Amount of money earned per number of hours of work = [tex]f(g(x)) = 6x^{3} + 4[/tex]
What is a composite function?A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.To evaluate a composite function f(g(x)) at some x = a, first compute g(a) by substituting x = a in the function g(x). Then substitute g(a) into the function f(x) by substituting x = g(a). In the same way, we can calculate g(f(a)) as well.
Required calculation -
Amount of money (the earning) per unit x = [tex]f(x) = 2x^{2} + 4[/tex]
Number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works = [tex]g(x) = \sqrt{3x^{3}}[/tex]
we are to find the composite function [tex]f(g(x))[/tex]
Substituting g(x) into the x of f(x), we find:
[tex]f(g(x)) = 2(\sqrt{3x^{3} } )^{2} + 4\\\\= 2(3x^{3} ) + 4\\= 6 x^{3} + 4[/tex]
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Answer:
f(g(x)) = 6x3 + 4 dollars over hour
Step-by-step explanation:
PLEASE HELP ITS MATH
Answer:
y=[-4]x+[10]
Step-by-step explanation:
For a line to be perpendicular to another it must have the reverse reciprocal of the opposite line, to find the reverse reciprocal you take your slope, flip the numerator and denominator, and multiply it by -1.
The slope [tex]\frac{1}{4}[/tex] turns into [tex]\frac{4}{1}[/tex] and is then multiplied by -1 to become [tex]\frac{-4}{1}[/tex] which can be simplified down to: [tex]-4[/tex]
Now that we know the slope we need the line to pass through a point, so we will use point slope form:
[tex]y-y1=m(x-x1)[/tex]
Substitute in our slope and point values:
[tex]y-2=-4(x-2)[/tex]
Now solve for y:
[tex]y-2=-4(x-2)\\y-2=-4x+8\\y=-4x+10[/tex]
Then you will find that line [tex]y=-4x+10[/tex] runs perpendicular to [tex]y=\frac{1}{4}x-8[/tex] and intersects point (2,2).
PLEASE HELP BRAIBLIST ANSWER PLS
Answer:
[tex]m=-3[/tex]
Step-by-step explanation:
Given points:
[tex](5,3),(8,-6)[/tex]
1. Find the slope
The slope of a line between two points equals the change in the points' y-coordinates (rise) over the change in their x-coordinates (run).
The coordinates of point 1 are: [tex]x_1=5,y_1=3[/tex]
The coordinates of point 2 are: [tex]x_2=8,y_2=-6[/tex]
To find the slope, plug the points' x and y-coordinates into the formula and combine to simplify:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-6-3}{8-5}[/tex]
[tex]m=\frac{-9}{3}[/tex]
[tex]m=-3[/tex]
Mike repairs televisions. his revenue, in dollars, can be modeled by the equation y = 25 30x, where x is the number of hours spent repairing televisions. his overhead cost, in dollars, can be modeled by the equation y=5x2−10, where x is the number of hours spent repairing televisions. after how many hours does he break even?
The number of hours spent repairing televisions. after how many hours does he break even is 7 hours
System of equationsThese are equations that contains several equations with unknowns. Given the function that modelled the revenue generated from television repair as;
y = 25 + 30x
where:
x is the number of hours spent repairing televisions.
If his overhead cost, in dollars, is modelled by the equation y=5x^2−10, the company breaks even when;
25 + 30x = 5x^2 -10
Divide through by 5
5 + 6x = x^2 - 2
Equate to zero to have:
x^2 - 6x -2 - 5 = 0
x^2 - 6x - 7 = 0
x^2 - 7x + x - 7 = 0
x(x-7)+1(x-7) =0
x = -1 and 7
Hence the number of hours spent repairing televisions. after how many hours does he break even is 7 hours
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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 64 meters cubed.
A sphere with height h and radius r. A cylinder with height h and radius r.
What is the volume of the sphere?
Solve this question with full working and explanation and I will mark you as brainliest.
Answer:
The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.
Step-by-step explanation:
The hand moved from 3 to 12, that is, it moved:
12 - 3 = 9 hours
In a clock, 12 hours represent a complete turn.
∴ Using the unitary method:
12 hours ⇒ 1 turn
1 hour ⇒ [tex]\frac{1}{12}[/tex] turns
9 hours ⇒ [tex]\frac{1}{12}[/tex] × 9 = [tex]\frac{9}{12}[/tex]
= [tex]\bf \frac{3}{4}[/tex] turns (simplified)
∴ The hand moved [tex]\bf \frac{3}{4}[/tex] of a complete turn.
