Two possible ways to write 9/10 as a sum of fractions are 1/2 + 4/5 and 3/5 + 3/10.
To write9/10 as a sum of fragments, we need to find two fragments with a common denominator that add up to9/10. One way to do this is to express9/10 as the sum of two fragments with denominators that are multiples of 10. One possible way to do this is = 1/24/5 Both fragments on the right- hand side have denominators that are multiples of 10, and when we add them together, we get9/10.
9 = 2x + y
We can then solve for x and y by trying different values until we find a solution that works. One possible solution is x=3 and y=3:
9/10 = 3/5 + 3/10
3/5 + 3/10 = 6/10 + 3/10 = 9/10
Since 9/10 is equal to 9/10, we have shown that 9/10 can be written as a sum of fractions.
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A hotel has four elevators. One of them
is a freight elevator. When pressing the
button, one of the elevators randomly
services your floor. If you use the
elevators seven times, what is the
probability that you use the freight
elevator exactly four times?
O 57.68%
O 5.768%
O 68%
O 5.6%
On solving the provided question, we can say that probability, P( use the freight elevator exactly four times) = 4/7 *100 = 57.1428571429 %
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
the favorable out come is 4 times
total outcomes = 7 times
Probability, P( use the freight elevator exactly four times) = 4/7 *100 = 57.1428571429 %
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What is the area and uncertainty in area of one side of a rectangular wooden board that has a length of (21.4±0.4)cm
2
and a width of (9.8 ±0.1)cm ? (Give your answers in cm
2
.) (4.9□±cm
2
(b) What If? If the thickness of the board is (1.2±0.1)cm, what is the volume of the board and the uncertainty in this volume? (Give your answers in cm³.) (4.9□±4.9□∣cm
3
The volume of the wooden board is (249.984 ± 1.414) cm³.
Given information: Length of rectangular wooden board, l = (21.4 ± 0.4) cm
Width of rectangular wooden board, w = (9.8 ± 0.1) cm
(a) The area and uncertainty in area of one side of the rectangular wooden board: Area of the wooden board, A = lw
Putting the given values, we get,
A = (21.4 ± 0.4) cm × (9.8 ± 0.1) cm= (21.4 × 9.8) ± (0.4 × 9.8 + 0.1 × 21.4 + 0.1 × 0.4) cm²= 209.72 ± 1.09 cm²
Therefore, the area of one side of the rectangular wooden board is (209.72 ± 1.09) cm².
(b) The volume and uncertainty in volume of the rectangular wooden board: Volume of the wooden board, V = lwh
Given thickness of wooden board, h = (1.2 ± 0.1) cm
Putting the given values, we get,V = (21.4 ± 0.4) cm × (9.8 ± 0.1) cm × (1.2 ± 0.1) cm= (21.4 × 9.8 × 1.2) ± (0.4 × 9.8 × 1.2 + 0.1 × 21.4 × 1.2 + 0.1 × 0.4 × 1.2) cm³= 249.984 ± 1.414 cm³
Therefore, the volume of the wooden board is (249.984 ± 1.414) cm³.
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2- x+2/x-3 - x-6/x+3
A=
B=
It can be written in the form is like ax+b/x^2-9
so we only need the A and B.
Please reply to this ASAP
Step-by-step explanation:
so, if I understand your text correctly, we need to bring
2 - (x+2)/(x-3) - (x-6)/(x+3)
into a form
(ax + b)/(x² - 9)
what we notice immediately is
(x+3)(x-3) = x² - 9
that makes sense, as we want to transform all terms into fractions with the same denominator.
and the necessary "criss-cross" multiplication leads to (x² -9) as denominator.
so, let's transform every term to a fraction with that denominator, and then we add or subtract them all up as per the original expression.
