Factorization of 6ax - 15x is 3x.(2a - 5)
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given expression,
6ax - 15x
It can be written as
3×2 . a . x - 3×5 . x
Factoring out common factor
3x.(2a - 5)
Hence, 3x.(2a - 5) is the factorization of 6ax - 15x.
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The number of Barnes & Noble bookstores has increased, then decreased through the years. The piecewise function () given below shows how “pieces of” two functions can help determine the number of Barnes & Noble stores for particular intervals of years. Use =6 for the year 2006, =7 for the year 2007, etc. ()= { −3.692 +65.28+437.30 6≤ <12 −10.17+691 ≥12 a. According to (), how many Barnes & Noble stores were there in 2009?
The required number of Barnes & Noble stores in 2009 is 725.28.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
To determine the number of Barnes & Noble stores in 2009, we need to evaluate the piecewise function for t = 2009.
Since 2009 is between the interval 6 ≤ t < 12, the number of stores is given by the first piece of the function:
y = -3.692 × x² + 65.28 × x + 437.30
put x = 9 for the year 2009
y = -3.692 × 9² + 65.28 × 9 + 437.30 = 725.28
So, there were 725.28 Barnes & Noble stores in 2009.
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Find the maximum value of the function z=5x+3y subject to the following constraints.
x≥2
y22
6x+7y≤68
The maximum value of the function z = 5x + 3y subjected to the constraints is given as follows:
48.1665.
How to obtain the maximum value of the function?The function for this problem is defined as follows:
z = 5x + 3y.
The constraints are given as follows:
x ≥ 2.y ≥ 3.6x + 7y ≤ 68.x has a higher multiplier than y, hence the value of y should be minimized to obtain the maximum value, hence:
y = 3.
Then the value of x is obtained as follows:
6x + 7(3) = 68
6x = 47
x = 7.8333.
Then the maximum value of the function is given as follows:
z = 5(7.8333) + 3(3)
z = 48.1665.
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What is the area of a 7 by 10 grid?
The area of a 7 by 10 grid would be 70 square units.
This is calculated by multiplying the length (7 units) by the width (10 units), resulting in 7 x 10 = 70.
2.
1.
Naira
280
400
800
2500
Change each of the given amounts in Naira to the following currencies. Use the exchange
rates given in the previous page.
3750
Pound sterling
Amount in
Us dollars
Cedis
Leones
Franc (CFA)
In each of the following are two equivalent amounts of money. Find the exchange rate
terms of N1. Limit your answer to 2 decimal places.
a. N150 = £18
d. N80 = US$20
b. £52 = N400
e. N9.36 = Le 72
h. N25 = 1 178 frs
A book costs £3. If the rate of exchange is £1 = N8.33, find its cost in Naira
Mr Awolowo wants to send £500 to his brother in the United Kingdom How much
pay in Naira at the post office?
The cost of the book in Naira is N 24.99
Mr. Awolowo needs to pay N 4165 at the post office.
Rate of exchange of currency:An exchange rate determines the value of one unit of currency in relation to another type of money. Which means exchanging the price from one currency to another currency.
People use the exchange rates when they want to travel abroad and It is necessary to convert cash into local currency in order to do purchases locally.
Here we have
The book costs £3. If the rate of exchange is £ 1 = N 8.33
Cost of the book in Naira = 3 × N 8.33
= N 24.99
Mr Awolowo wants to send £500 to his brother in the United Kingdom
As we know the rate of exchange, is £ 1 = N 8.33
=> £500 = 500 × 8.33 = N 4165
Therefore,
The cost of the book in Naira is N 24.99
Mr. Awolowo needs to pay N 4165 at the post office.
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Apple crumble is made using the following ingredients.
a) Farid makes apple crumble for 16 people.
How much flour does he need?
b) Amal makes apple crumble for 2 people.
How much sugar does she need?
g
g
Serves 8 people
700g apple
240g sugar
180g flour
40 g
butter
c) Shahina has 550 g of apples and plenty of the other ingredients.
