The direction and slope of line A'B' would still be the same as that of line AB, but the positioning of A'B' would depend on the location of line AB with respect to the origin and the value of g.
What is a scale factor ?
A scale factor is a number that scales or multiplies the size or dimensions of an object or a geometric figure by the same amount in all directions. It can be used to describe changes in size or magnification of an object or figure, and is often expressed as a ratio or a percentage.
When line AB is dilated with a scale factor of 3 and a center of dilation at the origin, the resulting line A'B' will be three times as long as line AB and will pass through the origin.
The direction and slope of line A'B' will be the same as that of line AB, but it will be positioned closer to the origin.
If line AB were dilated with a scale factor of g, then the resulting line A'B' would be g times as long as line AB and would also pass through the origin.
Therefore, The direction and slope of line A'B' would still be the same as that of line AB, but the positioning of A'B' would depend on the location of line AB with respect to the origin and the value of g.
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Solve for x
.............
Answer:
3
Step-by-step explanation:
BT ≅ TD
[tex]19=5x+4\\15=5x\\3=x[/tex]
How many different possible outcomes are there if you spin 4 spinners labeled Red,
Blue, Yellow?
From the information given, there are 81 different possible outcomes if you spin 4 spinners labeled Red, Blue, Yellow.
A permutation is an arrangement of objects in a specific order, and spinning involves generating a random outcome from a set of possible outcomes.
When spinning the spinner, each outcome has an equal chance of occurring, so we can say that the set of possible outcomes is being randomly permuted.
Spinning can be thought of as a way to generate a random permutation of a set of possible outcomes.
Each spinner has three possible outcomes, so the total number of different possible outcomes for all four spinners is:
3 x 3 x 3 x 3 = 81
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Doretta offers cleaning services to families in her city. She charged $25 per month for maintaining a house and $15 per hour for each extra call. Write an equation to represent the total monthly cost, C, for maintaining a house and for h hours of extra work.
6 bags of coins each contain 10 nickels and the same number of pennies. Altogether, the bags contain 180 coins. Write and solve an equation to find the number of pennies in each bag.
Each bag contains 20 pennies and we have 6 such bags.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information let the number of pennies in each bag is 'x'
and we have 6 such bags.
Therefore, The equation can be formed as,
6(10 + x) = 180.
60 + 6x = 180.
6x = 180 - 60.
6x = 120.
x = 120/6.
x = 20.
So, The number of pennies in each bag is 20.
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Determine if the points are solution points to the inequalities below. If the point is a solution, enter yes.
If the point is not a solution, enter no. Enter yes or no in lower case letters (no capital letters).
a. Is (2, 10) a solution to y < 12- x?
b. Is (3, 13) a solution to y ≤ 15 - x?
c. Is (4, 19) a solution to y > 19 - x?
d. Is (5, 13) a solution to y ≥ 12 - x?
The solution is;
a. (2, 10) is not a solution to y < 12- x.
b. (3, 13) is a solution to y ≤ 15 - x
c. (4, 19) is a solution to y > 19 - x
d. (5, 13) is not a solution to y ≥ 12 - x
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
A Set of such values is called a solution set to the considered equation or inequality.
Substitute the values where the variables are, and simplify to the point where you can tell whether the statement is true.
Each ordered pair is (x, y), thus the first value gets substituted for x; the second value gets substituted for y.
a. (2, 10)
11 < 13 -2 = 11
no
b.(3, 13)
8 ≤ 16 -3 = 13
yes
c. (4, 19)
20 > 18 -4 = 14
yes
d. (5, 13)
9 ≥ 15 -5 = 10
no
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820.98 rounded to nearest 10th
Answer: 821
Step-by-step explanation: The nearest tenth is the first digit after the decimal point.
Could anyone help with #1 and #2 PLEASE.
URGENT! DUE TOMORROW!!
Answer:
Do the graph Then Solve for y
Answer:
1. Yes, a graph of this relationship will be linear.
2. The y-intercept of the graph is (0, 2).
Step-by-step explanation:
1. The equation will be linear because it can be written in the standard form for the equation of a line. The standard form for the equation of a line is Ax + By = C. Eight can be subtracted from both sides of the equation to get 3x - 4y = -8, which fits the format for standard form. A, B, and C are integers, which includes negative numbers, zero, and whole numbers.
