Yes, both the rates i.e. 24 laps in 6 minutes and 72 laps in 18 minutes are equivalent.
The unit rates for equivalent rates are the same. Similar to equivalent ratios, equivalent rates can be calculated by multiplying or dividing the numerator and denominator by the same amount.
When two expressions can be reduced to a single-third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if the two expressions are equal.
To determine whether the rates are equivalent, we need to compare the number of laps completed per unit of time. In the first case, the rate is 24 laps in 6 minutes, which is equal to 4 laps per minute. In the second case, the rate is 72 laps in 18 minutes, which is also equal to 4 laps per minute. Since both rates are equal to 4 laps per minute, the rates are equivalent.
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The rates of 24 laps in 6 minutes and 72 laps in 18 minutes are equal, therefore yes.
Equivalent rates have the same unit rates. Equivalent rates can also be determined by multiplying or dividing the numerator and denominator by the same number, just like equivalent ratios.
Two expressions are considered to be equivalent if one of them can be written in the same way as the other or if they can both be condensed to a single-third expression. You may also tell if two expressions are equivalent if, when the values for the variable are changed, both expressions provide the same outcome.
In order to determine whether the rates are similar, we must compare the number of laps completed per unit of time. The pace in the first scenario is 4 laps per minute, or 24 laps done in 6 minutes. When 72 laps are completed in 18 minutes, the rate is similarly 4 laps per minute. Due to the fact that they both equal 4 laps per minute, their rates are equal.
How do you solve 2 5 to the second power?
Enter 5/100 for five hundredths to divide the numerator by the denominator using a forward slash. Make sure there is space between the whole and fraction components when using mixed numbers.
what is exponentiation ?The procedure used to express repeated multiplication is known as exponentiation in mathematics. As an illustration, 10 can be expressed as "10 raised to 3," which equals [tex]10^{3}[/tex] , if it is multiplied three times.
here ,
Exponentiation: 2/5^ 2 = 4/25
Or, two fifths raised to the power of squared is equal to four twenty-fifths. The mathematical equivalent of multiplying a number by itself a certain number of times is what is known as the number's exponential value.
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What is the quotient 6x4 15x3 10x2 10x 4 3x2 2 )? 6 points group of answer choices 2x2 − 5x 2 2x2 5x − 2 2x2 − 5x − 2 2x2 5x 2?
The quotient is 2x2+5x2+2.
The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, both the constant term (the term without a variable) and the leading coefficient (the coefficient of the highest power) must be divisible by the fraction's denominator.
Since we have already provided it
[tex]\frac{(6x^2+15x^3+10x^2+10x+4)}{(3x^2+2)}[/tex]
We will now factor the numerator to determine the quotient:
Use the theorem that says [tex]a_0=4[/tex] and [tex]a_n=6[/tex].
[tex]a_0[/tex] divisions are 1, 2, and 4.
[tex]a_n[/tex] is divided into 1, 2, 3, and 6.
Check the following logical figures as a result: ±[tex]\frac{1,2,4}{1,2,3,6}[/tex]
[tex]-\frac{2}{1}[/tex] is a root of the expression, so factor out [tex]x+2[/tex]
[tex]=(x+2)\frac{6x^4+15x^3+10x^2+10x+4}{x+2}[/tex]
[tex]= \frac{6x^4+15x^3+10x^2+10x+4}{x+2} \\=6x^3+3x^2+4x+2[/tex]
We'll factor it in once more now:
[tex]=(6x^3+3x^2)+(4x+2)\\=2(2x+1)+3x^2(2x+1)\\=(2x+1)(3x^2+2)[/tex]
Finally, we have our factored form:
[tex]= (x+2)(2x+1)(3x^2+2)\\=\frac{(x+2)(2x+1)(3x^2+2)}{3x^2+2} \\=(x+2)(2x+1)\\=2x^2+5x+2[/tex]
The complete question is:-
What is the quotient: (6x4 + 15x3 + 10x2 + 10x + 4) ÷ (3x2 + 2)?
a. 2x2 – 5x + 2
b. 2x2 + 5x – 2
c. 2x2 + 5x + 2
d. 2x2 – 5x – 2
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All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday. 10% of students brought their lunch. 31 students brought their lunch. How many students in total are in Ridgewood Junior High School?
Answer:
If 10% of the school brings lunch, and it's 31 people, we know that there are a total of 310 students. 10 times 31 is 310.