Can she make apple crumble for 6 people? Yes/No
Explain how you got your answer.
Show your working
|+
Answer: a) To make apple crumble for 16 people, Farid will need to double the ingredients as compared to serving 8 people. Hence, he will need:
700g * 2 = 1400g of apples
240g * 2 = 480g of sugar
180g * 2 = 360g of flour
So, Farid needs 360g of flour to make apple crumble for 16 people.
b) To make apple crumble for 2 people, Amal will need to use 1/8 of the ingredients as compared to serving 8 people. Hence, she will need:
700g / 8 = 87.5g of apples
240g / 8 = 30g of sugar
So, Amal needs 30g of sugar to make apple crumble for 2 people.
c) To make apple crumble for 6 people, Shahina will need to adjust the ingredients based on the apples she has available. To calculate the amount of sugar and flour required, she can use the ratio of sugar and flour to apples as follows:
Sugar: 700g / 8 = 87.5g per serving * 6 people = 525g
Flour: 700g / 8 = 87.5g per serving * 6 people = 525g
Since Shahina has plenty of the other ingredients, including butter, she can make apple crumble for 6 people with the amount of apples she has available. So, the answer is Yes, Shahina can make apple crumble for 6 people.
Step-by-step explanation:
MP Model with Mathematics Jonathan uses this
area model to show the product of two mixed
numbers. What equation models the product?
The equation which models the product is, A = 6 x 8
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
Given that,
A area model,
which has 6 box in column arrangement and 8 box in row arrangement,
Suppose, each box has 1 unit square area
Now, area of a model can be written as,
Area = Number of box in column x Number of box in row
Number of box in column = 6
Number of box in row = 8
Each box has 1 unit square area,
So,
A = 6 x 8
= 48 unit square
Hence, it can be represented as, A = 6 x 8
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If yk how to do this pls help me
The linear function for the population in t years after 2000 is given as follows:
P(t) = 2200t + 44000.
The estimate for the population in 2010 is given as follows:
66,000.
How to obtain the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial value.Two points for the function are given as follows:
(5, 55000) and (8, 61600).
Dividing the change in the output by the change in the input, the slope m is given as follows:
m = (61600 - 55000)/(8 - 5)
m = 2200.
Hence:
P(t) = 2200t + b.
When x = 5, y = 55000, hence the intercept b is given as follows:
55000 = 2200(5) + b
b = 55000 - 2200(5)
b = 44000.
Hence the function is:
P(t) = 2200t + 44000.
2010 is 10 years after 2000, hence the estimate is given as follows:
P(10) = 2200(10) + 40000
P(10) = 66,000.
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eigen values of A= [1 2 1
0 2 1
0 0 3]
The eigen values of matrix A [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex] are respectively, 1, 2, 3
What are eigen values?In mathematics, the eigen values are characteristic roots of the equation
| A - λI |,
where, A is matrix and λ is eigen value of the matrix
Properties of matrix,
1. Sum of diagonal elements = Sum of eigen values
2. Determinant of matrix = Product of eigen values
Given that,
Matrix A = [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex]
The eigen values of A = ?
It is known that,
For the upper and lower triangular matrix, eigen values of the matrix are diagonal elements,
given matrix is, upper triangular,
Diagonal elements are 1, 2, 3
So, The eigen values will be 1, 2, 3
Thus, the eigen values are 1, 2, 3
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In a random survey, 9 out of 36 people preferred vanilla ice cream. What percent of people preferred vanilla ice cream? I would appreciate any help :)
Suppose you plan to buy many blank compact disks. You check price lists and find out that
if you buy 100 CDs or fewer you pay $0.74 each. However, if you buy over 100 CDs the pricedrops to $0.69 for each additional CD up to 300.
(a)Write a function that describes the cost C(n) of n number of CDs purchased.
(b)What is the cost of 53 CDs?
(c)What is the cost for 201 CDs?