2. 3x - 4y + 8 = 0
3(0) - 4y + 8 = 0
-4y + 8 = 0
-4y = -8
y = 2
what could be a ratio between the lengths of the two legs of a 30-60-90 triangle
Answer:
Below
Step-by-step explanation:
One leg would be hyp * cos 30 and one would be hyp cos 60
hyp cos 30 : hyp cos 60
cos 30 : cos 60
= ratio sqrt (3) /2 : 1/2 or sqrt 3 : 1
A total of 360 people voted in an election. The circle graph shows the results.
(a) How many people (number of people, not the percentage) voted for Goron?
Show your work.
(b) How many people (number of people, not the percentage) voted for Fishman
and Other? Show your work. PLEASE HELP
a. There were 126 people who voted for Goron.
b. There were 144 people who voted for Fishman.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The given circle graph shows the results.
There were 360 people who voted in the election.
According to the question, the required solution would be as:
number of people who voted for Goron = 35% of 360
15% is expressed as 15/100 in fractional form
number of people who voted for Goron = (35/100) × 360
number of people who voted for Goron = 126
number of people who voted for Fishman = 40% of 360
number of people who voted for Fishman = (40/100) × 360
number of people who voted for Fishman = 144
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The missing figure has been attached below
A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25500 kilograms. Other shipments weighing 6400 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x, the number of 40-kilogram crates that can be loaded into the shipping container.
If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is: x=≤ 477.5.
What is inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
Inequality
x is the integer
First step is to formulate the inequality
40x≤ 25,500-6,400
Now let determine the x by using the inequality
40x≤ 25,500-6,400
40x≤19,100
x=≤19,100/40
x=≤ 477.5
Therefore If a shipping container will be used to transport several 40-kilogram crates across the country by rail. The inequality that can be used to determine x is: 40x≤ 25,500-6,400 and the number of 40-kilogram crates that can be loaded into the shipping container is: x=≤ 477.5.
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9. Evan and Yong used this shape
, representing the unit fraction, to draw 1 whole.
Shania thinks both of them did it correctly. Do you agree with her? Explain your answer.
From the given figure we can say that , Evan's used the given shape correctly to represent the unit fraction .
What is a unit fraction ?
A unit fraction is a fraction whose numerator (top number) is equal to 1. For example, 1/2, 1/3, 1/4, and so on are all unit fractions. Unit fractions are commonly used to represent parts of a whole, and they can also be used to perform certain mathematical operations such as addition and multiplication.
Given ,
Evan and Yong used the given shape representing the unit fraction, to draw 1 whole.
so,
from the given figure ,
in the evan diagram we can say it was mentioned correct, as we need to write down that in 1/3 where as in the Yong's case we can say that it does not come to 1/3 as a final resultant.
Therefore, From the given figure we can say that , Evan's used the given shape correctly to represent the unit fraction .
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5a - 26 = -10
6a + 46 = 36
If (a,b) is the solution to the system of equations shown above, what is the value of a?
Answer:
Step-by-step explanation:
To solve for the value of "a", we can isolate "a" in one of the equations and then substitute the result into the other equation. Here's how we can do that:
Starting with the first equation:
5a - 26 = -10
5a = -10 + 26
5a = 16
a = 16 / 5
a = 3.2
Now that we know the value of "a", we can substitute it into the second equation:
6a + 46 = 36
6 * 3.2 + 46 = 36
19.2 + 46 = 36
65.2 = 36
This means that the system of equations has no solution, as the values of "a" and "b" can't both satisfy both equations at the same time.
Which of the contexts below represents linear growth?
A music service has a fixed monthly cost and charges $0.35 for each downloaded
song.
An elevator descends at a rate of 32 feet per second.
OA town's population shrinks at a rate of 9.4% every year.
The amount of a certain medication in a person's bloodstream decreases by 1/4
every day.
The context that represents linear growth is "A music service has a fixed monthly cost and charges $0.35 for each downloaded song".
What is linear Growth:A linear growth function has a constant slope, increases by a consistent amount over time, and is represented graphically as a line.
In other words, when a quantity rises in proportion to another factor or variable in a connection it is said to be a linear growth.
Let's check the given option to check whether it is linear growth or not.
1. A music service has a fixed monthly cost and charges $0.35 for each downloaded song.
Here there is a fixed cost and the cost will increase when the number of songs is increased
Let's say the constant charge is 'y' and the number of songs is 'x' then the equation that can represent the situation is
=> f(x) = y + x(0.35)
Here there is a constant increase in cost
∴ The given situation can represent Linear growth.
2. An elevator descends at a rate of 32 feet per second.
Here descends indicated the elevator decreases in speed of the elevator at a point the elevator speed will be zero
∴ It doesn't show the linear growth
3. OA town's population shrinks at a rate of 9.4% every year.
Here the town's population is shrinking means It doesn't show any growth
∴ It doesn't show the linear growth
4. The amount of certain medication in a person's bloodstream decreases by 1/4 every day.
Here, the person's bloodstream decreases by 1/4 every day.
