If [tex]A[/tex] is the set of positive divisors of [tex]m[/tex] and [tex]B[/tex] the set of positive divisors of [tex]n[/tex], then [tex]A\cup B[/tex] is the set of positive divisors of [tex]mn[/tex].
Use the inclusion/exclusion principle:
[tex]|A \cup B| = |A| + |B| - |A \cap B|[/tex]
where [tex]|\cdot|[/tex] denotes set cardinality (the number of elements the set contains). The set [tex]A\cap B[/tex] is the set of common divisors of [tex]m[/tex] and [tex]n[/tex]. Then
[tex]14 = 5 + 6 - |A\cap B| \implies |A\cap B| = 3[/tex]
so that [tex]m[/tex] and [tex]n[/tex] share 3 divisors [tex]d_1,d_2,d_3[/tex]; let [tex]k=d_1d_2d_3[/tex] be their product. They must be prime
This means we can write
[tex]m = p_1 p_2 k[/tex]
[tex]n = p_3 p_4 p_5 k[/tex]
[tex]\implies mn = p_1 p_2 p_3 p_4 p_5 k^2 = p_1 p_2 p_3 p_4 p_5 {d_1}^2 {d_2}^2 {d_3}^2[/tex]
so that [tex]mn[/tex] has up to 8 distinct prime factors.
On january 1, 2020, gators corp. acquired a machine at a cost of $900,000. it is to be depreciated on the straight-line method over a five-year period with no residual value. because of a bookkeeping error, no depreciation was recognized in gators' 2020 financial statements. the oversight was discovered during the preparation of gators' 2021 financial statements. depreciation expense on this machine for 2021 should be:
Option b. The oversight was discovered during the preparation of gators' 2021 financial statements. depreciation expense on this machine for 2021 should be $372,000.
The yearly straight-line devaluation cost for the machine would be $186,000 ($930,000/5). In any case, since no deterioration was perceived in 2020, the collected devaluation toward the start of 2021 would be $0 rather than $186,000. In this manner, the complete devaluation cost for 2021 would be the yearly deterioration of $186,000 in addition to the get up to speed devaluation for 2020 of $186,000, for a sum of $372,000. This make up for lost time devaluation is important to address the blunder made in the earlier year and guarantee that the resource is appropriately recorded on the asset report. Accordingly, the right response is $372,000.
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The complete question is:
On January 1, 2020, Oriole Corp. acquired a machine at a cost of $930000. It is to be depreciated on the straight-line method over a 5-year period with no residual value. Because of a bookkeeping error, no depreciation was recognized in Oriole's 2020 financial statements. The oversight was discovered during the preparation of Oriole's 2021 financial statements. Depreciation expense on this machine for 2021 should be
$232500.
$372000.
$186000.
$0.
If the cost for both models continues in this pattern will the cost of model be ever be lower than the cost of model a explain
Answer:
NO
Step-by-step explanation:
2. Please answer the question on exponential growth or decay. Round to
the nearest whole number or penny if the question is concerning money if
necessary.
A company promises to release a new
smartphone model every month. Each
model's battery life will be 3% longer than
the previous model's. If the current
model's battery life is 748.0 minutes, what
will the latest model's battery life be 10
months from now?
Your answer
A line passes through the points (-6, 4) and (-2, 2). Which is the equation of the line?
y=-x+1
y=1/√x+7
y=-2x-8
y = 2x + 16
Answer:
Correct answer not shown on the options.
y = -(1/2)+1
Step-by-step explanation:
Let's find an equation in the format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
The slope can be calculated as the Rise/Run of the line between the two given points (-6,4) and (-2,2):
Rise = (2 - 4) = -2
Run = (-2 - (-6)) = 4
Slope = Rise/Run = -2/4 or -(1/2)
In fact, the actual full equation is y= -(1/2)x+1 (See attached graph).
None of the options have a slope of -(1/2). Either the information on the two points or the options are incorrect.
Answer:
y=[tex]-\frac{1}{2}x[/tex]+1
Step-by-step explanation:
y = mx plus c,where m is the gradient.