2 :
multiply by (x²-9)/(x²-9)
2(x²-9)/(x²-9) = (2x²-18)/(x²-9)
(x+2)/(x-3) :
multiply by (x+3)/(x+3)
(x+2)(x+3)/(x²-9) = (x²+3x+2x+6)/(x²-9) =
= (x²+5x+6)/(x²-9)
(x-6)/(x+3) :
multiply by (x-3)/(x-3)
(x-6)(x-3)/(x²-9) = (x²-3x-6x+18)/(x²-9) =
= (x²-9x+18)/(x²-9)
for the whole expression we get then
(2x²-18)/(x²-9) - (x²+5x+6)/(x²-9) - (x²-9x+18)/(x²-9) =
= (2x²-x²-x² -5x+9x -18-6-18)/(x²-9) =
= ( 0 + 4x - 42 )/(x²-9)
a = 4
b = -42
Find the volume of a pyramid with a square base, where the perimeter of the base is 12. 8\text{ m}12. 8 m and the height of the pyramid is 12. 5\text{ m}12. 5 m. Round your answer to the nearest tenth of a cubic meter.
A pyramid with a square base has a volume of 42.67 cubic meters.
What is perimeter?A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter. The perimeter of a shape is the distance around its edge. A shape's perimeter is always computed by summing the lengths of each of its sides. The perimeter of a thing is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length.
Here,
perimeter=12.8 m
side=12.8/4
=3.2 m
volume=1/3*3.2²*12.5
=1/3*128
=42.67 m³
The volume of a pyramid with a square base is 42.67 m³.
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3 raise to the power 0 + 2 raised to the power negative 2 . find this value leaving your answer in standard form.
Answer:
5
Step-by-step explanation:
3 to the power of 0 is 1
Why? n to the power of 0 is 1 independent of n
2 to the power of 2 is 4
Why? 2 × 2 = 4
So it's 1 + 4 = 5
I hope this helps you :)
Please help solve this! Thank you in advance!
4) a) Expand the function f =y' x + x'z with respect to a) x b) y c) z = b) Design the function for each case by using only 2-to-1 multiplexer
The expansion of the function f = y'x + x'z with respect to x yields (x + y')(x + z'), and the expansion with respect to y gives (x' + y)(x + z').
(a) To expand the function f = y'x + x'z with respect to x, we use the distributive property and apply De Morgan's law to simplify the expression:
f = y'x + x'z
= x'y + x'z
= (x'y)'(x'z)' [Using De Morgan's law]
= (x + y')(x + z') [Using De Morgan's law again]
(b) Designing the function using a 2-to-1 multiplexer for the case of expanding f with respect to x involves using the inputs x, y, and z as the select lines of the multiplexer. The inputs x + y' and x + z' will be connected to the data inputs of the multiplexer, and the output of the multiplexer will be the expanded function f.
(c) Similarly, for expanding f with respect to y, the expansion is:
f = y'x + x'z
= xy' + x'z
= (xy')'(x'z)' [Using De Morgan's law]
= (x' + y)(x + z') [Using De Morgan's law again]
For this case, the inputs x', y, and z will serve as the select lines of the 2-to-1 multiplexer. The inputs x' + y and x + z' will be connected to the data inputs, and the output of the multiplexer will represent the expanded function f.
In both cases, the 2-to-1 multiplexer is used to implement the logic function by selecting the appropriate data inputs based on the select lines, which are derived from the expansion of the function with respect to the corresponding variable.
In conclusion, the expansion of the function f = y'x + x'z with respect to x yields (x + y')(x + z'), and the expansion with respect to y gives (x' + y)(x + z'). By utilizing 2-to-1 multiplexers, the expanded functions can be designed by connecting the appropriate data inputs to the multiplexer based on the select lines derived from the expansions. This allows for the implementation of the logic functions using multiplexers, providing a compact and efficient circuit design.
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Reptile stickers come in sheets of 10 and fish stickers come in sheets of 25. Antonio buys the same
number of both types of stickers and he buys at least 100 of each type.
What is the least number of sheets of each type he might buy?
Antonio might buy
sheets of reptile stickers and
sheets of fish stickers.
100 is the least number of sheets of each type he might buy given that reptile stickers come in sheets of 10 and fish stickers come in sheets of 25 and Antonio buys the same number of both types of stickers and he buys at least 100 of each type. This can be obtained by finding LCM(Least Common Multiple) of 10 and 25 and identifying the multiple nearest to 100.
What is the least number of sheets of each type he might buy?Here in the question it is given that,
Reptile stickers come in sheets of 10Fish stickers come in sheets of 25Antonio buys the same number of both types of stickersHe buys at least 100 of each typeWe have to find the least number of sheets of each type he might buy.
