Designing a Garden
In this activity, you will apply mathematics to problems arising in everyday life and communicate
mathematical ideas using multiple representations.
Part
Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of
the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width
to exceed the width of the tomato patch by 5 feet.
Let x represent the length, in feet, of the square tomato patch.
Question 1
? Question
Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.
Enter the correct answer in the box. Y= ?+?
Answers
The length of the vegetable garden as a function of its length will be given as: y = 3x + 2.
The expression of the garden width in terms of the width of the tomato patch is given as y = x + 5
How to illustrate the equation?Let the length of the garden be y
Let the length of the tomato patch be x
If Melissa wants the length of the garden to exceed three times the length of the tomato patch by 2 feet, the length of the vegetable garden as a function of its length will be given as: y = 3x + 2
If she also wants the garden's width to exceed the width of the tomato patch by 5 feet, the expression of the garden width in terms of the width of the tomato patch is given as: y = x + 5
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Related Questions
What is the total amount required to pay off a loan of $16000 plus interest at the end of 8 years if the interest is compounded half- yearly and the rate is 14% p.a.
Answers
The total amount required to pay off the loan at the end of 8 years would be $37,784.09.
To calculate the total amount required to pay off a loan of $16,000 with an interest rate of 14% per annum compounded half-yearly over 8 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the total amount, P is the principal (or loan amount), r is the interest rate per annum, n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, P = $16,000, r = 14%, n = 2 (since the interest is compounded half-yearly), and t = 8 years.
Plugging in the values, we get:
A = $16,000(1 + 0.14/2)^(2*8)
= $37,784.09
Therefore, the total amount required to pay off the loan at the end of 8 years would be $37,784.09, including the principal amount of $16,000 and the accumulated interest.
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Please help ASAP! 20 points!!
Answers
Answer:
They are increasing at the same rate.
Describe the shape of the distribution.
A. It is symmetric.
B. It is uniform.
C. It is bimodal.
D. It is skewed.
Answers
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in the simplest form 15,11,7
Answers
Step-by-step explanation:
the sequence is arithmetic due to the common difference that is equal
d=11-15=7-11=-4
a(n) = a1 +(n-1)d
a1=15
Then :
a(n) = 15+(n-1)-4
hope this helps
Answer: I think the answer is arithmetic sequence and the common ration is equal to 1/3.
Step-by-step explanation:
The one-to-one functions g and h are defined as follows.g={(-9, -3), (2, -5), (3, -6), (5, 2)}h(x) = 4x -13Find the following.
Answers
We have been given the domain-range pairs of the function g.
We have a pair of domain-range pair as (5, 2)
Therefore,
\(\begin{gathered} g^{-1}(2)=5 \\ \text{The }g^{-1}\text{ refers to the inverse and indicates that the domain and range places are } \\ interchanged. \\ \text{The range and domain of }g^{-1}\text{ is the domain and range of g respectively} \end{gathered}\)Next, we find
\(\begin{gathered} h^{-1}(x)\text{ where h(x)=}4x-13 \\ We\text{ can call h(x) = y} \\ \text{therefore, y = }4x-13 \\ \text{Making x the subject of the formulae yields} \\ y+13=4x\text{ | Adding 13 to both sides} \\ x=\frac{y+13}{4}\text{ | Dividing both sides by 4} \\ h^{-1}(x)=\frac{y+13}{4} \\ \text{Lastly, we interchange y with x} \\ h^{-1}(x)=\frac{x+13}{4} \end{gathered}\)Lastly, we find:
\(\begin{gathered} (h.h^{-1})(x)=\frac{x+13}{4}\times4x-13 \\ (h.h^{-1})(1)=\frac{1+13}{4}\times4(1)-13 \\ (h.h^{-1})(1)=\frac{14}{4}(4-13) \\ (h.h^{-1})(1)=\frac{14(-9)}{4}=-\frac{63}{2}=-31.5_{} \end{gathered}\)1. When is it best to solve a system of equations using graphing?
2. When is it best to solve a system of equations using substitution?
3. When it is best to solve a system of equations using elimination? When it is
Answers
1. You can solve a system of equations using graphs when there are no decimals or fractions in the equations. This can allow you to almost precisely plot a graph, and determine the values of the variables.