∴m =[tex]\frac{y2-y1}{x2-x1}[/tex]=[tex]\frac{2-4}{-2-(-6)}[/tex]=[tex]\frac{-2}{4}[/tex]=[tex]-\frac{1}{2}[/tex]
Equation of a line equals
y-y1=m(x-x1) (Using point (-6, 4) for x1 and y1 values)
y-4=[tex]-\frac{1}{2}[/tex](x-(-6))
y-4=[tex]-\frac{1}{2}[/tex](x+6)
y-4=[tex]-\frac{1}{2}[/tex]x-3
2(y-4)=-x-3(2)(multiply through by 2)
2y-8=-x-6
2y=-x+2(divide through by 2)
y=[tex]-\frac{1}{2}x[/tex]+1
∴the equation of the line is y=[tex]-\frac{1}{2}x[/tex]+1
A population has a standard deviation of 7.89. what is the approximate standard error of the mean for a sample size of 300?
Answer:
Below.
Step-by-step explanation:
Standard error =
standard deviation / √n
= 7.89 / √300
= 0.456 approx.
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Answer:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Find the image of (-1, 2) reflected across the y-axis.
Answer: (1,2)
Step-by-step explanation:
Reflecting across the y-axis means [tex](x,y) \longrightarrow (-x,y)[/tex]
So, [tex](-1,2) \longrightarrow \boxed{(1,2)}[/tex]
If a linear function contains the pairs (5,7) and (9,11), which pairs should have the reciprocal function to this one?
Please choose an answer.
a.
(7.5) and (11.9)
b.
(5.7) and (11.9)
c.
(5.7) and (9.11)
d.
(7.5) and (9.11)
The new coordinates will be ( 7,5) and (11,9) , Option A is the correct answer.
What is a Reciprocal Function ?The reciprocal function is the inverse of the function, such that 1/ f(x) is the reciprocal of f(x).
The given linear function has pairs of points
(5,7) and (9,11)
The reciprocal of this will be
interchanging of the coordinates
Therefore the new coordinates will be
( 7,5) and (11,9)
Option A is the correct answer.
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Geometry question I need help finding the x, MB, CM, and CB
Answer:
x=10, MB=19 CM=16 CB=35
Step-by-step explanation:
Since M is the midpoint of line CB
CM=MB
x+6=2x-4
6+4=2x-x
10=x
The rest is pretty simple, plug 10 in for x
hey guys please help me I'm lowkey confused on how to do this :)
Answer:
x = [tex]\frac{2}{7}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2}[/tex](7x+2) = 2
7x+2 = 2÷[tex]\frac{1}{2}[/tex]
= 2×2
= 4
7x = 4-2
= 2
∴x = 2÷7
= [tex]\frac{2}{7}[/tex]
Answer:
[tex]\displaystyle \frac{2}{7} = x[/tex]
Step-by-step explanation:
[tex]\displaystyle 2 = \frac{1}{2}(7x + 2) \Rightarrow 2 = 3\frac{1}{2}x + 1 \hookrightarrow \frac{1}{3\frac{1}{2}} = \frac{3\frac{1}{2}x}{3\frac{1}{2}} \\ \\ \boxed{\frac{2}{7} = x}[/tex]
I am joyous to assist you at any time.
simplify square root one minus cos squared theta, need explanation please
what is the volume of the regular pyramid below?
The volume of the regular pyramid is 128 unit³.
Option D) 128 unit³ is the correct answer.
This question is incomplete, the missing image is uploaded along this answer below.
What is the volume of the regular pyramid?The volume of pyramid is expressed as;
V = ( 1/3 ) × l × w × h
Given that;
Length l = 8Width W = 8Height h = 6We substitute our given values into the equation above.
V = ( 1/3 ) × 8 × 8 × 6
V = 128 unit³
The volume of the regular pyramid is 128 unit³.
Option D) 128 unit³ is the correct answer.
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The proper sequence of steps in implementing the model in Excel presented in the textbook is: a. Represent the decision variables, organize the data, represent the objective function, represent the constraints, and represent the bounds on the decision variables. b. Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables. c. Organize the data, represent the objective function, represent the decision variables, represent the constraints, and represent the bounds on the decision variables. d. Organize the data, represent the bounds on the decision variables, represent the objective function, represent the constraints, and represent the decision variables.
The proper sequence of steps in implementing the model in Excel presented in the textbook is option b which is organize the data, represent the decision variables, represent the objective function, represent the constraints and represent the bounds on the decision variables.
Given process of implementing the model in Excel and we have to choose the correct process.