First we have to find the LCM(Least Common Multiple) of 10 and 25
10 = 2 × 5
25 = 5 × 5
LCM(10,25) = 2 × 5 = 50
But he buys at least 100 of each type, then we recall the multiples of 18 to find the least number which is nearest to 100.
Multiples of 50 = 50, 100, 150,...
The number nearest to 100 is 100 itself.
Hence 100 is the least number of sheets of each type he might buy given that reptile stickers come in sheets of 10 and fish stickers come in sheets of 25 and Antonio buys the same number of both types of stickers and he buys at least 100 of each type.
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Select the two statistical questions that Gary could ask,
A How old is your school?
B How many pets do you have?
C What is your favorite flavor of ice cream?
D How many states are in the United States?
E In what year was the Declaration of Independence signed?
(Ignore the blue part)
Answer:
the 2 statistical questions are B and C
To get from one term to the next in a sequence, we multiply by 2 and then
add 4.
The third term in the sequence is 48.
What is the first term in the sequence?
Answer: the first term in the sequence is 9.
Step-by-step explanation:
Let the primary term be x.
At that point the moment term is 2x + 4.
And the third term is 2(2x + 4) + 4 = 4x + 12.
Since the third term is given as 48, we will set up an condition and unravel for x:
4x + 12 = 48
4x = 36
x = 9
An object with negligible air resistance is dropped from a plane. During the first second of fall, the object falls 4.9 meters; during the second second, it falls 14.7 meters; during the third second, it falls 24.5 meters; during the fourth second, it falls 34.3 meters. If this arithmetic pattern continues, how many meters with the object fall in 10 seconds?
i know the answer is 490 meters but i don’t know how to get there. PLEASE HELP!!
Answer:
The object falls 4.9 meters in the first second, 14.7 meters in the second second, 24.5 meters in the third second, and 34.3 meters in the fourth second. We can see that the object is falling 9.8 meters per second per second, which is the acceleration due to gravity.
To find how far the object falls in 10 seconds, we can use the formula for the sum of an arithmetic sequence:
S = n/2(2a + (n-1)d)
where S is the sum of the sequence, n is the number of terms, a is the first term, and d is the common difference between the terms.
In this case, we have:
n = 10 (since we want to find the total distance in 10 seconds)
a = 4.9 (the first term is the distance fallen in the first second)
d = 9.8 (the common difference is the acceleration due to gravity)
Plugging in these values, we get:
S = 10/2(2(4.9) + (10-1)9.8) = 10/2(9.8 + 88.2) = 10/2(98) = 490
Therefore, the object will fall a total of 490 meters in 10 seconds.
The object will fall 495 meters in 10 seconds.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
We can see that the object is falling with a constant acceleration of 9.8 meters per second squared (which is the acceleration due to gravity near the surface of the Earth).
Each second, the distance the object falls increases by an additional 9.8 meters.
So, during the fifth second, the object will fall 44.1 meters (34.3 + 9.8), during the sixth second it will fall 53.9 meters, during the seventh second it will fall 63.7 meters, during the eighth second it will fall 73.5 meters, during the ninth second it will fall 83.3 meters, and during the tenth second it will fall 93.1 meters.
The total distance the object will fall in 10 seconds is:
= 4.9 + 14.7 + 24.5 + 34.3 + 44.1 + 53.9 + 63.7 + 73.5 + 83.3 + 93.1
= 495 meters
Thus,The object will fall 495 meters in 10 seconds.
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The expression 42 plus 57 shows how much money Nate spent at a store. Which expression also shows how much money Nate spent?
Make a bowl of Pho wit 3 ingredients that cost 14.50.
Will choose brainliest
Answer: $8 bowl, noodles, bean sprouts, beef
Step-by-step explanation:
Write the quotient and remainder when we divide (x^3 -4x^2 + 2x + 5) by (x - 2)
Answer:
Step-by-step explanation:
Sorry I can't explain how it is done. It is very difficult to explain on paper.
Expand the following
Answer:
A) 3x +15
B) 8x -2
C) 20x + 10
D) 4x - 8y
Step-by-step explanation:
A) 3x+3 x 5 = 3x + 15
B) 2 x 4x -2 = 8x -2
C) 5 x 4x +5 x 2 = 20x + 10
D) 4x -4 x 2y = 4x - 8y
(Hope this helps can I pls have brainlist (crown)☺️)
The price of an apple is $1.25. If you get 20% discount, how much do you have to pay?
