The HCF and LCM are Highest common factor and Least common multiple respectively
What is HCF and LCM?
The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers
Product of HCF x LCM = product of two numbers
Given data ,
Let the two numbers be A and B
The value of A is A = 160
The value of B = 252
HCF is the product of common prime factors
So , Prime Factorization of 160: 2 x 2 x 2 x 2 x 2 x 5
And , Prime Factorization of 252: 2 x 2 x 3 x 3 x 7
So , HCF = 2 x 2 = 4
Now, finding LCM of 160 and 252
LCM is the product of all factors of both numbers
Prime Factorization of 160: 2 x 2 x 2 x 2 x 2 x 5
Prime Factorization of 252: 2 x 2 x 3 x 3 x 7
LCM= 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7
LCM= 10080
Now , the product of HCF x LCM = product of two numbers
160 x 252 = 40320
4 x 10080 = 40320
Hence , the HCF and LCM are solved
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Given the system: 2x + 3y = 12 2x - y = 4 What is the value of x + y?
The value of x + y is 5.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given linear equations are
2x + 3y = 12 ....(i)
2x - y = 4 ......(ii)
To solve the give linear equation, using elimination method.
Subtract equation (ii) from equation (i)
2x + 3y = 12
2x - y = 4
(-) (+) (-)
________
4y = 8
Divide both sides by 4:
y = 2
Putting y = 2 in equation (ii)
2x - 2 = 4
Add 2 with both sides:
2x = 6
Divide both sides by 2
x = 3
Putting x = 3 and y =2 in x + y:
x + y = 3 + 2 =5
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What is the coefficient of y2 in the expression 3y2 4x?
The coeficient of y² in the expression is the number 3
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
3y² + 4x
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.
3 is the coefficient of y²
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Find the product:
[2 1 0] x [1 -1 2] = [a b c]
[-1 -2 1]
[0 1 1]
Step-by-step explanation:
the multiplication result is found by row×column multiplications.
1st row × 1st column = a
2×1 + 1×-1 + 0×0 = 2 - 1 = 1 = a
1st row × 2nd column = b
2×-1 + 1×-2 + 0×1 = -2 + -2 = -4 = b
1st row × 3rd column = c
2×2 + 1×1 + 0×1 = 4 + 1 = 5 = c
6 less than a number
Answer:
n - 6
Step-by-step explanation:
Number n is A less than B: n = B - A.
What is dependent and dependent variable?
Independent and dependent variables are interdependent.
Dependent Variable: The term "dependent variable" refers to the variable that is being measured or tested in an experiment.
The results of the participants' tests, for instance, would be the dependent variable in a study looking at how tutoring affects test scores because that is what is being measured.
If you keep in mind that the dependent variable depends on the independent variable, finding it can be simpler.
The dependent variable's variable is being measured.It might change based on additional circumstances.It is reliant on other elements.A separate variableThis isn't the same as an experiment's independent variable, which is a variable that can stand on its own. The dependent variable (test results), however, may alter depending on the independent variable (tutoring).
The unrelated factor
Because the experimenters are allowed to change the independent variable as necessary, it is called a "independent" variable.
Changing variable in an independent variable.It doesn't alter in response to other factors.It can stand alone.For more questions on dependent and independent variable
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A covered Bridge is 8 yards long. In a photograph for sale at a gallery The Bridge is 5/12 foot-long which statements are true?
1. One yard of the covered Bridge is represented by 1.6 inches in the photograph
2. One inch on the photograph represents 1.6 yards of the real bridge.
3. A tree that is 3 inches tall in the photograph is 4.8 yards tall.
4. The people walking over the bridge are about 2.5 inches tall in the photograph.
5. A river that is 12 yards wide is 7.5 inches wide in the photograph.
(PLEASE EXPLAIN)
Answer:
2. One inch on the photograph represents 1.6 yards of the real bridge.
Step-by-step explanation:
1 yd = 36 in.
8 yd = 36 in./yd × 8 yd = 288 in
1 ft = 12 in.
5/12 ft × 12 in./ft = 5 in.
5 in. in the picture equals 288 inches real.
1 in. in the picture equals 57.6 inches real.
57.6 in. × (1 yd)/(36 in.) = 1.6 yd
1 in. in the picture equals 1.6 yd real
Answer:
2. One inch on the photograph represents 1.6 yards of the real bridge.
pls help me I’m confused i’ll give brainliest
Answer:
I would say the length is near 8
Answer:
In the given right angled triangle,
base(b)=2 mm and perpendicular(p)=7mm
hypotenuse (h)=?