The process of implementing the model in Excel is as under:
1) Organize the data: In excel, to organize the data we have to put similar items in the same column. We have to design the data so that all rows have similar items in the same column. We have to keep a range of data separate and leave at least one blank column and one blank row between a related data range.
2) Represent the decision variables: Now we have to represent the decision variables according to which logical function performs tasks.
3)Represent the objective function: It is important because on the basis of this all the logical function perform tasks.
4) Represent the constraints: In excel when we are using solver we have to now represent the constraints of the objective function.
5) Represents the bounds on the decision variables.
Hence the proper sequence of steps in implementing the model in excel is Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables.
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look at image please answer both
6. The system of equations has no solution.
7. B. Tables - 15 lbs, chairs - 3.5 lbs.
How to Find the Solution to the System of Equations?The values of x and y that makes two equations equal is the solution of a system of equations.
6. 3x + 4y = 12 --> eqn. 1
y = 3 - 3/4x --> eqn. 2
Substitute y = (3 - 3/4x) into eqn. 1 to find x:
3x + 4(3 - 3/4x) = 12
3x + 12 - 3x = 12
12 = 12 [unable to solve further for x]
This means that the system of equations has no solution.
7. t = tables
c = chairs
3t + 5c = 62.5 --> eqn. 1
3t + 2c = 52 --> eqn. 2
Subtract
3c = 10.5
c = 3.5 [chairs]
Substitute c = 3.5 into eqn. 2
3t + 2(3.5) = 52
3t + 7 = 52
3t = 52 - 7
3t = 45
t = 15 [table]
Therefore, the answer is: B. Tables - 15 lbs, chairs - 3.5 lbs.
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Many electronic devices use disposable batteries, which eventually have to be replaced. Assume that for one particular brand and type of battery, the distribution of the hours of useful power can be approximated well by a Normal model. The mean is 140 hours, and the stand deviation is 4 hours. The marketing department wants to write a guarantee for battery life. What lifespan should they quote so that they can expect 98% of the batteries to meet the guarantee
They should quote 150 hours so that they can get 98% of the batteries to meet the guarantee.
Given mean of 140 hours and standard deviation of 4 hours with confidence level=98%.
We have to find the lifespan which they should quote to get 98% confident that their batteries meet the guarantee.
We have to use z test for this .
μ=140 hours and σ=4 hours
Z=X-μ/σ
When p value is 0.98 then from z table z value will be 2.58.
Z=X-140/4
2.58=X-140/4
2.58*4=X-140
10.32=X-140
X=150.32
after rounding off we will get 150 hours.
Hence they should quote 150 hours of lifetime on batteries.
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Answer:
132
Step-by-step explanation:
Write the following linear equations into the standard form Ax+ By=c DETERMINE the values of A, B and C
Answer:
[tex] < 25 = 56. < { \times 4 \div hwh3 \times }^{?} [/tex]
Answer:
Attached
Step-by-step explanation:
See attached image
Which of the following functions cannot be odd?
Polynomials
Rationals
Trigonometric
Exponential
Step-by-step explanation:
Exponential can't be odd, because any exponential function has a range that isn't defined for all reals
The graph of f(x) = x² is shown.
Compare the graph of f(x) with the graph of d(x) = x² - 27.
Answer:
The graph of [tex]d(x)[/tex] is [tex]f(x)[/tex] shifted right by [tex]27[/tex] units.
WHAT IS THE AVERAGE NUMBER OF POINTS THAT CHANGED HANDS
The average number of points will be 15 points.
How to calculate the average?It should be noted that average or mean simply means the total added values fall the data in a set which is then divided by the number of data.
Let the assumed points be 10, 12, 24, 15, 23, and 6.
In this case, the average number of points will be:
= (10 + 12 + 24 + 15 + 23 + 6)/6
= 90/6
= 15 points
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URGENT NEED ANSWER NOWWWWW!!!!!!WORTH 27 POINTS!!!
Black Diamond Ski Resort charges $25 for ski rental and $10 an hour to ski. Bunny Hill Ski Resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same.
a.10x+25=5x+50
b.10x-25=5x-50
c.10x+50=5x+25
d.10x-50=5x-25
Answer:
A
Step-by-step explanation:
because for black diamond its 10x+25
and for bunny hill its 5x+50
Use the information provided to answer Part A and Part B for question 22.