Could anyone give me a formula or insight on how to solve this problem?
16 is the diameter of circle .
What is a circle, exactly?
The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape.
The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the centre at all angles.
In triangle
10² = 6² + o²
100 = 36 + o²
100 - 36 = o²
64 = o²
o = 8
diameter = 8 * 2 = 16
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5) There are 7,213 applicants Only one half of the applicants which is about will be accepted in the program for the astroment progogiem
In a case whereby there are 7213 applicants for the astronaut program only one half of the applicants which is about 3607 applicants will be accepted into the program.
How can the number of the applicants be determined?The concept that will be used here is multiplication. One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.
The symbols for multiplication are cross (), asterisk (*), and dot (). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).
Total applicants =7213 applicants
Then one half of the applicants = 1/2 of 7213
=7213/2
= 3607 applicants
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complete question:
There are 7213 applicants for the astronaut program only one half of the applicants which is about ______will be accepted into the program
pls help if you can asap!!!!
Answer: x= 6
Step-by-step explanation:
Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.
You can see they do not look the same so they add up to equal 180
12x + 3 +105 = 180
12x + 108 = 180
12x = 72
x = 6
Compute f′(a) algebraically for the given value of a. f(x)=−7x+5;a=−6
The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.
To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.
This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.
Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:
f(x) = −7x + 5
⇒ f′(x) = d/dx (−7x + 5)
⇒ f′(x) = d/dx (−7x) + d/dx(5)
⇒ f′(x) = −7(d/dx(x)) + 0
⇒ f′(x) = −7⋅1 = −7
Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7
Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.
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Please help with homework! I don't understand this
Answer:
B.
Step-by-step explanation:
Basic Power Rule: f'(x) = n · xⁿ⁻¹
Step 1: Define
\(\frac{dy}{dx} [6x^{\frac{-2}{3} }]\)
Step 2: Use Basic Power Rule
\(f'(x)=6(\frac{-2}{3})x^{\frac{-2}{3} -1}\)
\(f'(x)=-4x^{\frac{-5}{3}}\)
Step 3: Simplify
\(f'(x)=\frac{-4}{x^{\frac{5}{3} }}\)
\(f'(x)=\frac{-4}{\sqrt[3]{x^5} }\)
show that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.
We have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.
What is rectangle?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Let A and B be two sets in a generalized rectangle R, i.e., R = A x B. The boundary of R, denoted by bd(R), is defined as the closure of the set of points that are not in the interior of R. In other words, bd(R) = cl(R) \ int(R), where cl(R) is the closure of R and int(R) is the interior of R.
To show that bd(R) is the union of finitely many closed generalized rectangles with volume zero, we first note that the closure of R can be expressed as the union of R and its boundary, i.e., cl(R) = R ∪ bd(R). Therefore, it suffices to show that R can be expressed as the union of finitely many closed generalized rectangles with volume zero and that bd(R) can also be expressed as the union of finitely many closed generalized rectangles with volume zero.
Let (a,b) be a point in R. Then there exists an open ball B((a,b), r) around (a,b) that is contained in R, where r > 0. Without loss of generality, we can assume that r is small enough so that B((a,b), r) is a generalized rectangle. Since B((a,b), r) is open, it follows that int(R) is the union of all such generalized rectangles. Therefore, R can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such generalized rectangles.
Next, we show that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero. Let (a,b) be a point in bd(R). Then every open ball B((a,b), r) around (a,b) contains points both in R and in the complement of R. By definition of bd(R), the closure of B((a,b), r) intersects both R and the complement of R. Therefore, B((a,b), r) can be expressed as the union of two closed generalized rectangles, one contained in R and one contained in the complement of R. It follows that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such balls B((a,b), r) and their decompositions into closed generalized rectangles.
Therefore, we have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.
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f () = 6x + 4. Find the inverse of f(x).
Answer:
F-1 (x)=1/6x-2/3
Step-by-step explanation:
Use substitution, Interchange the variables, Swap the sides, movthe constant to the right, Divide both sides, Use substitution, and youll find your solution. By the way the -1 is in scientific notation!