The answer is [tex]\boxed{\frac{3}{4}}[/tex].
To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.
Hours covered between 3 and 12 : 12 - 3 = 9Hours covered in a complete turn = 12Fraction of a complete turn it moved : 9/12 = 3/4Jeremy likes to paint. he estimates the number of paintings he completes using the function p of w equals one third times w plus four, where w is the number of weeks he spends painting. the function j(y) represents how many weeks per year he spends painting. which composite function would represent how many paintings jeremy completes in a year? p of j of y equals j times the quantity one third times w plus four j of p of w equals one third times j of y plus four p of j of y equals one third times j of y plus four j of p of w equals j times the quantity one third times w plus four
composite function J[P(W)=J(1/3w+4) represent paintings Jeremy completes in a year .
this equation means number of paintings= weeks(rate)
The function P takes a number of weeks as an argument and returns the number of paintings.
The function J takes some argument (unspecified) and returns a number of weeks per year.
The composite function that will give the number of paintings per year will be P(weeks per year) = P(J(y)).
P(J(y)) = 1/3·J(y) +4 .
Looking at the units of the input and output of each of the functions is called "units analysis."
What is Unit analysis?Unit analysis means using the rules of multiplying and reducing fractions to solve problems involving different units.
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Answer:
P[J(y)] = 1/3 (Jy) + 4
Answered the quiz and it's correct.
Identify the elevation and the percentage of oxygen available at each elevation. 8,850 m 57% 33% 4,500 m 100%
1. Sea level (0 m) - 100%
2. Mid-level elevation (4,500 m) - 57%
3. Peak (8,850 m) - 33%
What does oxygen mean?Oxygen is a colorless, odorless, and tasteless gas necessary for all living things. Animals take it up and then change it into carbon dioxide, which plants then use as a carbon source to release oxygen back into the atmosphere.The energy-producing process that powers the metabolisms of most living organisms, respiration, depends heavily on oxygen. All living things, including humans, depend on oxygen in the air we breathe to survive. The process of photosynthesis is where plants and certain bacteria produce oxygen.Identify the elevation and the percentage of oxygen available at each elevation.
Elevation has a significant impact on the amount of oxygen in the atmosphere. The oxygen level increases with decreasing height and decreases with increasing elevation. Thus, we have a situation where the oxygen concentration is highest at sea level or 0 elevations. The oxygen level drops dramatically when we ascend to greater elevations, say 4,500 m, making breathing difficult. Even at higher altitudes, such as 8,850 m, the oxygen level will drop significantly, making it necessary for a person to undergo extensive training and carry oxygen to survive.
1. Sea level (0 m) - 100%
2. Mid-level elevation (4,500 m) - 57%
3. Peak (8,850 m) - 33%
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. An ant is standing at the center of a perfectly circular plate. If the ant crawled in a straight line, he would have to crawl 6 inches to reach the edge of the plate. How many inches would he crawl if he crawled a full circle around the edge of the plate?
The size around the circular edge of the plate is 37.68 inches
How to find the circumference of a circle?The circumference of a circle can be solved as follows:
The ant is standing at the centre of a perfectly circular plate and it walks to the edge of the plate .
The centre of the plate to the edges is 6 inches. Therefore, the radius of the circular plate is 6 inches.
Hence, the distance around the edge of the plate is the circumference of the plate.
Therefore,
circumference of the circular plate = 2πr
circumference of the circular plate = 2 × π × 6
circumference of the circular plate = 12π
circumference of the circular plate = 12 × 3.14
circumference of the circular plate = 37.68 inches
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What is the equation of a line in point-slope form passing through (-4,6) and (2, 3)?
The answer is y - 3 = -1/2 (x - 2).
First, let's find the slope.
m = y₂ - y₁ / x₂ - x₁m = 3 - 6 / 2 + 4m = -3/6m = -1/2Then, the point slope form will be :
y - 3 = -1/2 (x - 2)Answer: y=-0,5x+4.
