The correct answer should be 32.
To simplify the expression (4 + 3i)(2 - 8i), we can use the distributive property of multiplication.
First, we multiply the real parts of the two complex numbers:
(4)(2) = 8.
Next, we multiply the imaginary parts of the two complex numbers:
(3i)(-8i) = -24i^2.
Remember that i^2 is defined as -1, so we can substitute -1 for i^2:
-24i^2 = -24(-1) = 24.
Now, we combine the real and imaginary parts:
8 + 24 = 32.
Therefore, the simplified expression is 32.
Since none of the given answer choices match the simplified expression, it appears that there may be an error in the options provided. The correct answer should be 32.
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Suppose X is a random variable with pdf "u(x + 1). Random variable Y is defind as Y=g(X). y = g(x) f(x) = {"(x+1) f (x) х X -1 1 -2 Then, (1) Fx0= (a) e 2 (b) 1+e-2 (c)e-1 (d) 1-e-1 (e) None of them
F(x<=0) = 1/2.The correct option is (b) 1+e-2.
The probability distribution function of the random variable X is given by;
`f(x) = {(x+1), for x between -1 and 1, 0 elsewhere}.
The random variable Y is defined as Y = g(X), and y = g(x).
Find the probability that F(X) is less than or equal to 0. That is; F(x <= 0).
To find this, we need to evaluate the integral of the function over the interval (-infinity, 0).
Thus, F(x<=0) = ∫[from -∞ to 0] f(x) dx.
We know that the function is zero for all values of x, except when -1 < x < 1.
Therefore, we can break up the integral into two parts. We get:
F(x<=0) = ∫[from -∞ to -1] 0 dx + ∫[from -1 to 0] f(x) dx
Thus;
F(x<=0) = ∫[from -∞ to -1] 0 dx + ∫[from -1 to 0] (x + 1) dx
F(x<=0) = 0 + [(x^2/2) + x] [from -1 to 0]F(x<=0) = (0 - [(1/2) - 1]) = (1/2)
Therefore, F(x<=0) = 1/2.The correct option is (b) 1+e-2.
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Please consider the following linear congruence, and solve for x, using the steps outlined below. 57x + 13 = 5 (mod 17) (a) (4 points) Use the Euclidean algorithm to find the correct GCD of numbers 57 and 17.
The correct GCD of 57 and 17 is 1, obtained through the Euclidean algorithm.
To find the correct GCD (Greatest Common Divisor) of 57 and 17 using the Euclidean algorithm, we follow these steps:
1.) Divide the larger number (57) by the smaller number (17) and find the remainder:
57 ÷ 17 = 3 remainder 6
2.) Replace the larger number with the smaller number and the smaller number with the remainder:
17 ÷ 6 = 2 remainder 5
3.) Repeat step 2 until the remainder is 0:
6 ÷ 5 = 1 remainder 1
5 ÷ 1 = 5 remainder 0
4.) The GCD is the last nonzero remainder, which is 1.
Therefore, the correct GCD of 57 and 17 is 1.
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How many slices of pizza can I eat for it to be one serving is one serving is 1/4 of the pizza and the pizza itself equal 4 servings
Define the two sets A = {x E Zx = 5a + 2, for some integer a} and B = {y € Z | y = 10b - 3, for some integer b}. . a. Does € A? Does –8 € A? Does – 8 € B? b. Disprove that AB. C. Prove that B CA
a. € A. Yes, 27 € A. To see this, we set a = 5, so that x = 27.
Does –8 € A? No. If –8 were in A, then –8 = 5a + 2 for some integer a. But then a = (–10)/5, which is not an integer, a contradiction.
Does – 8 € B? Yes, we set b = 0, so that y = –3, which is in B.
In either case, we have expressed y as a member of A or C, which means that B CA.
b. AB. We claim that AB. To see this, we assume the contrary, namely, that there is an integer z which is in both A and B. This means that z = 5a + 2 and z = 10b – 3 for some integers a and b. Adding these two equations, we get 7 = 5a + 10b, or 1 = a + 2b. Since the left-hand side is odd, so is the right-hand side, which means that a and b have opposite parity. However, this is impossible since 1 is not odd. Therefore, the assumption that there is such a z is false, which means that AB, as desired. C. B CA. We claim that B CA. To see this, we need to show that every element of B is in A or C. Let y be an element of B, so that y = 10b – 3 for some integer b. If y is even, then we can set a = (y + 1)/5, and we have x = 5a + 2 = y/2 + 3/2. If y is odd, then we can set c = (y + 3)/7, and we have z = 7c – 4 = y/2 + 5/2.