To check this, 90% of 310 is 279, and 310-279=31!
Answer:
310
Step-by-step explanation:
100 / 10 = 10
31 * 10 = 310
PLEASE MARK AS BRAINLIEST!!!Find the slope of the line that passes through (6, 1) and (10, 8).
The slope of the line that passes through (6, 1) and (10, 8) is 7 / 4.
How to find the slope of a line?The slope of a line is the change in dependent variable with respect to the change in the independent variable. The slope of a line is rise over run.
In other words, the slope of a line is a measure of its steepness.
Hence, let's find the slope of the line that passes through (6, 1) and (10, 8).
Therefore,
slope = Δy / Δx
slope = y₂ - y₁ / x₂ - x₁
x₁ = 6
x₂ = 10
y₁ = 1
y₂ = 8
Therefore,
slope = 8 - 1 / 10 - 6
slope = 7 / 4
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Answer: 7/4 is the slope
How many terms does the expression 5xyz2 3zy have?
The expression 5xyz2 3zy have 5 and -3. It is possible to compare expressions and phrases.
What is meant by expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between.In the expression
5xyz² – 3zy, the terms are 5xyz² and –3zy.
Coefficient of xyz² in the term 5xyz² is 5.
coefficient of zy in the term –3zy is –3.
In the expression 1 + x + x² , the terms are 1, x and x²
Therefore,
5xyz² = 5
- 3zy = -3
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How do you prove a square is congruent?
Answer:
How To Find if Triangles are Congruent 1 SSS (side, side, side) 2 SAS (side, angle, side) 3 ASA (angle, side, angle) 4 AAS (angle, angle, side) 5 HL (hypotenuse, leg)
hope this helps
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Step-by-step explanation:
What are the factors of polynomial P x )= 2x² 7x 3?
The factors of polynomial P(x)= 2x² -7x + 3 is x =1/2 and x =3.
Factoring polynomials is the opposite method of the multiplication of things of polynomials. An expression of the shape
axⁿ + bxⁿ⁻¹+kcxⁿ⁻² + ….+kx+ l, wherein every variable has a regular accompanying it as its coefficient is known as a polynomial of diploma ‘n’ in variable x. hence, a polynomial is an expression wherein a mixture of a regular and a variable is separated with the aid of an addition or a subtraction signal.
For a polynomial of the form:
ax²+ bx +c, rewrite the middle term as a sum of two terms whose product is a × c =2×3 = 6 and whose sum is b= −7.
Now,
Factor −7 out of −7x
2x²−7(x)+3
Rewrite −7 as −1 plus −6
2x²+ (−1−6)x +3
Apply the distributive property.
2x²−1x−6x+3
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(2x²−1x)− 6x + 3
Factor out the greatest common factor (GCF) from each group.
x(2x−1)−3(2x−1)
Factor the polynomial by factoring out the greatest common factor,
(2x−1)(2x-1)(x−3)
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in the equation 5x + 9 = 3x, _______ and ________ are like terms.
Answer:
5x and 3x are like term
Step-by-step explanation:
as per the question 5x plus 9 is equal to 3x The common is X that means 5x and 3x as 5 plus 3 is nine
What are the names of the two types of angle, below?
Type of angle:
Type of angle:
Answer:
there is supplementary angle
What are the top 3 factors that contribute to your success?
The top three factors that contribute leading to my success are
HonestyPurpose and Intuition.There are several factors that I believe are important to a successful venture, business or individual. But in my opinion my main factors are:
Honesty really is the best policy. If you aren't honest with your work and yourself, you won't be successful.Purpose is born from stronge self-honesty . You can find a lot of freedom working for yourself, but make no mistake, it's work. Life is meaningless without any purpose of life.Getting started on your path to success isn't always obvious. Through experience, I have learned that sometimes you need to try different states of mind and learn along the way.To learn more about sucess factors , refer:
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(a) describe a procedure for identifying potential outliers, and use the procedure to decide whether there are outliers among the responses for the money spent on textbooks. (b) based on the stemplot, write a few sentences describing the distribution of money spent on textbooks for the 34 students.
a) A procedure for identifying outliers is identifying if there are values that are more than 1.5 IQR from the quartiles. Thus, the value of 810 is an outlier in the given distribution.
b) As the distribution contains a high outlier, it means that the distribution is right skewed.