2. You can use the substitution method when one (or both) of the equations is already solved for one of the variables.
3. Elimination is best used when the equations are written in the form Ax + B = C, and also when the coefficients are values not equal to 1.
convert x>4 to interval notation
Answers
Converting x > 4 to interval notation, we have:
\((\text{ -}\infty\text{ , 5 ) }U\text{ ( 5, }\infty\text{ )}\)
15x-8-3x=16 pls help
Answers
Answer:
x=2
Step-by-step explanation:
Combine like terms, add 8 to both sides of the equation, simplify, divide both sides by the same term, simplify
Answer:
x = 2
Step-by-step explanation:
1. Combine like terms
15x - 8 - 3x = 16
1 2 − 8 = 1 6
2. Add 8 to both sides of the equation
1 2 − 8 = 1 6
+8 +8
3. Simplify
12x = 24
12x/12 = 24/12
x = 2
The sum of two polynomials is –yz2 – 3z2 – 4y 4. if one of the polynomials is y – 4yz2 – 3, what is the other polynomial? –2yz2 – 4y 7 –2yz2 – 3y 1 –5yz2 3z2 – 3y 1 3yz2 – 3z2 – 5y 7
Answers
Polynomial are expression that have a leading degree of 3. The other polynomial function will be 3yz^2 – 3z^2 – 4y^4 - y + 3
Difference of polynomialsPolynomial are expression that have a leading degree of 3. Given the following expression
Sum = –yz^2 – 3z^2 – 4y^4.
One of the polynomial = y – 4yz^2 – 3
Required
The other polynomial
Let the unknown polynomial be "a" such that:
a = –yz^2 – 3z^2 – 4y^4 - (y – 4yz^2 – 3)
Expand
a = –yz^2 – 3z^2 – 4y^4 - y + 4yz^2 + 3
a = 3yz^2 – 3z^2 – 4y^4 - y + 3
Hence the other polynomial function will be 3yz^2 – 3z^2 – 4y^4 - y + 3
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Answer: D. or 3yz^2-3z^2-5y+7
Step-by-step explanation: got it right on edge
what two situations involving rational exponents or radicals will never result in a negative real soltution
Answers
Answer:
There are two situations involving rational exponents or radicals that will never result in a negative real solution:
Even-indexed roots: If we take the square root, fourth root, sixth root, etc. of a non-negative real number, the result will always be non-negative. For example, the square root of 9 is 3, and the fourth root of 16 is 2, both of which are non-negative. This is because even-indexed roots always produce a non-negative result, regardless of the sign of the original number.
Exponents with even denominators: If we raise a non-negative real number to an exponent with an even denominator, the result will always be non-negative. For example, (4^2/4) is equal to 4, which is non-negative. This is because any negative base raised to an even power results in a positive number, and any positive base raised to an even power also results in a positive number. Therefore, any exponent with an even denominator will always produce a non-negative result, regardless of the sign of the original number.
for the demand function, q=-5p 1200, determine the price p, that maximizes revenue
Answers
The price that maximizes revenue is p = 120.
The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.
Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:
R = p × q
R = p × (-5p + 1200)
To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.
dR/dp = -10p + 1200 = 0
Solving this equation for p:
-10p + 1200 = 0
-10p = -1200
p = -1200 / -10
p = 120
Therefore, the price that maximizes revenue is p = 120.
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The primary purpose of the passage is to show how
the author
(A) discovered Black women’s history when she
was in graduate school
(B) became a historian to help Black people in
America achieve social justice
(C) developed her research skills by undertaking
a challenging project
(D) became a more renowned scholar due to the
influence of two interesting individuals
(E) came to view Black women as a worthy subject
for historical analysis
Answers
The primary purpose of the passage is to show how the author discovered Black women’s history when she was in graduate school.
What was Black women’s history?
People of color play played numerous significant parts in U.S. history since the times of the American Revolution. A large number of these ladies are key figures in the battle for social liberties, however they have likewise made significant commitments to human expression, science, and common society. People of color play played numerous significant parts in U.S. history since the times of the American Revolution. A considerable lot of these ladies are key figures in the battle for social liberties, however they have likewise made significant commitments to human expression, science, and common society. Even with orientation and racial predisposition, African American ladies have broken obstructions, rocked the boat, and battled for equivalent privileges for all. The achievements of dark female verifiable figures in governmental issues, science, artistic expression, and more keep on affecting society.