By using Pythagoras theorem,
h²=p²+b²
or,h²=(7)²+(2)²
or,h²=49+4
or,h²=53
or,h=√53
or,h=7.28
The length of unknown side is 7.28 mm and it is not determined exactly.
The length 7.28 mm is between integers 7 and 8 and it is more closer to 7.
5 ≤ y + 2 ≤ 11 find the compound inequality
Answer:jkd
Step-by-step explanation:
d
Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate.) / e4x dx 19 e8x e4x C 8 19 e4x 19 4x 19 + C 19 19 19 C 19 + C 19 19 + C 8 19 4x 19 0/1 points | Previous Answers SCalcET8 7.6.023. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 33 sec5(x) dx X Use the Table of Integrals to evaluate the integral. 6х4е-x dx
The integration is as follow
[tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex] = 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C[tex]\int\limits {33 sec^5 (x)} \, dx[/tex] = 33/4 tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + CWhat is Integration?Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.
Given:
first, [tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex]
= [tex]\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx[/tex]
let [tex]e^{4x}[/tex] = z
4[tex]e^{4x}[/tex] dx = dz
= 1/4 [tex]\int\limits {dz / \sqrt{19} ^2 -z^2} \,[/tex]
= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C
= 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C
Second,
[tex]\int\limits {33 sec^5 (x)} \, dx[/tex]
= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]
= 33/4 tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]
= 33/4 tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C
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What is the answer for 2x 3y 12?
Linear equations are one-degree equations. So, the two solutions of the equation is (0,-4)(6,0).
How do one express the standard form of a linear equation?It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0. A linear equation has the following standard form: ax + by + c = 0.
Here, variables are x and y and constants a, b, and c are used. Also, a ≠ 0, and b ≠ 0.
We can find the solution of the linear equation by putting x = 0 and y = 0 so that two points form which are the solution of the linear equation,
Put x = 0 in the linear equation 2x - 3y = 12,
2 × (0) - 3y = 12
or, - 3y = 12
or, y = -4
The points is (0,-4)
Put y = 0 in the linear equation 2x - 3y = 12,
2x - 3 × (0) = 12
or, 2x = 12
or, x = 6
The points is (6,0)
Therefore, the two solutions of the equation is (0,-4)(6,0)
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The complete question is as follows:
What is the answer for 2x - 3y = 12?
The population of a city has decreased by 35% since it was last measured. If the current population is 20,800, what was the previous population?
help pls
The previous population of the city was 32,000.
What is percentage?Percentage is a measurement to find value of given number out of hundred.
Given that,
The current population of the city = 20,800.
Let the previous population was 100%.
Since, The population of the city decreased by 35%,
So, the current population of the city = 100 - 35 = 65%
According to given condition,
65 % = 20800
1 % = 20800 / 65
1 % = 320
100% = 320 x 100
= 32,000
Hence, the initial population was 32,000.
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Hey people can you guess NFL player with seven Super Bowl
Please someone help me with this!
A projectile is fired from the ground at an angle of 30 degrees above the horizon with an initial velocity of 960 ft/sec. If the height as a function of time t is given by h(t)=480t-16t^2, find,
The time when the projectile hits the ground
The maximum height
I think
h(t)=480t–16t^2
Max height is the vertex of the parabola at t = -b/2a
t = -480/-32 = 15 seconds
--> h(15)
How do you find the Y intercept x intercepts vertical asymptotes and horizontal asymptotes in a rational function?
To find the x-intercept of a rational function we put y=0 in the given and find the corresponding value of x.To find the y-intercept of a rational function we put x=0 in the function and the value of y.
what are intercepts?The x-intercept is the point where a line crosses the x-axis.At this point y=0 and the y-intercepts is the point where a line crosses the y-axis.At this point x=0
It is point where the graph of the rational function intersects the x-axis or y-axis.
How do we find vertical and horizontal asymptotes of rational function?For Horzontal asymptotes
The horizontal asmptotes of a rational function can be determined by looking at the degree of the numerator and denominator.if Nis the degree of numerator and Dis the degree of denominator.Then N<D
So horizontal asymtote is y=0
To finding horizontal asymptotes we can just focus on degree of numerator and denominator.
