ABC, M is the midpoint of AB. Let D be the point on BC such that AD bisects angle BAC, and let the perpendicular bisector of AB intersect AD at E. If AB = 44, AC = 30, and ME = 10, then find the area of triangle ACE.
Help Please!
Answers
The area of Triangle ACE from the given diagram is; 150 sq.units
What is the area of the triangle?We are given;
AB = 44
AC = 30
ME = 10
Now, to find the area of triangle ACE, we need to know the length KE where K is the midpoint of AC.
Now, since AD bisects angle BAC. This means that ∠KEA = ∠MEA.
By ASA Congruence Postulate, we can say that; ΔAEK ≅ AEM
Thus, we can say that KE = ME = 10
Formula for area of triangle is;
A = ¹/₂ * base * height
where;
base = AC = 30
Height = KE = 10
Thus;
A = ¹/₂ * 30 * 10
A = 150
Read more about area of the triangle at; https://brainly.com/question/17335144
write an equation of the line below
Answers
Answer:
y=-1/3x+1
Step-by-step explanation:
The slope of this line is negative, and is equal to rise over run.
To find slope, count the number of spaces it has moved down or up, and then the number of spaces it has moved left or right.
The y intercept is represented by +1, and is where the line crosses the y axis.
Hope this helps!
In rectangle EFGH, EH I FG and EH crosses the y-axis at (0.-2). If the equation of the line containing FG is x + 3y = 12, write the equation of the line containing EH in slope- intercept form. Show your work to justify your answer.
Answers
Answer:
y = (-1/3)x - 2
Step-by-step explanation:
First we should put the equation for FG into slope intercept form, which is y = mx + b. For this step, just solve for the y in the equation, which should be y = (-1/3)x + 4.
Next, since we know that FG and EH are parallel, their slopes must also be the same. We also know the (0, -2) is a point on EH, and also happens to be the y-intercept. Therefore, we can plug it back into the slope intercept equation and get y = (-1/3)x - 2, since the m is the same and the -2 is just the y-intercept given in the problem.
select the digit in the ten thousand place for 542,970
Answers
Answer:
the 4
Step-by-step explanation:
Answer:
The answer is 4
Step-by-step explanation:
500,000, 40,000, 2,000, 900, 70
H2+2h-120
The first 2 (one after H) is square
Answers
Answer:
(h + 12)(h - 10)
Step-by-step explanation:
Assuming you require to factor the expression
Given
h² + 2h - 120
Consider the factors of the constant term (- 120) which sum to give the coefficient of the h- term (+ 2)
The factors are + 12 and - 10 , since
12 × - 10 = - 120 and 12 - 10 = + 2 , thus
h² + 2h - 120 = (h + 12)(h - 10) ← in factored form
See steps
Step by Step Solution:
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "h2" was replaced by "h^2".
STEP
1
:
Trying to factor by splitting the middle term
1.1 Factoring h2+2h-120
The first term is, h2 its coefficient is 1 .
The middle term is, +2h its coefficient is 2 .
The last term, "the constant", is -120
Step-1 : Multiply the coefficient of the first term by the constant 1 • -120 = -120
Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is 2 .
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14
-15 + 8 = -7
-12 + 10 = -2
-10 + 12 = 2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 12
h2 - 10h + 12h - 120
Step-4 : Add up the first 2 terms, pulling out like factors :
h • (h-10)
Add up the last 2 terms, pulling out common factors :
12 • (h-10)
Step-5 : Add up the four terms of step 4 :
(h+12) • (h-10)
Which is the desired factorization
Final result :
(h + 12) • (h - 10)
z^3 - z^2 + z for z = -10
Answers
Answer:
[tex] - 1110[/tex]
Step-by-step explanation:
STEP1:
1.1 10 = 2•5
(10)2 = (2•5)2 = 22 • 52
Equation at the end of step1:
((0 - (103)) - (22•52)) - 10
STEP2:
2.1 10 = 2•5
(10)3 = (2•5)3 = 23 • 53
Equation at the end of step2:
((0 - (23•53)) - (22•52)) - 10
STEP3:
Final result :
-1110
Emilio is pickling tomatillos with his grandfather. The tomatillos are approximately
spheres with a diameter of 6 cm. The pickling jar they are using has a diameter of
8 cm and a height of 21 cm. The jar can hold 3 tomatillos.
Answers
The jar can hold a total of three tomatoes at a time.
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
The tomatoes is spherical with a diameter of 6 cm (radius = 6/2 = 3cm), hence:
Volume of tomatoes = (4/3) * π * radius³ = (4/3) * π * 4³ = 268 cm³
The jar is cylinder with diameter of 8 cm (radius = 8/2 = 4) and a height of 21 cm, hence:
Volume of jar = π * radius² * height = π * 4² * 21 = 1055.6 cm³
Amount of tomatoes that can be contained in jar = 1055.6 cm³ / 268 cm³ = 3.9
The jar can hold a total of three tomatoes at a time.