Step-by-step explanation:
[tex]A(-4;6)\ \ \ \ B(2;3)\\Straight \ line\ equation\ is:\\\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}} \\\frac{x-(-4)}{2-(-4)}=\frac{y-6}{3-6} \\ \frac{x+4}{2+4}=\frac{y-6}{-3} \\\frac{x+4}{6}=\frac{y-6}{-3} \\ Multiply\ the\ left\ and\ right\ sides\ of\ the\ equation \ by\ -3:\\\frac{-(x+4)}{2} =y-6\\-0,5x-2=y-6\\y=-0,5x+4.[/tex]
Evaluate the expression under the given conditions. cos(2); sin() = − 3 5 , in quadrant iii
The value of a particular trigonometric expression that is cos 2θ under the third quadrant is -119/169
Given:
sin θ = -⁵/₁₃
This can be seen from the trigonometric identity.
cos 2θ = 1 - 2sin²θ
From trigonometric identities, we know that;
cos 2θ = 1 - 2sin²θ
Thus;
cos 2θ = 1 - 2(-⁵/₁₃)²
cos 2θ = 1 - 2(25/169)
cos 2θ = 119/169
since cos θ is negative in the third quadrant, then we have;
cos 2θ = -119/169
so; cos θ is negative in the third quadrant, so ;
cos 2θ = -119/169
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A deli sells sliced meat and cheese. One customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. A sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50. The system of equations below represents the situation.
4x + 5y = 30.50
11x + 14y = 84.50
The variable x represents the
✔ cost per pound of meat
.
The variable y represents the
cost per pound of cheese
.
The deli charges $
.
The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.
What is the quantity of meat and cheese sold by the deli?The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.
The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.
Consequently, solving the system of equations by means of substitution, we have;
y = (30.50-4x)/5
Hence, we have;
11x + 14((30.50-4x)/5) = 84.50
x = 4.5 pounds of meat and
y = 2.5 pounds of cheese.
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A 3 tonne mix of gravel contains blue
metal and gravel in the ratio 2:3.
How much gravel is in the mix?
Answer:
1.8 tonne
Step-by-step explanation:
sum the parts of the ratio, 2 + 3 = 5 parts
divide the total mix by 5 to find the value of one part of the mix
3 tonne ÷ 5 = 0.6 tonne , then
3 parts = 3 × 0.6 = 1.8 tonne ← amount of gravel in the mix
Which of these tables represents a function?
Answer:
A. W
Step-by-step explanation:
Because their is a rhythm and pattern
la+xl/2 - la-xl/2, if a= -2, x= -6
HELP!!!
Answer: 2
Step-by-step explanation:
1) substitute
2) calculate the difference before the absolute value
3) calculate the absolute value
4) convert into whole numbers/reduce
5) subtract the whole numbers
this is what i think might be wrong
Help question below study island
Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation one-halfx2 4x 8 = 0. which explanation could anderson provide?
Anderson could provide 0.5x2 + 4x + 8 = 0 has exactly one real root if the discriminant is 0,
What is quadratic equation?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.
What is discriminant?A polynomial's discriminant is a quantity that depends on the coefficients and enables for some root attributes to be inferred without actually computing them. It is actually a polynomial function of the original polynomial's coefficients.
According to the given information:0.5x^2 + 4x + 8 = 0
The discriminant is computed utilizing:
d = b^2 - 4ac
Thus, we have:
d = 4^2 - 4 * 0.5 * 8
Evaluate
d = 0
The equation has only one real root since the discriminant is 0,
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An online retail company determined that their cost for each day, x, can be determined by the function C(x) = 2x^2 – 20x + 70 and their revenue by the function R(x) = –x^2 + 5x + 18. How many days will it take for the company to earn a profit?
4
5
20
22
Answer:
4
Step-by-step explanation:
revenue has to be greater than cost for a profit
revenue minus cost = profit
2x^2 – 20x + 70 - (–x^2 + 5x + 18) =
2x^2 – 20x + 70 + x^2 - 5x - 18 =
3x^2 – 25x + 52 ≤ 0
(x - 4) (3x - 13) ≤ 0
x ≤ 4
x ≤ 13/3
since its multiple choice you can enter one of the answers where the x is to get the answer
if you don't know what the question is and are short on time this may help
again:
revenue has to be greater than cost for a profit
revenue minus cost = profit
cost is 2x^2 – 20x + 70
revenue is –x^2 + 5x + 18
cost is
2(4)^2 – 20(4) + 70 =
32-80+70 =
102-80 =
22
revenue is
–x^2 + 5x + 18
–(4)^2 + 5(4) + 18
-16+20+18
-16+38
22
--------------------------------
cost is
2(5)^2 – 20(5) + 70 =
20
revenue is
–(5)^2 + 5(5) + 18
18
-------------------------------------
cost is
2(20)^2 – 20(20) + 70 =
470
revenue is
–(20)^2 + 5(20) + 18
-282
------------------------------
cost is
2(22)^2 – 20(22) + 70 =
598
revenue is
–(22)^2 + 5(22) + 18
-356
-----------------------------------------
cost is
2(3)^2 – 20(3) + 70 =
28
revenue is
–(3)^2 + 5(3) + 18
24
-------------------------------------
cost is
2(2)^2 – 20(2) + 70 =
38
revenue is
–(2)^2 + 5(2) + 18
24
An $8.5$-by-$11$-inch piece of paper is folded in half repeatedly (never being unfolded), each time shortening what was then the longer side. What is the length of the longest side, in inches, immediately after the second fold
Answer:
5.5
Step-by-step explanation:
For the first fold, we cut the 11-inch side in half, resulting in an 8.5-by-5.5-inch piece. After the second fold, we have a 4.25 by 5.5 piece after halving the 8.5 inch side. The length is 5.5 inches.