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Use Newton's method with the specified initial approximation X1 to find x3, the third approximation to the solution of the given equation. (Round your answer to four decimal places.) x5 = x2 + 4, X1 = 1 X3 =
The is specified initial approximation X1 x3 is equal to 5.
We absolutely need to accentuate using the recipe in order to find x3 using Newton's method:
In this particular instance, we are informed that x5 is equal to x2 minus 4 and that X1 equals 1. Because we need to find x3, let's use the given equation to find x2.
We can solve for x2 because we have x5: x2 + 4
As of now we have x2 = x5 - 4 from x2 = x5 - 4. This ought to be added to the Newton's system recipe, and afterward we can find x3:
We ought to portray our ability f(x) and its subordinate f'(x) as Xn+1 = Xn - f(Xn)/f'(Xn).
We can now calculate x3 by using X1 = 1 as our underlying estimate: X2 = X1 - f(X1)/f'(X1) = 1 - ((1)2 + 4 - 1)/(- 1) = 1 - (1 + 4 - 1)/(- 1) = 1 + 4 = 5 In this way, x3 is the same as 5.
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Prove that (A intersect B) is a subset of A. Prove that A is a subset of (A union B). Suppose that A is a subset of (B union C), B is a subset of D, and C is a subset of E. Prove that A is a subset of (D union E). Prove for any natural number n and real number x that |sin(nx)| <= n |sin(x)|.
(A intersect B) is a subset of A, A is a subset of (A union B), A is a subset of (D union E), and |sin(nx)| <= n|sin(x)| for any natural number and real number x.
To prove that (A intersect B) is a subset of A, we need to show that every element in (A intersect B) is also in A. Let x be an arbitrary element in (A intersect B). This means x is in both A and B. Since x is in A, it follows that x is also in the union of A and B, which means x is in A. Therefore, (A intersect B) is a subset of A.
To prove that A is a subset of (A union B), we need to show that every element in A is also in (A union B). Let x be an arbitrary element in A. Since x is in A, it follows that x is in the union of A and B, which means x is in (A union B). Therefore, A is a subset of (A union B).
Given A is a subset of (B union C), B is a subset of D, and C is a subset of E, we want to prove that A is a subset of (D union E). Let x be an arbitrary element in A. Since A is a subset of (B union C), it means x is in (B union C). Since B is a subset of D and C is a subset of E, we can conclude that x is in (D union E). Therefore, A is a subset of (D union E).
To prove |sin(nx)| <= n |sin(x)| for any natural number n and real number x, we can use mathematical induction. For the base case, when n = 1, the inequality reduces to |sin(x)| <= |sin(x)|, which is true. Assuming the inequality holds for some positive integer k, we need to show that it holds for k+1. By using the double-angle formula for sin, we can rewrite sin((k+1)x) as 2sin(x)cos(kx) - sin(x). By the induction hypothesis, |sin(kx)| <= k|sin(x)|, and since |cos(kx)| <= 1, we have |sin((k+1)x)| = |2sin(x)cos(kx) - sin(x)| <= 2|sin(x)||cos(kx)| + |sin(x)| <= 2k|sin(x)| + |sin(x)| = (2k+1)|sin(x)| <= (k+1)|sin(x)|. Therefore, the inequality holds for all natural numbers n and real numbers x.
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In the standard (x, y) coordinate plane which equation represents a line through the point (6, 1) and perpendicular to the line with the equation =3/2 + 1?