∴ It doesn't show the linear growth
Therefore,
The context that represents linear growth is "A music service has a fixed monthly cost and charges $0.35 for each downloaded song".
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Help please, thank you and have a wonderful day
Answer:
In order in which the boxes appear
[tex]\boxed{cubic}\\\\\boxed{3}\\\\\boxed{8}\\\\\boxed{x^3}\\\\\boxed{1}[/tex]
Step-by-step explanation:
Do not know the answer choices look like but this should fit
The polynomial has degree 3, therefore it is a cubic polynomial
There are 3 terms
The constant term is 8
The leading term is x³
and the leading coefficient is 1
Answer:
Cubic,3,8,x^3,1
Step-by-step explanation:
The polynomial is :
-x/10+x^3+8
The above polynomial, it contains 3 terms i.e, -x/10,x^3,8. The leading term is x^3 since it has power 3 so it is a cubic polynomial and its leading coefficient is 1.
The expression represents a cubic polynomial with 3 terms. The constant term is 8, the leading term is x^3, and the leading coefficient is 1.
2. The cost of an ad in a local paper is given by the piecewise function.
x ≤ 51
40,
(40+7(x-4), x>5)
Find the difference in cost between a one-line ad and a four-line ad.
c(x) = {40
please help
The difference in cost between a one-line ad and a four-line ad is 0
How to find the difference in cost between a one-line ad and a four-line ad.From the question, we have the following parameters that can be used in our computation:
c(x) = 40 x ≤ 5
c(x) = 40 + 7(x-4), x>5)
For one line add, we make use of the function
c(x) = 40 x ≤ 5
This is so because 1 is in the domain of x ≤ 5
For four line add, we make use of the function
c(x) = 40 x ≤ 5
This is so because 4 is in the domain of x ≤ 5
So, we have
C(1) = 40 and C(4) = 40
The difference, it
Difference = 40 - 40
Evaluate
Difference = 0
Hence, the difference is 0
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A cone has a volume of 30 in ³.
What is the volume of a cylinder with the same radius
and height?
Answer:
[tex]90 \ in^{3}[/tex]
Step-by-step explanation:
The volume of a cone is ¹/₃ the volume of the cylinder of a given radius and perpendicular height
[tex]V_{C} = volume \ of \ cylinder \\\\ V_{c} = volume \ of \ cone\\\\ r = radius \\\\ h = perpendicular \ height[/tex]
[tex]V_{C} = \pi r^{2}h \\\\ V_{c} = \frac{1}{3}\pi r^{2}h[/tex] → [tex]3V_{c} = \pi r^{2}h = V_{C}[/tex]
So if r and h are the same, then:
[tex]V_{C} = 3V_{c}[/tex]
Therefore:
[tex]V_{C} = 3(30) \\\\ V_{C} = 90[/tex]
Place the following set of scores in a frequency distribution table.
7, 5, 6, 4, 4, 3, 8, 9, 4, 7, 5, 5, 6
9, 4, 7, 5, 10, 6, 8, 5, 6, 3, 4, 8, 5
Are the scores clustered together, or are they spread out across the scale? a. Most of the scores are clustered within 1 or 2 points of X = 6. b. The scores are spread out fairly evenly across the scale. c. Most of the scores are clustered within 1 or 2 points of X = 8. d. The scores are clustered in two peaks near X = 3 and near X = 9.
GIven the set of scores, it is seen that a. Most of the scores are clustered within 1 or 2 points of X = 6.
What is a Frequency Table?
A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.
Here is a frequency distribution table for the given set of scores:
Score Frequency
3 2
4 5
5 5
6 5
7 2
8 3
9 2
10 1
You can see that the scores are clustered around X = 6, with the highest frequency (5) at score 6 and the next highest frequency (5) at score 5.
The scores are not evenly spread out across the scale.
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Please help me ASPA find the value of X
Answer:
9
Step-by-step explanation:
set up a ratio
20 is to 3x-2 as ( 20 + 28) is to 7x -3
20 / ( 3x-2) = ( 20 + 28) / (7x-3 ) cross multiply to get
140x - 60 = 144x - 96
36 = 4x
x = 9
Find the limit………………
[tex]\lim_{p \to \(-8}[/tex] = -59
What is a Limit?
Limit is the values that a function approaches the output for the given input values.