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x+4
Identify the domain of the following rational expression: x²+x-12
O All real numbers except - 3.
O All real numbers except 4 and -3.
O
All real numbers except -4 and 3.
O All real numbers except 3.
Answers
Answer:
Step-by-step explanation:
(x + 4)/(x+4)(x-3)
= 1/(x-3)
solution is option 4
SOLUTION: How much must you deposit into an account that pays 8.75% annual interest, compounded monthly, to have a balance of $1000 after one year?
Answers
Answer:
$917
Step-by-step explanation:
Let the money be $x
x×(1+(8.75%/12))^(12)=1000
x=916.5097877016
x=917(cor.to 3 sig.fig.)
Suppose Jessica places $4500 in an account that pays 6% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
$[]
(b) Find the amount in the account at the end of 2 years.
$0
X
S
Answers
(a) To find the amount in the account at the end of 1 year, we use the formula:
A = P(1 + r)^n
where A is the amount in the account at the end of the year, P is the principal (the initial amount deposited), r is the interest rate as a decimal, and n is the number of times the interest is compounded in a year. In this case, P = $4500, r = 0.06 (since the interest rate is 6%), and n = 1 (since the interest is compounded once a year). So, we have:
A = $4500(1 + 0.06)^1
= $4500(1.06)
= $4770
Therefore, the amount in the account at the end of 1 year is $4770.
(b) To find the amount in the account at the end of 2 years, we again use the formula:
A = P(1 + r)^n
However, in this case, n = 2 (since the interest is compounded twice in 2 years). So, we have:
A = $4500(1 + 0.06)^2
= $4500(1.1236)
= $5061.20
Therefore, the amount in the account at the end of 2 years is $5061.20.
Write in slope-intercept form with the given information. Show all work. Passes through (-8,3) with a slope of -2
Answers
Answer:
y=-2x-13
Step-by-step explanation:
y=mx+b
3=-2(-8)+b
3=16+b
3-16=b
-13=b
Graph the line that passes through the points (-9,5) and (-9,-5) and
determine the equation of the line.
Answers
Answer:
x=-9
Step-by-step explanation:
M(slope)=y2-y1/x2-x1
m=-5-5/-9+9
m= -10/0
This means the slope is undefined. Whenever the slope is undefined, the line is vertical and is passing through the x-axis and parallel to the y-axis. Take the given coordinate (-9,5) and all you do is put x= -9. That's the equation of the line.
what is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters? Write Your Answer In Terms Of pi.
Answers
Given the word problem, we can deduce the following information:
1. The diameter of the circle is 3 meters.
2. The side length of the square is 3 meters.
To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:
\(A_{circle}=\frac{\pi d^2}{4}\)where:
d=diameter
\(\text{A}_{square}=d^2\)where:
d=side length
The figures are shown below:
Based on this, the difference of areas would be:
\(\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ \end{gathered}\)Next, we plug in d=3:
\(\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ =(3)^2-\frac{\pi(3)^2}{4} \\ =9-\frac{9\pi}{4} \end{gathered}\)Therefore, the difference in areas is:
\(9-\frac{9\pi}{4}\)
how is jamal's wealth affected by an investment when the stakes are small? it is affected by a small amount in either a positive or a negative direction. it is affected more if the probability is great than if the probability is small. it is impacted more if the return is positive than if it is negative. it is impacted by a great deal in either a positive or a negative direction.
Answers
Jamal's wealth will be affected positively and negatively depending on the investment probability
If Jamal makes a small investment and the stakes are small, the small amount can affect his wealth in a positive or negative direction. The magnitude of the impact depends on the investment's probability of success and the investment's potential return.
If the probability of success is high and the potential return is positive, the impact on Jamal's net worth could be greater. On the other hand, a low probability of success and a negative potential return may have less impact on Jamal's fortunes.
Ultimately, the impact of a small investment on Jamal's wealth will depend on the specific details of the investment and the associated risks and potential rewards.
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The table below shows the hours the restaurant is open each week.
Monday through Friday 10 A.M.-7 P.M.
Saturday and Sunday 9:30 AM.-8 P.M.
How many hours is the restaurant open each week?