A.) = −3/2 − 8
B. ) = −2/3 − 3
C.) = −2/3 + 1
D.) = −2/3 + 5
E.) = −3/2 + 10
Answer:
d. -2/3x+5
Step-by-step explanation:
Because the line is perpendicular, the slope must be the inverse of the original slope. The inverse of 3/2 is -2/3. To find the b value, you plug (6,1) into the equation y=-2/3x+b
1=-2/3(6)+b
1=-4+b
5=b
The final equation is y=-2/3x+5
Given the following data set, calculate the values for the five-number summary and fill in the table below: -7, -5, -2, 0, 4, 6, 8, 8, 10, 22, 24 Name Number Minimum First Quartile Median Third Quartile Maximum
The five-number summary for the given data set is: Minimum = -7, First Quartile = 2, Median = 6, Third Quartile = 9, Maximum = 24.
To calculate the five-number summary for the given data set, we need to arrange the data in ascending order and then determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
The given data set: -7, -5, -2, 0, 4, 6, 8, 8, 10, 22, 24
Arranged in ascending order: -7, -5, -2, 0, 4, 6, 8, 8, 10, 22, 24
Now, let's calculate the values for the five-number summary:
Minimum: The smallest value in the data set is -7.
First Quartile (Q1): This represents the median of the lower half of the data set. Since we have 11 data points, Q1 is the median of the first 5 data points. Q1 = (0 + 4) / 2 = 2.
Median (Q2): The median is the middle value of the data set. Since we have an odd number of data points, the median is the 6th value, which is 6.
Third Quartile (Q3): This represents the median of the upper half of the data set. Q3 is the median of the last 5 data points. Q3 = (8 + 10) / 2 = 9.
Maximum: The largest value in the data set is 24.
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A jar contains 10 red marbles, 30 blue marbles, 10 green marbles, and 35 orange marbles. Find the probablilty of picking a marble.
Answer:
6/17
Step-by-step explanation:
The amount of blue marbles is 30, over the total number of marbles, which is 85. 30/85 simplifies to 6/17, which is the probability.
Hopefully this helps - let me know if you have any questions!
WHICH ONE SHOULD I CHOOSE
The true statements are:a. Angle R is congruent to angle R'
b. (P' * Q')/(PQ) = 4
e. (C * Q')/(CQ) = 4
To determine which statements are true about triangle PQR and its image P' * Q' * R' after dilation, let's analyze each statement:
a. Angle R is congruent to angle R': This statement is true. When a triangle is dilated, the corresponding angles remain congruent.
b. (P' * Q')/(PQ) = 4: This statement is true. The scale factor of dilation is 4, which means the corresponding side lengths are multiplied by 4. Therefore, (P' * Q')/(PQ) = 4.
c. (QR)/(Q' * R') = 4: This statement is false. The scale factor of dilation applies to individual side lengths, not ratios of side lengths. Therefore, (QR)/(Q' * R') will not necessarily be equal to 4.
d. (C * P')/(CP) = 5: This statement is false. The scale factor of dilation is 4, not 5. Therefore, (C * P')/(CP) will not be equal to 5.
e. (C * Q')/(CQ) = 4: This statement is true. The scale factor of dilation is 4, so the corresponding side lengths are multiplied by 4. Therefore, (C * Q')/(CQ) = 4.
f. (C * P')/(CP) = (C * R')/(CR): This statement is false. The dilation does not guarantee that the ratios of the distances from the center C to the vertices will be equal.
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I need this done, please I need to pass these six weeks! Thanks
Please help, thank you
y = x + 4 y = −2x − 2 Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form. Source StylesNormal
Answer:
6x
Step-by-step explanation:
A glass bead has the shape of a rectangular prism with a smaller rectangular prism removed. What is the volume of the glass that forms the bead?
Thanks in advance!
Answer:
216 cm³
Step-by-step explanation:
large prism volume = 6 x 6 x 8 = 288 cm³
small cutout volume = 3 x 3 x 8 = 72 cm³
288- 72 = 216 cm³
I and my friends can't find the answer to this and we need help pls.
If AABC is reflected across the y-axis, what are the coordinates of A'?
Answer:
(-4, -2)
Step-by-step explanation:
A is initially (-4, 2); when we reflect over the y-axis, we will change from (x, y) to (x, -y). This gives us (-4, -2).
The coordinates of A' are (-5,-3).