How to calculate this
[tex]\lim_{p \to \(-8}[/tex] ( -[tex]p^{2}[/tex] - p -3)
when p = -8
By inserting the value of p
[tex]\lim_{p \to \(-8}[/tex] = {-(-8)^2 - (-8) - 3 }
open the bracket
[tex]\lim_{p \to \(-8}[/tex] = (-64 + 8 - 3 )
[tex]\lim_{p \to \(-8}[/tex] = ( - 59 )
So, [tex]\lim_{p \to \(-8}[/tex] =-59
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A plane traveled 3900 miles with the wind in 6.5 hours and 3120 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.
Answer:
the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.
Step-by-step explanation:
Step 1: Define the variables
Let's call the speed of the plane in still air "V". Let's call the speed of the wind "W".
Step 2: Write an equation for the distance traveled with the wind
The distance traveled by the plane with the wind in 6.5 hours can be represented by the equation:
D1 = (V + W) * t
where D1 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.
Substitute the known values into the equation:
3900 = (V + W) * 6.5
Step 3: Write an equation for the distance traveled against the wind
The distance traveled by the plane against the wind in 6.5 hours can be represented by the equation:
D2 = (V - W) * t
where D2 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.
Substitute the known values into the equation:
3120 = (V - W) * 6.5
Step 4: Solve for the speed of the wind
We can now use the two equations from Steps 2 and 3 to solve for the speed of the wind.
First, let's rearrange the equation from Step 2 to isolate "W":
W = (3900 / 6.5) - V
Next, substitute this expression for "W" into the equation from Step 3:
3120 = (V - ((3900 / 6.5) - V)) * 6.5
Expand the right side of the equation:
3120 = (V - 3900 / 6.5 + V) * 6.5
Simplify the equation:
3120 = 2V * 6.5 - 3900
Divide both sides of the equation by 2:
1560 = V * 6.5 - 1950
Multiply both sides of the equation by 2:
3120 = V * 13 - 3900
Add 3900 to both sides of the equation:
7020 = V * 13
Divide both sides of the equation by 13:
V = 540
Step 5: Solve for the speed of the wind
Now that we know the speed of the plane in still air, we can use the equation from Step 2 to find the speed of the wind:
W = (3900 / 6.5) - V
Substitute the value of "V" that we found in Step 4 into the equation:
W = (3900 / 6.5) - 540
Simplify the equation:
W = 280
Step 6: Conclusion
Therefore, the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.
Hexagonal prism B is the image of
hexagonal prism A after dilation by a scale
factor of 2. If the surface area of hexagonal
prism B is 172 cm2, find the surface area of
hexagonal prism A, the preimage.
The surface area of hexagonal prism A is 9√3x² cm². We are given that hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2.
Therefore, all corresponding sides of prism A and prism B are in the ratio of 1:2. Let the side length of the base of hexagonal prism A be 'x'. Then, the side length of the base of hexagonal prism B is '2x'.
We know that the surface area of hexagonal prism B is 172 cm². Using the formula for the surface area of a hexagonal prism, we can write:
172 = 2(3√3)(2x)^2 + 6(2x)h
where h is the height of hexagonal prism B.
Simplifying this equation, we get:
172 = 24√3x² + 12xh
Dividing both sides by 12, we get:
14.33 = 2√3x² + h
Now, since hexagonal prism B is a dilation of hexagonal prism A by a scale factor of 2, the height of hexagonal prism A is half the height of hexagonal prism B. So, the height of hexagonal prism A is h/2.
Using the formula for the surface area of a hexagonal prism, we can write:
SA(A) = 2(3√3)x² + 6x(h/2)
Substituting h/2 for the height of hexagonal prism A, we get:
SA(A) = 2(3√3)x² + 3xh
Substituting 2√3x² + h/2 for h, we get:
SA(A) = 2(3√3)x² + 3x(2√3x² + h/2)
SA(A) = 6√3x² + 3√3x² + (3/2)xh
Substituting 2√3x² for h in the above equation, we get:
SA(A) = 6√3x² + 3√3x² + (3/2)x(2√3x²)
SA(A) = 9√3x²
Therefore, the surface area of hexagonal prism A is 9√3x² cm².
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Determine the value for m in the equation 1.4m = 0.42. HELP ASAP
Answer:
Below
Step-by-step explanation:
1.4 m = .42 divide both sides of the equation by 1.4 to get
m = .3 Done.
three more than product of 15 and a number n is 153. wright an equation that describes this situation
The equation that describes this situation is, 3 + 15n = 153
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
Given that,
Three more than product of 15,
And a number n is 153.