Answer:
a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)
b) 39.22
c) 143.69
Step-by-step explanation:
(a) We can write a piecewise function to describe the cost C(n) of n CDs purchased:
C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)
(b) The cost of 53 CDs is:
C(53) = 0.74 * min(53, 100) + 0.69 * max(53 - 100, 0) = 0.74 * 53 = 39.22
(c) The cost for 201 CDs is:
C(201) = 0.74 * min(201, 100) + 0.69 * max(201 - 100, 0) = 0.74 * 100 + 0.69 * 101 = 74 + 69.69 = 143.69
GIVING BRAINLIEST! CHECK IMAGE. is it possible for this function to have a degree of 5 and a positive leading coefficient? explain please!
HELP
_________________________________
Answer: It's the fourth option; f^-1(x)=x^3/125 -7
A water sport shop rents tubes, kayaks, canoes, skis, and rafts. The circle graph below shows the rentals from June.
There were 300 items rented in June. Based on the circle graph, how many of those rentals were tubes or rafts?
A.
180
B.
120
C.
150
D.
225
The required, 180 items rentals were tubes or rafts of 300 items.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The circle graph shows that tubes and rafts made up 60% of the total rentals. If there were 300 items rented in June, then 60% of those rentals were tubes or rafts:
300 items × 60% = 180 items
So the answer is A. 180.
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Which of the following sets of numbers could not represent the three sides of a triangle?
{
10
,
17
,
27
}
{10,17,27}
{
9
,
22
,
30
}
{9,22,30}
{
6
,
16
,
19
}
{6,16,19}
{
4
,
7
,
9
}
{4,7,9}
The set {10,17,27} does not represent the three sides of a triangle,
What are triangles?Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Given the sets for the triangles,
property of triangles says that,
The length of a triangle's two longest sides added together is longer than the third side.
Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.
1: given sides are 10, 17, 27
according to the property sum of 10 and 17 should be greater than 27 but sum is equal to 27,
10 + 17 = 27,
so the sides do not represent the triangle
2: sides are 9, 22, 30
here 9 + 22 > 30
the set represents the triangle.
3: sides 6, 16, 19
6 + 16 > 19
the set represents the triangle.
4: sides 4, 7, 9
4 + 7 > 9
set represents the triangle.
Hence option A is correct.
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Please help I need this
1 Find the measure of angle BOC. I
2 Find the measure of angle DOE.
3 Find the measure of angle AOE
Answer:
see below
Step-by-step explanation:
60+75=135
BOC =180 -135 =45
DOE = BOA =60
AOE =180-DOE =120
According to the audio, what can be inferred from the fairy’s action?
She was appreciative.
She was a gossiper.
She was dishonest.
She was vengeful.
From the audio, what is inferred from the fairy's action is that she was appreciative. The Option A is correct.
What does the word fairy mean?A fairy tale is a story, typically intended for children, that features fantastic and wondrous characters such as elves, goblins, wizards, and even, but not always, fairies. The term "fairy" tale appears to refer to a story's fantastic and magical setting or magical influences, rather than the presence of a fairy character within that story.
Fairy tales are frequently traditional; many were passed down from storyteller to storyteller before being written down in books. Examples of Fairy Tale includes Snow White, Cinderella, Rip Van Winkle, The Twelve Dancing Princesses, Rumpelstiltskin, Thumbelina
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Answer: She was vengeful
Step-by-step explanation:
The audio states that the other fairies were giving the princess positive spells while a fairy that wasn't invited to the party casted an evil spell on the princess, making her sleep for a 100 years. (It's based on the sleeping beauty story)
You are applying fondant to the exterior edges of a large rectangular cake. If the cake's dimensions are 21.9 inches long by 18.3 inches wide, how many inches of fondant do you need?
Answer:
Step-by-step explanation: A rectangle's perimeter formula is P=2(l+w), therefore,
P=2(21.9+18.3)
P=2(40,2)
P=80,4
You will need 80,4 inches of fondant to cover all the edges of the cake
Find the domain of the following piece wise function.