Classify the following function.
The equation is neither geometric nor arithmetic
How to classify the function?The function is given as
f(x) = 2x^2 + 6x - 9
As a general rule, arithmetic functions or sequences have a common difference while geometric functions or sequences have a common difference
Set x = 0, 1 and 2
f(0) = 2(0)^2 + 6(0) - 9 = -9
f(1) = 2(1)^2 + 6(1) - 9 = -1
f(2) = 2(2)^2 + 6(2) - 9 = 11
Calculate the common difference (d)
d = 11 --1 = -1--9
d = 12 = 8 ---- false equation i.e. no common difference
Calculate the common ratio (r)
r = 11/-1 = -1/-9
d = -11 = 1/9 ---- false equation i.e. no common ratio
The above function is not an arithmetic function.
This is so because it does not have a common difference
Also, the function is not a geometric function.
This is so because it does not have a common ratio
Hence, the true statement about the function is (c) the equation is neither geometric nor arithmetic
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If the function f(x)= 3ax+b, x>1 11. 5ax-2b, x = 1 is continuous at x = 1, then find the values of a and b x
It looks like the function might be defined by
[tex]f(x) = \begin{cases} 3a{}x + b & \text{if } x > 1 \\ 11 & \text{if } x = 1 \\ 5a{}x - 2b & \text{if } x < 1 \end{cases}[/tex]
To ensure continuity at [tex]x=1[/tex], we need both one-sided limits to exist and have the same value.
[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} (5a{}x - 2b) = 5a - 2b[/tex]
[tex]\displaystyle \lim_{x\to1^+} f(x) = \lim_{x\to1} (3a{}x + b) = 3a + b[/tex]
Both limit values must be equal to [tex]f(1) = 11[/tex], so that
[tex]\begin{cases} 5a - 2b = 11 \\ 3a + b = 11 \end{cases}[/tex]
Eliminating [tex]b[/tex], we have
[tex](5a - 2b) + 2 (3a + b) = 11 + 2\cdot11 \implies 11a = 33 \implies \boxed{a=3}[/tex]
Solving for [tex]b[/tex], we get
[tex]5\cdot3 - 2b = 11 \implies -2b = -4 \implies \boxed{b=2}[/tex]
MULTIPLY (x^2-5x)(2x^2+x-3)
[tex]\bf{ (x^2-5x)(2x^2+x-3)}[/tex]
[tex]\bf{Distribute \ the \ sum \ group. }[/tex]
[tex]\boldsymbol{\sf{x^{2} (2x^{2} +x-3)-5x(2x^{2} +x-3) }}[/tex][tex]\bf{Expand \ the \ distribution \ of \ terms. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -5x(2x^{2} +x-3) }}[/tex][tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -(10x^{3}+5x^{2} -15x) }}[/tex][tex]\bf{Remove \ parentheses. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -10x^{3}+5x^{2} -15x }}[/tex][tex]\bf{Collect \ like \ terms. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+(x^{3}-10x^{3})+(-3x^{2} -5x^{2} )+15x }}[/tex][tex]\bf{Simplify}[/tex]
[tex]\boxed{\boldsymbol{\sf{2x^{4}-9x^{3}-8x^{2} +15x }}}[/tex]If a true-false test with 10 questions is given what is the probability of scoring?
Answer:50%
Step-by-step explanation: It doesn't matter how many questions there are because for each question, you have a 50% chance of getting it right. So, the probability is 50%.
The idea that group work theories are appropriate for all clients all the time is a(n)? empirical truth professional tenet myth lie
The idea that group work theories are appropriate for all clients all the time is a myth (Third option).
About Group Process:
The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.
Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.
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What is the location of point g, which partitions the directed line segment from d to f into a 5:4 ratio? a number line goes from negative 5 to positive 10. point d is at negative 2 and point f is at positive 7. a line is drawn from point d to point f.
the location of the g point is 3.
What is Proportion?Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls.