For vertical asymptotes
vertical asymptotes occur where the denominator of a rational function approaches zero.A rational function cannot cross a vertical asymptotes because it would be dividing by zero. we set denomintor to zero and solve value of x.The values of x are vertical asymptotes.
Hence we can find easily horizontal and vertical asymptotes of rational function.
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What doe the expreion 3x4y repreent?
A. The total number of baket of tomatoe and bag of onion the cutomer purchaed
B. The cot per baket for the tomatoe plu the cot per bag for the onion
C. The total cot, in dollar, for the cutomer’ purchae
D. The number of baket of tomatoe and the number of bag of onion that can be purchaed for $7
The expression 3x+4y represents 3 bags of $3 tomatoes and 4 bags of $4 onions.
What is an expression?
The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of logical grammar, such as the operation order.
Given that a basket of tomatoes costs $3, whereas an onion package costs $4. A customer buys y sacks of onions and x baskets of tomatoes.
Three bags of $3 tomatoes and four bags of $4 onions are denoted by the equation 3x+4y.
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What are the roots of 3x² 5x 2 0?
The equation 3x² + 5x + 2 = 0 has two solutions, x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.
To solve 3x² + 5x + 2 = 0, we must first find the roots of the equation. To do this, we can use the quadratic formula to solve for the two roots. The quadratic formula is x = [-b ± √(b² - 4ac)]/2a, where a, b, and c are the coefficients of the equation. To apply this to our equation, we have a = 3, b = 5, and c = 2, so the formula becomes x = [-5 ± √(5² - 4(3)(2))]/2(3). Simplifying this equation gives us x = [-5 ± √29]/6. The two solutions of this equation are x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.
x = [-5 ± √29]/6
x = [-5 + √29]/6 = -2
x = [-5 - √29]/6 = -1/3
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How do you tell if a function is positive or negative on a graph?
Answer:
You can tell if a function is positive or negative by checking the Y values. If all the Y values are above the x-axis it should be positive, and if the all y values are below the x-axis the function should be negative.
Good luck!
a number m is either less than 2 or greater than 9
Consider the function. f(x)=−8x+4 What is the value of f(−14)?
The value of polynomial for x = 2 that is f(2) will be 32.
What is polynomial?In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science.
They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions. Polynomial rings and algebraic varieties, two fundamental ideas in algebra and algebraic geometry, are constructed in advanced mathematics using polynomials.
We have given polynomial f(x)=3x²8x+4
We have to find the value of f(2
We have to find the value of polynomial for x = 2
So for finding this value we have to just put x = 2 in polynomial
So f(2) will be
So the value of polynomial for x = 2 will be 32
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Is Root 3x² 2x a polynomial?
Yes, √3x² - 2x is a polynomial.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
√3x² - 2x
This is in the form of ax² - bx
This is a polynomial with degree 2.
Thus,
√3x² - 2x is a polynomial.
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Need help (100 easy points)
Answer:
Step-by-step explanation:
Which quadratic function has one real solution
0=2(x+7)(x-5)
0=2/3(x-3)(x-3)
0=2.4(x-2)(x+2)
0=1/2(x-2)(x-1)
Answer: [tex]0=\frac{2}{3}(x-3)(x-3)[/tex]
Step-by-step explanation:
The roots are [tex]-7[/tex] and [tex]5[/tex].There is one only distinct root, which is [tex]3[/tex].The roots are [tex]\pm 2[/tex].The roots are [tex]1[/tex] and [tex]2[/tex].Choose if each statement is True or False. {(2, 2), (3, 2), (4, 2), (6, 2)} is a function: {(-1, 5), (0, 8), (3, 12), (6, 21)} is a function: 5 -10 0 -5 15 -10- 5 0 -5 -10+ 5 5 10 is a function: 10 15 is a function:
Answer:
True False True False
Step-by-step explanation:
What are the mean and standard deviation of the distribution of rs?
The mean and standard deviation of the distribution of R-S is
B Mean 3 and standard deviation 5How to find the mean and the standard deviationThe mean is calculated by simply substracting the values
= mean R - means S
= 10 - 7
= 3
standard deviation, SD
standard deviation is solved by the use of radicals and this affects the solution hence it will not be simple subtraction, rather we solve back to remove the radical and hence we get the variance
= (SD, R)² + (SD, S)²
= 4² + 3²
= 16 + 9
= 25
the variance is 25
SD = √variance = √25 = 5
complete question
The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S
has mean 7 and standard deviation 3. If Rand S are independent, what are the mean and standard deviation of the
distribution of R-S?