[4,8)
(2,8]
[2,8)
(4,8]
The domain is the second option:
(2, 8]
Which is the domain of the piece wise function?For a function y = f(x), we define the domain as the set of the possible inputs for the function.
Here we have a piecewise function that is defined in the 3 regions:
2 < x ≤ 4
4 < x < 8
x ≥ 8
So the domain is the set of any value larger than 2, and we can write that as:
(2, 8]
We end it at "8" becase is the last defined value and that is the only option that makes sense.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
The three statements about his solution that are true include the following:
1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
2. He did not multiply the numerator and denominator by the correct number to equal 1,500.
5. He should have multiplied the numerator and denominator by 75, not 30, because 20 × 75 = 1,500.
How to determine the true solutions?Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:
here, we have,
10/20 = x/1500
Multiplying the mathematical expression by 75, we have the following:
75 × (10/20) = x/1,500
750/1500 = x/1500
1,500x = (750 × 1,500)
x = (750 × 1,500)/1,500
x = 750.
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-50 + 5/13p. When p = -26
The value of the given expression, -50 + 5/13p, when p = -26 is -60
Evaluating an expressionFrom the question, we are to evaluate the given expression for the given value of p
The given expression is
-50 + 5/13p
and
The given value of p is p = - 26
Substitute the given value of p into the given expression
That is,
-50 + 5/13p
When p = -26, the expression becomes
-50 + 5/13(-26)
Simplify
-50 + 5(-2)
-50 - 10
= - 60
Hence, the value of the expression is -60
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PLEASE HELP QUICKKKK
Answer:
Step-by-step explanation:
If 3<y<7 then,
0 < 14-2y < 8
14 - 2(3) = 8
14 - 2(7) = 0
Canal Industries has provided the following information:
Net income, $260,000
Preferred shares issued, 6,200
Weighted average number of shares of common stock issued, 24,200
Cash dividends declared and paid on common stock, $32,000
Market price per share, $38
Weighted average number of treasury shares of common stock, 4,200
What is Canal's price/earnings ratio?
The Canal's price/earnings ratio is 2.92.
To calculate Canal's price/earnings ratio, we need to find the earnings per share (EPS) first. The EPS can be calculated by dividing the net income by the weighted average number of common shares outstanding.
The weighted average number of common shares outstanding can be calculated as follows:
Weighted average number of common shares outstanding = Total number of common shares - Weighted average number of treasury shares
Weighted average number of common shares outstanding = 24,200 - 4,200 = 20,000
EPS = Net income / Weighted average number of common shares outstanding
EPS = $260,000 / 20,000 = $13
Finally, the price/earnings ratio can be calculated by dividing the market price per share by the EPS:
Price/earnings ratio = Market price per share / EPS
Price/earnings ratio = $38 / $13 = 2.92
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certain date, there had been a total
16,756 Performances of two Shows on broadway,
with 3312 more Performances of Show A than
were there of
Show B. How many Performances
each show?
There were _____ performances for Show A
The system of equations are solved and the number of performers for the show A is 10,034
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as T
Now , the value of T is
The total number of performers in the two shows T = 16,756
A + B = 16,756
The number of performers in show A = 3312 + number of performers in show B
Substituting the values in the equation , we get
A = B + 3,312
On simplifying the equation , we get
A + A - 3,312 = 16,756
Subtracting 3,312 on both sides of the equation , we get
2A = 16,756 + 3,312
2A = 20,068
A = 10,034
Hence , the equation is A = 10,034
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7. Joanna took 35 minutes to and from school. If the journey to school was 5 minutes faster than the return journey, find the time taken: a. to school b. from school
Answer:
Step-by-step explanation: https://flexbooks.ck12.org/cbook/ck-12-middle-school-math-concepts-grade-6/section/6.15/primary/lesson/elapsed-time-msm6/
A paper mill cuts posterboards that are 36 inches long a posterboard is acceptable if the percent error of its length is less than one. 5% what is the range of acceptable length show your work
Answer:
The range of acceptable length is between 35.28 inches and 36.72 inches.