Answers
Answer:
66 hours
Step-by-step explanation:
Monday through Friday is 45 hours
and Saturday and Sunday is 21 hours
a coin is flipped 6 times. if more heads are flipped than tails, the probability that all 6 are heads is , what is the value of ?
Answers
The probability that all 6 flips result in heads is 1/64
The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0
For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,
P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64
P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)
P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64
Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.
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choose what the expressions below best represent within the context of the word problem. if sarah is 24 years younger than her mother and if the sum of their ages is 68, how old is sarah? x best represents sarah's age . x - 24 best represents the mother's age .
Answers
The expressions below best represent within the context of the word problem is x + (x - 24) = 68, Sarah's age is 46 years. Mother's age is 46 - 24 = 22. Therefore, Sarah is 46 years old, and her mother is 22 years older than her, making her mother 68 years old.
In the given word problem, we are given two pieces of information about Sarah and her mother's ages. Firstly, we know that Sarah is 24 years younger than her mother. Secondly, we know that the sum of their ages is 68. To find out Sarah's age, we need to represent it using an expression. Let's say Sarah's age is 'x'. Therefore, the expression that best represents Sarah's age is 'x'.
Now, we also need to represent Sarah's mother's age using an expression. As we know that Sarah's mother is 24 years older than her, we can subtract 24 from Sarah's age to get her mother's age. So, the expression that best represents Sarah's mother's age is 'x - 24'.
To find Sarah's age, we can use the sum of their ages, which is 68. We know that Sarah's age is 'x', and her mother's age is 'x - 24'. Therefore, we can write an equation:
x + (x - 24) = 68
Solving this equation, we get:
2x - 24 = 68
2x = 92
x = 46
Hence, Sarah is 46 years old.
In the given word problem, we are asked to find the age of Sarah, knowing that she is 24 years younger than her mother and the sum of their ages is 68. We can use the expressions x and x - 24 to represent Sarah's and her mother's ages, respectively.
Let x represent Sarah's age. Since Sarah is 24 years younger than her mother, we can represent her mother's age as x - 24. According to the problem, the sum of their ages is 68. We can now set up an equation using this information:
x (Sarah's age) + (x - 24) (Mother's age) = 68
Solve the equation to find the value of x, which represents Sarah's age:
x + x - 24 = 68
2x - 24 = 68
Now, add 24 to both sides of the equation:
2x = 92
Next, divide both sides by 2:
x = 46
So, Sarah's age is 46 years. To find her mother's age, we can substitute the value of x in the expression x - 24:
Mother's age = 46 - 24 = 22
Therefore, Sarah is 46 years old, and her mother is 22 years older than her, making her mother 68 years old.
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I’m confused on what number 4 means. Can someone please help?
Answers
Answer:I think you can say like the most bought music in class B is alternative and the lowest one is classical and so on
Step-by-step explanation:
Pls help I don’t have much time.
Answers
Answer:
Dude dont spend 100 points! This place is scamming people
Step-by-step explanation:
Write Down the possible values of x
Answers
Answer:
2,3,4,5,6,7,8
Step-by-step explanation:
In words, the expression 2 ≤ x ≤ 8 translates to
"values of x between and inclusive of 2 and 8"
since we are being asked for integers, the possible values that match this description are 2,3,4,5,6,7,8
Answer:
The correct answer is 3,4,5,6,7
Step-by-step explanation:
The signs < and > infer that the correct answer can it be either of these.
Because x is greater than two but less that eight, the number 3,4,5,6, and 7 are the only possible answers for x
Read the word problem below.
Soni has 196 pencils. If she puts equal amounts of pencils into eight boxes, she has four pencils left. How many pencils does she put in each box?
Which strategy could help solve this word problem?
If x represents the number of pencils per box, solve the equation 4x + 8 = 196.
Divide 196 by the sum of 4 and 8 and find the quotient.
Divide 196 by 4 and check that the remainder is 8.
If x represents the number of pencils per box, solve the equation 8x + 4 = 196.
Answers
Answer:
The last option 8x + 4 = 196
Step-by-step explanation:
8x + 4 = 196
8x = 192
x=192/8
x=24
The strategy that can help solve this word problem is : If x represents the number of pencils per box, solve the equation 8x + 4 = 196.
What is the strategy?A strategy is an approach that leads someone to the nearest of the solution of a problem.