What are coordinates?A coordinate system in geometry is a system that uses one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space. The order of the coordinates matters and they are sometimes identified by their position in an ordered tuple, and other times by a letter, as in "the x-coordinate." In elementary mathematics, the coordinates are assumed to be real numbers, but they can also be complex numbers or members of a more abstract system, such as a commutative ring. The use of a coordinate system allows geometry issues to be transformed into numerical problems and vice versa; this is the foundation of analytic geometry.Solution -If AABC is reflected across the y-axis, the coordinates of A' are (-5,-3).
The reflected graph is given below.
Therefore, the coordinates of A' are (-5,-3).
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Which group of numbers is listed from least to greatest?
-4, -6, -7, -8, -9
-2, 3, 5, -8, 9
7, 4, -6, -7, -9
-2, -1, 0, 4, 9
Answer:
-2, -1, 0, 4, 9
Step-by-step explanation:
A ship sails 20 km due East, then 12 km due South.
Find the bearing of the ship from its initial position.
Give your answer correct to 2 decimal places.
Answer:
Step-by-step explanation:
20km east - 12km south= 8km east
Answer:
its 120.96
Step-by-step explanation:
i dont have any but i know that is the answer
Solve the LP problem using graphical method
Minimize and maximize objective function = 12x + 14y
–2x + y ≥ 6
x + y ≤ 15
x ≥ 0, y ≥ 0
The minimum value of the objective function 12x + 14y is 156 at point C(6, 9).Answer: 156.
Given:
Minimize and maximize objective function = 12x + 14y–2x + y ≥ 6x + y ≤ 15x ≥ 0, y ≥ 0.
The graphical method is a simple and easy method of solving a linear programming problem (LP).
LP issues are represented on a graphical scale using graphical method.
Let's plot the given inequalities on the graph. The graph of all inequalities must be in the first quadrant since x, y ≥ 0.Initially, let us consider x = 0 and y = 0 for (2) and (3) respectively.
(2) y ≤ 15 - x On plotting the line y = 15 - x in first quadrant, we get the following graph:
(3) x ≤ 15 - y On plotting the line x = 15 - y in first quadrant, we get the following graph:Now let's check for the first inequality, -2x + y ≥ 6.It can be written as y ≥ 2x + 6.
On plotting the line y = 2x + 6 in first quadrant, we get the following graph:The region containing common feasible points for all the three inequalities is shown in the figure below:Thus, the feasible region is OACD.The corner points of the feasible region are A(2, 13), B(3.8, 11.2), C(6, 9) and D(15, 0).
We need to determine the minimum and maximum values of the objective function 12x + 14y at each corner point as follows:At point A, 12x + 14y = 12(2) + 14(13) = 194At point B, 12x + 14y = 12(3.8) + 14(11.2) = 184.8At point C, 12x + 14y = 12(6) + 14(9) = 156At point D, 12x + 14y = 12(15) + 14(0) = 180.
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To find the minimum and maximum values of the objective function 12x + 14y subject to the given constraints using graphical method.
Therefore, the minimum value of the objective function is 210 at (10.5, 3) and the maximum value of the objective function is not bounded.
We can follow these steps:
Step 1: Convert the inequality constraints into equation form by replacing the inequality signs with equality signs. So, -2x + y = 6 and
x + y = 15
Step 2: We find the values of x and y for each equation.
Step 3: Plot the two lines on the coordinate axis formed by the values obtained in Step 2.
Step 4: Determine the feasible region by identifying the portion of the plane where the solution satisfies all the constraints. In the present case, it is the region
above the line -2x + y = 6 and
below the line x + y = 15 and
to the right of the y-axis.
Step 5: Plot the objective function 12x + 14y on the same graph.
Step 6: Move the objective function line either up or down until it just touches the highest or lowest point of the feasible region. The point of contact is the solution to the linear programming problem. The graph of the feasible region and the objective function is shown below:
graph
y = 15 - x [-10, 20, -5, 25]
y = 2x + 6 [-10, 20, -5, 25]
y = -(6/7)x + 180/7 [-10, 20, -5, 25](-1/2)x+(1/14)
y = 0.5[0, 20, 0, 20](-1/2)x+(1/7)
y = 1[0, 20, 0, 20]12x + 14
y = 210[0, 20, 0, 20]
Therefore, the minimum value of the objective function is 210 at (10.5, 3) and the maximum value of the objective function is not bounded.