A street sign that is 8 feet tall casts a shadow that is 5 feet long. At the same time, a nearby tree casts a shadow that is 28 feet long. What is the height of the tree?
Answer:
44.8 feet
Step-by-step explanation:
What is 12 1/2% of 300
Answer:
37.5
Step-by-step explanation:
Answer: 37.5
Step-by-step explanation:
12.5% of 300=37.5
literally help meee because I don't understand
Answer and Step-by-step explanation:
You are being asked to find the area of a trapezoid. The area of a trapezoid is:
\(\frac{a+b}{2}\) × h
Where:
a = Top base
b = Bottom base
h = Height
Plug in the values given to you via from the page.
\(\frac{7+11}{2} (3)\\\\\\\frac{18}{2}(3)\\\\(9)(3) = 27\)
The answer (the area) is 27 \(cm^2\).
#teamtrees #PAW (Plant And Water)
Rewrite the following without an exponent.
(5/7)-1
The expression (5/7)^-1 can be written without an exponent as 8/5.
How can the exponent be written?Exponents have a number of important properties, such as the product rule (a^m × a^n = a^(m+n)) and the power rule ((a^m)^n = a^(m*n)). They are used in a wide range of mathematical contexts, including algebra, calculus, and geometry.
Given that (5/8)^-1, then we can deduced that the negative exponent is the samething as putting it in the denominator, which can be exprtessed as;
=[1/ (5/8)]
=[1 ÷ (5/8)]
[1 * 8/5]
=8/5
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Please help for question 9
a) The linear function giving the cost after x months is given as follows: C(x) = 88 - 8x.
b) The cost of the shoes after 8 months is given as follows: $24.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.Each month, the balance decays by $8.00, hence the slope m is given as follows:
m = -8.
Hence:
y = -8x + b.
When x = 1, y = 80, hence the intercept b is given as follows:
80 = -8 + b
b = 88.
Hence the function is:
C(x) = 88 - 8x.
The cost after 8 months is given as follows:
C(8) = 88 - 8(8) = 88 - 64 = $24.
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a pita ya or dragon fruit is a tropical fruit with pink skin and pulp filled with tiny black seeds the weight of a pitaya is 1x10~3 ounces what is the weight of the pitaya seed in standard form
Answer:
To convert the weight of the pitaya seed from ounces to standard form, we need to express it in scientific notation.
Given: Weight of the pitaya seed = 1x10^(-3) ounces
In standard form, the weight can be written as a decimal number between 1 and 10 multiplied by a power of 10.
1x10^(-3) in standard form is 0.001.
Therefore, the weight of the pitaya seed in standard form is 0.001.
The weight of a pitaya, or dragon fruit, is given as 1x10^3 ounces in scientific notation, which converts to 1000 ounces in standard form.
Explanation:Scientific notation is a concise way to express very large or small numbers, using powers of 10. In this case, the weight of a pitaya, represented as 1x10^3 ounces in scientific notation, can be easily converted into standard form. The exponent, 3 in this instance, indicates the number of places the decimal point should be moved. Therefore, an exponent of 3 means shifting the decimal point three places to the right. Consequently, the weight of the pitaya in standard form is 1000 ounces. This method provides a clear and efficient way to handle large numbers, making complex calculations and comparisons more manageable.
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If there are 63 peaches in 7 bowls, how many peaches are in one bowl?
Answer:
9
Step-by-step explanation:
63/7 is 9
Answer:
9
Step-by-step explanation:
Divide 63 and 7
63/7=9
What is the maxima set from the following set of points {(7,2),(3,1),(9,3),(4,5),(1,4),(6,9),(2,6),(5,7),(8,6)}
The maxima set from the given set of points is {(6,9),(5,7),(8,6)}.
The maxima set is the set of points in a given set that have the maximum y-coordinate values.
To find the maxima set from the set of points {(7,2),(3,1),(9,3),(4,5),(1,4),(6,9),(2,6),(5,7),(8,6)}, we need to determine the points with the highest y-coordinate values.
From the given set, the points with the maximum y-coordinate values are (6,9), (5,7), and (8,6). These points have the highest y-coordinate values of 9, 7, and 6 respectively.
Therefore, the maxima set from the given set of points is {(6,9),(5,7),(8,6)}.
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