Point P is plotted on the number line.
Point Q is the opposite of point P. Determine the location of point Q on the
number line. Explain how you determined the location of point Q on the
number line.
Enter your answer and your explanation in the space provided.
Point S is located at
number
on the number line. A student claims that the location
of point S is to the right of the location of point P on the number line.
Explain whether the student's claim is correct or incorrect.
• Write an inequality that describes the relationship between the value of
point P and the value of point S.
Enter your explanation and your inequality in the space provided.
The inequality is explained below.
How to illustrate the inequality?Inequality is a statement of an order relationship between two numbers or algebraic expressions
In this vase, with a number line with two points opposite from each other on a number line, the middle of it is always going to be 0.
Therefore, both points are the same distance away from 0 just in opposite directions.
That means point Q is always going to equal the negative of point P. An example of this is if point p equals 5, point p equals -5.
This method only works when it is specifically stated that the two points are opposite from each other.
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Landon is lying in the grass looking at the top of a tree that is 200 m away. The angle of elevation between Landon's head and the top of
the tree is 36 degrees.
What is the height of the tree?
O 145 m
O 275 m
O 118 m
162 m
200 m
The height of the tree which is the opposite side of the right triangle is 145 meters.
How to find height when given angle of elevation?The angle of elevation is 36 degrees.
The situation forms a right angle triangle.
Therefore,
base of the triangle = 200 m
Hence, using trigonometric ratios,
tan 36 = opposite / adjacent
tan 36 = x / 200
x = 200 tan 36
x = 200 × 0.726542528
x = 145.308505601
x = 145.31 m
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someone help me with this pleaseeeeeeeeeeeeee
Answer:
[a] 11 feet
[b] 7 feet
[c] 10 feet
Step-by-step explanation:
See attached. We will pull different details from the graph and information given to solve the different problems,
Answer:
See below
Step-by-step explanation:
Using the equation (instead of the graph....my answer got deleted for using the graph instead of the equation)
When the ball leaves fingers x = 0 :
a) -1/25 ( 0-10)^2 + 11 = 7 ft
b) max height will be at - b/2a
-1/25 ( x^2 -20x +100 ) + 11 <====expand
-1/25 x^2 + 4/5x +7 a = -1/25 b= 4/5
then - b/2a = - 4/5 / (2* -1/25) = 10=x
sub in this value of x into the equation to find max height = 11ft
c) when x = 15
-1/25 ( 15-10)^2 + 11 = 10 ft
Efraín es un vendedor de celulares, cada equipo cuesta 7500 pesos, el cuenta con su propia línea telefonica y tiene dos métodos de pago, una que es de contado y otra que es a creditó.
Si un cliente compra un celular a crédito aumenta un 20% a su costó inicial.
Samara quiere comprar un celular a crédito y otro de contado dando un total de 11 veces el 20%
¿Cuánto costará cada celular?
¿Cuanto es el valor de el 20%?
El celular de contado costará 7500 pesos, mientras que el celular a crédito tendrá un costo de 9000 pesos.
¿Cuál es el 20% de 7500?7500 / 100 = 75 (valor del 1%)
75 x 20 = 1500 pesos
¿Cuánto cuesta cada celular?Celular a contado: El precio no aumenta por lo que el valor sería de 7500 pesos.
Celular a crédito: 7500 + 1500 = 9000 pesos
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Given: ABCD is a quadrilateral, Segment AB is congruent to Segment CD, <1 is congruent to <2 Prove: ABCD is a parallelogram
Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.
Given that, ABCD is a quadrilateral, segment AB is congruent to segment CD, ∠1 is congruent to ∠2.
We need to prove that ABCD is a parallelogram.
How to prove a given quadrilateral is a parallelogram?If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram.
From the given quadrilateral ABCD:
AB=CD (Given)
∠1=∠2 (Given)
AC=AC (Diagonal)
From ASA congruency ΔABC and ΔADC are congruent.
By CPCT, AD=BC and ∠ABC=∠ADC.
Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.
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e) Explain the approach you would take to verify that the following equation is an identity and why you would choose that approach. Do not actually verify that the equation is an identity.