How to solve the equation?Soni has 196 pencils.
Let, one box can accommodate x number of pencils.
Therefore 8 boxes can accommodate 8x number of pencils.
But she has 4 more pencils.
Hence, the required equation is 8x+4=196.
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hello can anyone help me
Answers
Answer:
Its a
Step-by-step explanation:
since its moving 2 units to the right its only moving in the x direction so you just add 2 to each value of x
Let
= 377 , = 148and = 11α
(i) Find the value of such that , , and are linearly dependent.
(ii)State the "Basis Theorem". Use a value that is different from the one found in (i) and apply the "Basis Theorem" to obtain a basis for the three-dimensional space ℝ3 using the vectors , , . Find the coordinates of 235 in terms of the basis. (Use Gaussian Elimination Method to find the coordinates.)
Answers
Summary:
(i) To find the value of α such that the vectors v1, v2, and v3 are linearly dependent, we can set up a system of equations and solve for α.(ii) The Basis Theorem states that any set of linearly independent
(i) To check if v1, v2, and v3 are linearly dependent, we can set up the following equation:
c1v1 + c2v2 + c3v3 = 0,
where c1, c2, and c3 are constants. Substituting the given values of v1, v2, and v3, we have:
c1(3,7,7) + c2(1,4,4) + c3(α,1,1) = 0.
Simplifying this equation, we get the following system of equations:
3c1 + c2 + αc3 = 0,
7c1 + 4c2 + c3 = 0,
7c1 + 4c2 + c3 = 0.
We can solve this system of equations to find the value of α that satisfies the condition.
(ii) The Basis Theorem states that any set of linearly independent vectors that span a vector space can be used as a basis for that vector space. By applying the Basis Theorem to the vectors v1, v2, and v3, we can check if they form a basis for ℝ3. If they do, we can find the coordinates of a given vector, such as (2,3,5), in terms of the basis using Gaussian Elimination.
To apply Gaussian Elimination, we set up the augmented matrix [v1 | v2 | v3 | b], where b is the given vector (2,3,5). Then we perform row operations to obtain the row-echelon form of the augmented matrix. The resulting matrix will allow us to determine the coordinates of b in terms of the basis vectors.
By performing the Gaussian Elimination process, we can find the coordinates of (2,3,5) in terms of the basis vectors.
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There is no value of α that makes the vectors linearly dependent, and the basis for ℝ³ using the vectors [377, 148, 11α] is {v₁, v₂, v₃}, with the coordinates of [2, 3, 5] in terms of the basis found through Gaussian Elimination.
(i) To find the value of α such that vectors v₁, v₂, and v₃ are linearly dependent, we need to determine if there exist scalars a, b, and c, not all zero, such that a(v₁) + b(v₂) + c(v₃) = 0. Substituting the given values, we have a(377) + b(148) + c(11α) = 0. By solving this equation, we can find the value of α that satisfies the condition for linear dependence.
(ii) The Basis Theorem states that any set of linearly independent vectors that spans a vector space forms a basis for that vector space. Using a different value of α than the one found in (i), we can apply the Basis Theorem to determine a basis for ℝ³ using the vectors v₁, v₂, and v₃.
By performing Gaussian Elimination or row reduction on the augmented matrix [v₁ v₂ v₃], we can determine the basis vectors. The coordinates of vector [2 3 5] in terms of the basis can be found by solving the system of equations formed by equating the linear combination of the basis vectors to [2 3 5].
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a. (5) The demand function for a good X is Qx= m-3Px+2Py, where m is income, Px is the price of X, Py is the price of a related good Y and Qx is the demand for X. Income and prices are all positive. X
Answers
The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.
The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.
To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.
Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.
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What is the factor of x³ 3x² 9x 5?
Answers
(x+1) & (x-5) are the factors of given equation.
The given Equation is,
x3- \(3x^{3}\) - 9
Substitute - Substitute means to put something in the place of another and in mathematics substitution means putting numbers in the place of letters. It is used to calculate the value of an expression.Here, If we substitute x =5, in the given equation, then we find
(5)3 - 3(5)3 - 9*5 -5 = 0
x-5 is factor of given equation to find another factor dividing given equation by x-5
we will get =(x2+2x+1) after dividing the equation by x - 5
Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)
=(x+2)2 (x-5)
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