According to the given Information:Point G Partition the directed line segment form d to f into a
5:4 ratio
so,
g - d = (5/9) x (f - d)
We have that d = -2 and f = 7, Therefore
g - d = (5/9) x (f - d)
g + 2 = (5/9) x (7 + 2)
g + 2 = 5
g = 3
Therefore the location of the g point is 3.
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Answer: OPTION D
Step-by-step explanation:
distance between −42 and −78
Answer:
36 units
Step-by-step explanation:
to find the distance take the absolute value of the difference, that is
| - 42 - (- 78) | = | - 42 + 78 | = | 36 | = 36
or
| - 78 - (- 42) | = | - 78 + 42 | = | - 36 | = 36
Answer:
-36
Step-by-step explanation:
-78 - (-42)
= -78 + 42
= -36
I do not understand the question
Answer: D. 5 choose 3
Step-by-step explanation:
The 'C' stands for Choose
and you read left to right, leaving you with "5 choose 3"
the price of a video game was reduced from 60 to 45. by what percentage was the price of the video game reduced
The percentage reduction of the price of the video game from 60 to 45 was 25%.
What is the percentage reduction?The percentage reduction refers to the fractional reduction in the price of the video game.
This implies that a percentage is a fraction of a value. Percentages are calculated over 100.
A percentage is, therefore, a number or ratio expressed as a fraction of 100, often denoted using the "%" sign.
Data and Calculations:The old price of the video game = 60
The new price of the video game = 45
Reduction in price = 15 (60 - 45)
Percentage reduction = 25% (15/60 x 100)
Thus, the percentage reduction of the price of the video game from 60 to 45 was 25%.
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Elliott is standing at the top of a store escalator that leads to the ground floor below. the angle of depression from the top of the escalator to the floor is 36.84°, and the escalator is 15 feet long. how far is the top of the escalator from the ground floor? round your answer to the nearest foot. 9 feet 12 feet 20 feet 36 feet
The top of the escalator exists 9 feet far from the ground floor.
How to estimate how far is the top of the escalator from the ground floor?
Let h denote the distance between the top of the escalator from the ground floor.
We have existed given that the angle of depression from the top of the escalator to the floor stands 36.84°, and the escalator exists 15 feet long.
The side h exists opposite side and 15 feet side exists hypotenuse of a right triangle.
[tex]$&\sin =\frac{\text { Opposite }}{\text { Hypotenuse }} \\[/tex]
[tex]$&\sin \left(36.84^{\circ}\right)=\frac{h}{15} \\[/tex]
[tex]$&\sin \left(36.84^{\circ}\right) * 15=\frac{h}{15} * 15 \\[/tex]
[tex]$&0.599582468446 * 15=h \\[/tex]
8.993737 = h
[tex]$&h \approx 9[/tex]
Therefore, the top of the escalator exists 9 feet far from the ground floor.
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Three interior angles of a quadrilateral measure 55°, 117°, and 120°. What is the measure of the fourth interior angle?
68°
78°
88°
98°
Answer:
68
Step-by-step explanation:
We know the sum of interior angles for a quadrilateral must equal 360, so we can create the following equation
[tex]55+117+120+x=360[/tex]
Simplify
[tex]292+x=360[/tex]
Subtract 292 from both sides
[tex]x=68[/tex]
Answer:
68
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360. The sum of the interior angles or a triangle is 180. If you think about a rectangle, you can cut that up into two triangles, so 180 + 180 = 360.
Now subtract out the 3 angles that you know
360-55-117-120 = 68
Factor the cubic polynomial 6x3 – 11x2 – 12x 5. use the rational root theorem and synthetic division
The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:
6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
For given question,
We have been given the cubic polynomial 6x³ - 11x² - 12x + 5
We need to factorize given cubic polynomial.
By the rational roots theorem, any rational zero of f(x) is expressible in the form ± [tex]\frac{p}{q}[/tex] for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.
Factors of p = 5: 1, 5
Factors of q = 6: 1, 2, 3, 6
That means that the only possible rational zeros are:
±{ [tex]\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }
= ±{ [tex]1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }
We need to find the exact zeros of given cubic polynomial.
For x = 1,
6(1)³ - 11(1)² - 12(1) + 5 = -12
This means, x = 1 is not a zero of given cubic polynomial.
For x = -1,
6(-1)³ - 11(-1)² - 12(-1) + 5 = 0
This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.
To factorize given cubic polynomial we use synthetic division.
The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.
⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)
The factors of above quadratic polynomial 6x² - 17x + 5 are:
⇒ 6x² - 17x + 5 = (x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
So, the factors of given cubic polynomial are:
⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is: 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
Learn more about the polynomial here:
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