(sin(x) + cos(x))² / sin(2x)= csc (2x) + 1
See below for the proof of the trigonometry identity
The approach to takeThe identity is given as:
(sin(x) + cos(x))² / sin(2x)= csc (2x) + 1
Start by expanding the numerator
(sin²(x) + cos²(x) + sin(2x)) / sin(2x)= csc (2x) + 1
Express sin²(x) + cos²(x) as 1
(1 + sin(2x)) / sin(2x)= csc (2x) + 1
Expand the fraction
1/sin(2x) + sin(2x)/sin(2x) = csc(2x) + 1
Evaluate the quotient
csc(2x) + 1 = csc(2x) + 1
Hence, the trigonometry identity has been proved
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What is the equation of the following line?
The equation of the given line is y=2/3x-6
We have given the graph of the line and also the equation of the line
[tex]y=-6x+\frac{2}{3}[/tex]
[tex]y=\frac{2}{3}x-6[/tex]
[tex]y=-6x+\frac{3}{2}[/tex]
[tex]y=\frac{3}{2}x-6[/tex]
We have to determine which equations graph is given here
We have to draw a graph of the given equation of the line
To find the coordinate of the given line
The equation of the line second is
x=0 then y=-6
and when y=0 then x=9
We get the points (0,-6) and (9,0)
plot this point and we get the given graph of the line.
Therefore the second option is correct.
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Which of the expressions below are equal to 8x² + 30x + 18?
Select all that apply.
A) (4x + 3) (2x + 6)
B) 6x² + 20x + 2x² + 10x + 18
C) 2(4x² + 15x + 9)
D) 4(2x² + 7x + 4)
Answer:
A, C, and D
Step-by-step explanation:
A) (4x + 3) (2x + 6) is equal to 8x² + 30x + 18 because when you multiply two binomials, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, (4x + 3) (2x + 6) can be rewritten as (4x)(2x) + (4x)(6) + (3)(2x) + (3)(6). This can further be simplified to 8x² + 24x + 18.
C) 2(4x² + 15x + 9) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 2(4x² + 15x + 9) can be rewritten as 2(4x²) + 2(15x) + 2(9). This can further be simplified to 8x² + 30x + 18.
D) 4(2x² + 7x + 4) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 4(2x² + 7x + 4) can be rewritten as 4(2x²) + 4(7x) + 4(4). This can further be simplified to 8x² + 28x + 16.
Use the image to answer the question.
A rectangle with length 15 inches and width 4 thirds feet.
© 2018 StrongMind. Created using GeoGebra.
What is the area, in square inches, of the rectangle?
Enter your answer as a number, like this: 42
The area of the rectangle is 240 square inches
How to determine the area?The dimensions are given as:
Length = 15 inches
Width = 4/3 feet
Start by converting feet to inches
Width = 4/3 * 12 inches
Width = 16 inches
The area is then calculated as:
Area = Length * Width
This gives
Area = 15 * 16
Evaluate
Area = 240
Hence, the area of the rectangle is 240 square inches
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please answer this question with steps
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - ( [tex]\frac{5}{2}[/tex] a² + [tex]\frac{3}{2}[/tex] a³ + [tex]\frac{a}{3}[/tex] - [tex]\frac{6}{5}[/tex] ) ← distribute parenthesis by - 1
= [tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - [tex]\frac{5}{2}[/tex] a² - [tex]\frac{3}{2}[/tex] a³ - [tex]\frac{a}{3}[/tex] + [tex]\frac{6}{5}[/tex] ← collect like terms
= ([tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{2}[/tex] a³ ) + (-[tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{5}{2}[/tex] + [tex]\frac{6}{5}[/tex] ) ← change to common denominators
= ([tex]\frac{2}{6}[/tex] a³ - [tex]\frac{9}{6}[/tex] a³ ) + (- [tex]\frac{3}{4}[/tex] a² - [tex]\frac{10}{4}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{25}{10}[/tex] + [tex]\frac{12}{10}[/tex] ) ← simplify
= - [tex]\frac{7}{6}[/tex] a³ - [tex]\frac{13}{4}[/tex] a² - [tex]\frac{1}{3}[/tex] a - [tex]\frac{13}{10}[/tex]
Answer:
Step-by-step explanation:
[tex]\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=[/tex]
[tex]\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]\\\\\\[/tex]
[tex]\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}\\\\[/tex]
[tex]\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}[/tex]