Find out more on volume at: https://brainly.com/question/12410983
Answer:
228\pi
Step-by-step explanation:
There are 13 boys and 10 girls in the classroom. What is the ratio of boys to girls?
A 10 to 13
B 13 to 10
C 23 to 13
D 23 to 10
Answers
Answer:
13 to 10
Step-by-step explanation:
13 boys, 10 girls
13:10
The ratio of boys to girls in the classroom is 13:10
hence option B is correct
According too the given situation
The number of boys in the classroom = 13
The number of girls in the classroom = 10
Ratio is a quantitative relationship between two numbers showing a comparable form of magnitudes of both the numbers/quantities.
Let "a" and "b" be two numbers then the Ratio of "a" and "b" is shown as formulated in equation (1)
[tex]\rm r = a:b ........(1)[/tex]
The ratio of two numbers can be found out in simplest form by dividing these two numbers such that the division results in positive natural numbers for both the quantities.
So we can conclude that the ratio of boys to girls in the classroom are
[tex]\rm \dfrac{Boys }{Girls } =\dfrac{13}{10} \\\\Boys : Girls = 13:10 \\[/tex]
So we can conclude that the ratio of boys to girls in the classroom is 13:10
hence option B is correct
For more information please refer to the link given below
https://brainly.com/question/25326254
factor the given expression 14x4 + 2x3
Answers
Answer:
2x^3·(7x+1)
Step-by-step explanation:
*Common factor
14x^4+2x^3 ⇒ 2(7x^4+x^3)
*Find one factor
2x^3(7x+1)
The formula for distance traveled d is d=rt, where r is the average speed of the object and t is time traveled. if an object travels 30 meters in 20 seconds, what is its speed?
Answers
Answer:
1.5 meters per second.
Step-by-step explanation:
Distance formula:
d = rt
where d = distance, r = average speed and t = time traveled.
They told us that an object travels 30 meters in 20 seconds.
So we can say d = 30 and t = 20
if you put these values back into the distance formula you get:
d = rt
30 = r times 20
30 = 20 r
So now we want to find what "r" (average speed) is.
Divide both sides by 20.
20 r = 30
r = = 1.5 meters per second.
If you answer all of these I will give brainliest if it will let me!!!!!
6x - x + 3 = _
-x - 2y - 8x - 2y = _
7p + 3 + 4p + 5 = _
2a + 4 + 2a + 9 = _
x + 5(6 + x) = _
4a - 3b - 7a - 3b = _
-3(6 - 2r) - 3r = _
-2(2x - 5) - 4x = _
2a + 3(2 + a) = _
2(x - y) + 3x = _
-4 (3m + 2n) - 5m + y = _
¼ (m + 2n) - ⅓ (3m - 3n) = _
⅖ (2a - b) + ⅔ (a + 2b) = _
Answers
Answer:
1-8
Step-by-step explanation:
I was only able to finish one through eight The rest follow the same concept though
Anyone Know This ????!?
Answers
Answer:
D
Step-by-step explanation:
As
[tex]\frac{8}{8}[/tex]
because the rate is of
1/8 and
8/8=1
Which of the following is a solution to the inequality below?
V + 12 < 0
V = -4
V = -5
V = -12
V = -8
Submit
TATO
Answers
Answer:
The anwser is:
C. V = -12
Find the value of x that will make A||B
Answers
Answer:
x=12
Step-by-step explanation:
Because the angles labeled 5x and 4x+12 ate opposite exterior angles, they are congruent. This means that we can set up the following equation:
5x=4x+12
Subtracting 4x from both sides, we have:
X=12
Answer:
x = 12
Step-by-step explanation:
When two parallel lines are intersected by a transversal, the alternate exterior angles are congruent.
5x = 4x + 12
Subtract 4x from both sides,
5x - 4x = 4x - 4x + 12
x = 12
PLEASE HELPPP!!! 20 PTS!
solve for x and y
Answers
Answer:
x= 19
y= 14
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Write 3/50 as a percentage
Answers
Answer:
6%
Step-by-step explanation:
i did some research and i hope i got this right if it isn't pls let me know
Answer:
6%
Step-by-step explanation:
3/50 as a percent is 6%
7. Find the value of x and the length of AB.
Answers
Answer:
length is 10 and X is 5
Step-by-step explanation:
A and D is 14 cm their opposite side is BC is 4 so AB is 10
X is 2x=10
X=10/2
X=5