To calculate the range of acceptable length:
Lower bound: 36 in. - (36 in. x 0.05) = 35.28 in.
Upper bound: 36 in. + (36 in. x 0.05) = 36.72 in.
Let A(7,10) and B(-5,5). What is the length of AB
The length of segment AB is determined as 13 units.
What is distance between two points?The distance between two points is the length of the line segment that connects the two points in a plane.
here, we have,
The length of segment AB is the distance between point A and point B, which is calculated as follows;
|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]
where;
x₁ is the x - component of point A
x₂ is the x - component of point B
y₁ is the y - component of point A
y₂ is the y- component of the point B
|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]
|AB| = √[(-5 - 7)² + (5 - 10)²]
|AB| = √[144+25]
|AB| = 13 units
Thus, the length of segment AB is the distance between point A and B.
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solve and graph the inequality 3x < 13
The solution of the inequality 3x < 13 is x < 4.33.
None of the given option is correct.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality,
3x < 13.
Simplifying,
x < 4.33
The graph is given in the attached image.
Therefore, the solution is x < 4.33.
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I’m not sure how to solve this, really need help, would appreciate if you showed work so i could learn how to solve it too thank you
Answer:
There are two solutions:
[tex]\boxed{v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}}\\\\or\\\\\boxed{v = 1.3333.... \text{ and }v= 1.5}\\[/tex]
Step-by-step explanation:
The given equation is :
[tex]\dfrac{2}{v-2}=-6\:+\:\dfrac {1}{v-1}\\\\[/tex]
Find the LCM of the denominators:
LCM = [tex]\left(v-2\right)\left(v-1\right)[/tex]
Multiply by LCM:
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right)[/tex]
Simplify
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right):\quad 2\left(v-1\right)[/tex]
[tex]\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right):\quad v-2[/tex]
So the equality becomes
[tex]2\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+v-2[/tex]
Expand the brackets:
[tex]2\left(v-1\right):\quad 2v-2[/tex]
[tex]\text {Right side becomes: }\\-6\left(v-2\right)\left(v-1\right)+v-2\\Expand \; \left(v-2\right)\left(v-1\right):\quad v^2-3v+2\\\\\text {Right side becomes}\\-6\left(v^2-3v+2\right) + v -2\\= -6v^2+6\cdot \:3v-6\cdot \:2 + v - 2\\\\\\= -6v^2+18v-12+v-2\\\\\text{Simplify}\\= -6v^2+19v-14\\\\\text{Left side}2(v-1= 2v-2\\\\\text{Finally we get}\\2v - 2 = 6v^2+19v-14\\\\[/tex]
Switch sides:
[tex]-6v^2+19v-14=2v-2[/tex]
Move 2 from right to left(sign changes)
[tex]-6v^2+19v-14 + 2 =2v\\\rightarrow -6v^2+19v-12=2v\\\\[/tex]
Move 2v to left side(sign changes)
[tex]-6v^2+19v-12-2v = 0\\\\\rightarrow -6v^2+17v-12=0\\\\[/tex]
This is a quadratic equation which can be solved with a quadratic equation calculator. I used a calculator to solve this:
The solutions are:
[tex]v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}\\\\\\\text{In decimal these would be}\\\\v = 1.3333.... \text{ and v}= 1.5\\[/tex]
Please help ASAP
Find the area of the rectangle
What is the area of the rectangle?
Need help here with solution please
The solution is Option D.
The derivative of the function is given by the equation f' ( x ) = -x / ( √5-x² )
What is implicit differentiation?In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately
Given data ,
Let the function be represented as f ( x )
Substituting the values in the equation , we get
f ( x ) = √ ( 5 - x² )
Now , the derivative of the function is f' ( x )
f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( d/dx ) ( -x² )
On simplifying the equation , we get
f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( -2x )
On further simplification , we get
f' ( x ) = ( -2x/2 ) 1 / √( 5 - x² )
f' ( x ) = -x / ( √5-x² )
Hence , the derivative of the function is f' ( x ) = -x / ( √5-x² )
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