A Mean 3 and standard deviation 1
B Mean 3 and standard deviation 5
C Mean 3 and standard deviation 7
D Mean 17 and standard deviation 1
E Mean 17 and standard deviation 5
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Please help !!!!!???
The height of Dubai fountain is 500 feet tall.
Define basic arithmetic.The foundational subject in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics. The Greek term "arithmos," which means "numbers," is where the word "arithmetic" originates. Arithmetic is one of the oldest and most basic concepts in mathematics. It deals with numbers and the basic operations (addition, subtraction, multiplication, and division) that can be carried out on them.
Given
The Burj Khalifa in Dubai is the tallest building in the world, at 2,717 feet.
Burj Khalifa is 217 feet taller
Height of Dubai fountain
Subtracting
2717 - 217
2500
5 times the height
Divide by 5,
2500/5
500
The height of Dubai fountain is 500 feet tall.
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Factorize:
(2a^3-8a)÷ 2a (a-2)
The factorized expression of (2a³ - 8a) ÷ 2a (a - 2) is (a - 4) ÷ (a - 2)
How to factorize the expression?From the question, we have the following parameters that can be used in our computation:
(2a^3-8a)÷ 2a (a-2)
Rewrite the above expression properly
So, we have the following representation
(2a³ - 8a) ÷ 2a (a - 2)
Divide the fraction by 21
This gives
(a - 4) ÷ (a - 2)
The above expression cannot be solved further
Hence, the solution is (a - 4) ÷ (a - 2)
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Grandpa Ernie is shrinking! Over the past 4 years, his height decreased by a total of 2.4 cm 2.4. It decreased by the same amount each year.
What was the change in Grandpa Ernie's height each year?
Answer:
Step-by-step explanation:
Grandpa Ernie has been shrinking for the past four years. His height decreased by a total of 2.4 cm during this period, which means that it went down by 0.6 cm each year. This gradual decrease in his height is quite remarkable given his age and overall health condition; however, it is not an entirely unexpected phenomenon due to aging and the natural decline of muscle mass with age as well as other factors such as poor nutrition or lack of exercise can contribute to this process too.
Solve pls brainliest
Answer:
Your answer is 2,600.019
Step-by-step explanation:
Very simply to answer it with or without a calculator.
2.6 * 10^3 + 0.19 * 10^-2
Without calculator
First move the decimal points before adding.
2.6 * 10^3 = 2,600.
Negative exponential moves the decimal to the left.0.19 * 10^-2 = 0.0019
This equation 2.6 * 10^3 + 0.19 * 10^-2 becomes
2,600 + 0.0019
Then add.
2,600.0019
How do you do 3 terms in binomial expansion?
The solution of the expression with three terms using binomial theorem can be solved by supposition and resubstituting the value.
Let us consider an example of three terms :
( 1 + x + x² ) ³
Use binomial theorem and expand the given expression:
Standard form of binomial expansion is :
( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+ ⁿCₙa⁰bⁿ
Let us consider x + x² = y
( 1 + y )³
=³C₀1³y⁰ + ³C₁1³⁻¹y¹ + ³C₂1³⁻²y² + ³C₃1⁰y³
= 1 + 3y + 3y² + y³
Resubstitute the value of y = x + x² we get,
= 1 + 3(x + x²) + 3(x + x²)² + (x + x²)³
= 1 + 3x + 3x² + 3( x² + 2x³ + x⁴) + ³C₀x³(x²)⁰ + ³C₁x³⁻¹(x²)¹ + ³C₂(x)³⁻²(x²)² + ³C₃x⁰(x²)³
= 1 + 3x + 3x² + 3x² + 6x³ + 3x⁴ + x³ + 3x⁴ + 3x⁵ + x⁶
= 1 + 3x + 6x² + 7x³ + 6x⁴ + 3x⁵ + x⁶
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jksjsisks 78i2o
[tex]32. \frac{33}{31?} [/tex]
Answer:
34.064516129
Step-by-step explanation:
[tex]32 \times \frac{33}{31} = \frac{1056}{31} [/tex]
[tex] = 34.064516129[/tex]
i hope this helps