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I'M GIVING BRAINLIEST TO WHOEVER ANSWERS FIRST! GOOD LUCK!
In the following problem, define the variable and then write an expression to represent the number of students at the elementary school. Finally, find the number of students at the middle school if the elementary school has 380 students: The middle school has 24 students less than 3 times the number of students at one of the elementary schools.
Answer:
3x - 24
Step-by-step explanation:
this is probably wrong
Answer:
1116
Step-by-step explanation:
Hey!
We can use the algebraic expression, 3x - 24, to solve.
Just substitute 380 in for x.
⇒3(380) - 24
⇒1140 - 24
⇒ 1116
--------------------------------------------------------------------------------------------------------------
Hope I Helped, Feel free to ask any questions to clarify :)
Have a great day!
More Love, More Peace, Less Hate.
-Aadi x
Any mind helping? 15 Points! :>
Answer:
(63a+54b) and (2xy+11yz)
Step-by-step explanation:
9*7a is 63a
9*6b is 54b
2x*y is 2xy
11z*y is 11yz
Let g be a twice-differentiable function with g'(x) > 0 andg''(x) > 0 for all real numbers x, such that
g(4) = 12 and g(5) = 18. Of the following, which is apossible value for g(6)?
a. 15
b. 18
c. 21
d. 24
e. 27
A possible value for g(6) is 27. The only option greater than 18 is:
e. 27
To determine a possible value for g(6), we can make use of the given information and the properties of the function g(x).
Since g'(x) > 0 for all real numbers x, we know that g(x) is strictly increasing. This means that as x increases, g(x) will also increase.
Furthermore, since g''(x) > 0 for all real numbers x, we know that g(x) is a concave up function. This implies that the rate at which g(x) increases is increasing as well.
Given that g(4) = 12 and g(5) = 18, we can conclude that between x = 4 and x = 5, the function g(x) increased from 12 to 18.
Considering the properties of g(x), we can deduce that g(6) must be greater than 18. Since the function is strictly increasing and concave up, the increase from g(5) to g(6) will be even greater than the increase from g(4) to g(5).
Among the given answer choices, the only option greater than 18 is:
e. 27
Therefore, a possible value for g(6) is 27.
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A dice has 6 sides numbered 1 to 6. What is the odds against rolling a 2 or a 4.
A. 4:2
B. 6:2
C. 2:4
D. 2:6
South Africa reported the number of people employed by sector in a given year as follows (in thousands) 6 678 in the formal business sector (excluding agriculture), 1 492 in the commercial agricultural sector, 653 in subsistence agriculture: 2 865 in the informal business sector and 914 in the domestic service sector Construct a percentage frequency distribution of employment by sector If an employed person is selected at random from the workforce, what is the likelihood that the person earns a living through agriculture?
The probability that an employed person earns a living through agriculture is ≈ 17%.
The frequency is the number of times the data appear within each category.
A percentage frequency distribution is used to summarize data and report on the proportion or percentage of observations that fall within a specified category.
It is the process of showing how often a particular value or category occurs in a set of data.
In order to create a percentage frequency distribution, we will first add all the values together:
Total number of people employed = 6,678 + 1,492 + 653 + 2,865 + 914
= 12,602
Now we can calculate the percentage of people employed in each sector:
Formal business sector =
(6,678 / 12,602) x 100% = 53.0%
Commercial agricultural sector =
(1,492 / 12,602) x 100% = 11.8%
Subsistence agricultural sector =
(653 / 12,602) x 100% = 5.2%
Informal business sector =
(2,865 / 12,602) x 100% = 22.7%
Domestic service sector =
(914 / 12,602) x 100% = 7.3%
The likelihood that an employed person earns a living through agriculture can be calculated by adding the number of people employed in the commercial agricultural sector and the number of people employed in subsistence agriculture.
This gives a total of 2,145 people employed in agriculture.
Therefore, the probability that a person earns a living through agriculture is:
Probability = (2,145 / 12,602) x 100% ≈ 17%
The probability that an employed person earns a living through agriculture is ≈ 17%.