More than = + (addition)
Product = x (multiplication)
Product of 15 and n = 15 x n = 15n
Therefore, the equation is 3 + 15n = 153.
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Tomas estimated that he would need to throw 22.52m in fact he threw 21.36m what is the percentage error
Answer:
5.15%
Step-by-step explanation:
Difference between estimated throw and actual throw
= estimated - actual
= 22.52 - 21.36
= 1.16 m
As a fraction of estimated throw:
1.16/22.52
As a percentage:
1.16/22.52 x 100 = 5.15%
What is the average of the points A, B, and C with weights 1, 3, and 4 respectively? A (-8, 5) B (8, 2) C (5, 4)
The average of the three weighted points, A, B, and C, is (-1, 2.875).
In mathematics, what does average weight mean?A technique known as a weighted average accounts for the varied levels of significance of the values in a data collection. Each number in the data set is multiplied by a predefined weight before the final computation is completed when calculating a weighted average.
weighted average = (w1 × x1 + w2 × x2 + w3 × x3) / (w1 + w2 + w3),
where wi is the weight of the ith point, and xi is the coordinate of the ith point.
Substituting the given values, we get:
weighted average = (1 × (-8, 5) + 3 × (8, 2) + 4 × (5, 4)) / (1 + 3 + 4)
= (-8, 5 + 3 × 2 + 4 × 4) / 8
= (-8, 23) / 8
= (-1, 2.875)
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integration of {√(4-9x²)/x}dx ??
The antiderivative of the given expression can be found using the substitution method. We'll make the substitution u = 4 - 9x^2, so du/dx = -18x.
Substituting these into the original expression, we get:
∫{√(4-9x²)/x}dx = ∫{√u/x}du = 2√u * ln|x| + C, where C is an arbitrary constant of integration.
Substituting back for u, we get:
∫{√(4-9x²)/x}dx = 2√(4 - 9x^2) * ln|x| + C.
To verify this result, we can differentiate the antiderivative and see if it matches the original expression. Taking the derivative of the antiderivative with respect to x, we get:
d/dx [2√(4 - 9x^2) * ln|x| + C] = -18x√(4 - 9x^2)/x + 2 * (-9x) / (2√(4 - 9x^2)) = (√(4-9x²)/x)
Thus, the antiderivative found is indeed correct.
Which expression is equivalent to 3x2 - 10x - 8?
A-(3x - 4)(x + 2)
B-(3x - 4)(x - 2)
C-(3x - 2)(x - 4)
D-(x - 4)(3x + 2)
Answer:
D
Step-by-step explanation:
3x² - 10x - 8
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 8 = - 24 and sum = - 10
the factors are - 12 and + 2
use these factors to split the x- term
3x² - 12x + 2x - 8 ( factor the first/second and third/fourth terms )
= 3x(x - 4) + 2(x - 4) ← factor out (x - 4) from each term
= (x - 4)(3x + 2)
B) The area of a triangle = ½ the base the
height
What is the area of an equilateral triangle where
every side measures 10 cm?
The area of the equilateral triangle with side length 10 cm is 25 cm².
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
To find the area of an equilateral triangle, we need to find the height first. The height of an equilateral triangle is equal to the length of the perpendicular line from the center of the triangle to one of its sides.
To find the height, we can divide the equilateral triangle into two 30-60-90 triangles. The height is equal to half of the hypotenuse of one of these triangles, which can be calculated as:
10 cm / 2 = 5 cm
Now that we have the height, we can find the area of the equilateral triangle as follows:
Area = ½ * base * height
Area = ½ * 10 cm * 5 cm
Area = 25 cm²
Hence, The area of the equilateral triangle with side length 10 cm is 25 cm².
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Multiplying a number by which of the following would result in a smallest number?
O 10-1
O 10⁰
O 10¹
102
The product of a non-zero rational and an irrational number isa. always irriationalb. always rational c. rational or irrationald. one
The product of a non-zero rational and an irrational number is always irrational number.
To prove this statement:
Let x be a rational number and y be an irrational number.
Let xy=a.
Let us assume that a is rational.
Since, a is rational it can be expressed as p/q , where p and q are integers.
Let x= m/n , where m and n are integers.
Now, xy=a
[tex]\frac{my}{n} = \frac{p}{q}[/tex]
On cross multiplying we get,
y = pn/qm
Now, pn and qm are integers.
Hence, pn/qm is a rational number.
However, y is irrational.
Hence, our assumption is incorrect.
Hence, the product of a non-zero rational and an irrational number is always an Irrational number.
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