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y=-2x-10
2x+5y=6
i need it solved with the substitution method.
Mrs.sorestam bought one ruler for 0.49$ one compass for 1.49$ and one mechanical pencil 0.49 at the price shown in the table for each of her 12 students
Answer:
12(x−2.57)=0.36
Step-by-step explanation:
Let x represent the initial amount of money Mrs. Sorenstam had to spend on each student.
The cost of the 3 items is:
1.49+0.59+0.49=2.57
The change left for each student will be:
x−2.57
For 12 students, the change left will be
12(x−2.57) which equals 36 cents, according to the problem
So, the equation to represent this situation will be:
12(x−2.57)=0.36
Find all the solutions to [x^3 - 1] = 0 in the ring Z/13Z. Make sure you explain why you have found all the solutions, and why there are no other solutions.
The solution to the equation [x³ - 1] = 0 is x = 1
How to determine the solutions to the equationFrom the question, we have the following parameters that can be used in our computation:
[x³ - 1] = 0
Remove the square bracket in the equation
So, we have
x³ - 1 = 0
Add 1 to both sides
This gives
x³ = 1
Take the cube root of both sides
x = 1
Hence, the solution to the equation [x³ - 1] = 0 is x = 1
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Question is in picture
9 x 10^7 is how many times as large as 3 x 10^3
Answer:
30000 times
Step-by-step explanation:
3 x 10^3 x 30000 = 90000000
Answer:
30000
Step-by-step explanation:
9×10^7 =90000000
also
3×10^3 =3000
divide 90000000 by 3000
=30000
Sketch the curve with the given vector equation. indicate with anarrow the direction in which t increases
r(t) = t^2i +t^4j +t^6k
I have no idea how to go about drawing the vector. I knowthat
x=t^2
y=t^4
z=t^6
and that a possible subsititution can be y=x^2and z=x^3
The vector equation r(t) = t^2i + t^4j + t^6k represents a parametric curve in three-dimensional space. To sketch the curve, we can substitute values of t and plot corresponding points in the coordinate system.
By examining the components of the vector equation, we can observe that x = t^2, y = t^4, and z = t^6. This implies that the curve lies in the x-y-z coordinate system, where the x-coordinate is determined by t^2, the y-coordinate is determined by t^4, and the z-coordinate is determined by t^6.
To start sketching, we can choose a range of values for t and substitute them into the equations. For example, for t = -1, 0, 1, we can calculate the corresponding x, y, and z values.
By plotting these points and connecting them, we can obtain an approximate shape of the curve. Additionally, we can observe that as t increases, the curve moves in the direction of increasing t, which can be indicated by an arrow along the curve.
Note that without specific values for t or a specific range, the sketch will be a general representation of the curve.
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complete this item. (enter letter variables in alphabetical order.) rewrite the expression so that it has no denominator.
The given expression is $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ and we need to rewrite this expression without any denominator in it. Step-by-step explanation: We can use the concept of the Least Common Multiple (LCM) of the denominators to remove the fractions in the expression. By taking the LCM of the denominators of the given expression, we have,$LCM\text{ of }t, u, v = t \cdot u \cdot v$ Now, multiplying each term of the given expression with the LCM $t \cdot u \cdot v$, we get,$\frac{6}{t}\cdot t \cdot u \cdot v+\frac{8}{u}\cdot t \cdot u \cdot v-\frac{9}{v}\cdot t \cdot u \cdot v$$6uv + 8tv - 9tu$$\therefore \text{The given expression without any denominator is } 6uv + 8tv - 9tu.$Thus, we can rewrite the given expression $\frac{6}{t}+\frac{8}{u}-\frac{9}{v}$ without any denominator in it as $6uv + 8tv - 9tu$.
LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM. Take the positive integers 4 and 6 as an illustration.
There are four multiples: 4,8,12,16,20,24.
6, 12, 18, and 24 are multiples of 6.
12, 24, 36, 48, and so on are frequent multiples for the numbers 4 and 6. In that lot, 12 would be the least frequent number. Now let's attempt to get the LCM of 24 and 15.
LCM of 24 and 15 is equal to 222235 = 120.
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