How to identify the outliers?The first quartile of a data-set is the element that represents the 25th percentile of the distribution.
For a distribution of 34 students, the first half of the distribution has 16 values, hence the first quartile is the mean of the 8th and 9th values.
From the stemplot, these values are 170 and 180, hence:
Q1 = (170 + 180)/2 = 175.
The third quartile is the 75th percentile of the distribution, hence it is the mean of the 8th and 9th values of the second half of the distribution.
From the stemplot, these values are 39 and 41, hence:
Q3 = (390 + 410)/2 = 400.
The IQR is the difference between the quartiles, hence:
IQR = Q3 - Q1 = 400 - 175 = 225.
Values that are more than 1.5 IQR from the quartiles are considered outliers, hence the bounds are given as follows:
Lower outliers: less than 175 - 1.5 x 225 -> there are no lower outliers.High outliers: higher than 400 + 1.5 x 225 = 737.5.Hence the value of 810 is a high outlier. This high outlier will influence the mean, making it higher than the median, and thus the distribution is right skewed.
Missing InformationThe stemplot is given by the image shown at the end of the answer.
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What is the area of this rectangle?
P(2, 3), Q(4, -1), R(-8, -7), S(-10, -3)
The area of the rectangle is 12 square units which vertices are P(2, 3), Q(4, -1), R(-8, -7), and S(-10, -3).
To find the area of the rectangle, we need to first find the side lengths of the rectangle. We can do this by using the coordinates of the points to find the distances between them.
The side length of the rectangle along the x-axis is the distance between points P and Q, which is 4 - 2 = 2 units.
The side length of the rectangle along the y-axis is the distance between points P and S, which is 3 - (-3) = 6 units.
Now that we know the side lengths of the rectangle, we can use the formula for the area of a rectangle, which is length x width, to find the area.
The area of the rectangle is 2 x 6 = 12 square units.
Therefore, the answer is 12 square units.
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What is the value of 5 2 10 4 2 5x5 6?
The simplification of the given expression is found as 2.
Explain the concept of the indices?We can determine how several times a phrase has already been multiplied in and of itself using an index, which is a tiny number.Indexes is the plural of index.The stated expression is-
= (5⁻² x 10⁻⁴) / (2⁻⁵ x 5⁻⁶)
Taking the reciprocal of the numbers.
= (2⁵ x 5⁶) / (5² x 10⁴)
Cancel the common power
= (2⁵ x 5⁴) / ( (2x5)⁴)
Expanding the power
= (2⁵ x 5⁴) / ( 2⁴ x 5⁴)
Again cancel the common power.
= 2
Thus, the simplification of the given expression is found as 2.
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The correct question is-
What is the value of (5⁻² x 10⁻⁴) / (2⁻⁵ x 5⁻⁶)?
What are the slope and Y − intercept of the equation y 2x − 4 *?
The equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.
The equation y = 2x - 4 can be written in slope-intercept form as y = 2x + b, where b is the y-intercept. To find the slope and y-intercept of the equation, we need to solve for b.
The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we can set x equal to 0 in the equation to get y = 2(0) - 4. This simplifies to y = -4, so the y-intercept is -4.
The slope is the rate at which the line rises. To find the slope, we can take the coefficient of x, which is 2. So the slope of the equation y = 2x - 4 is 2.
In summary, the slope of the equation y = 2x - 4 is 2 and the y-intercept is -4. We can write the equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.
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Which expression is equivalent to 18x + 6y - 3
By using the concept of algebraic expression, it can be calculated that-
Expression equivalent to 18x + 6y - 3 is 3(6x + 2y - 1)
What is algebraic expression?
An algebraic expression is an expression that consists of numbers, variables, and operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to represent relationships between numbers, or to represent solutions to equations. These expressions are often used in mathematics, engineering, and computer programming. Algebraic expressions can also be used to create equations or to solve problems. Algebraic expressions can be written in both standard form and expanded form, and can be evaluated to find values for the variables.
The given expression is 18x + 6y - 3
Now,
18x + 6y - 3
3(6x + 2y - 1)
Expression equivalent to 18x + 6y - 3 is 3(6x + 2y - 1)
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Damon says -3/4=3/-4=-3/4 Is he correct? Why or why not
Answer:
Step-by-step explanation:
Yes, he is correct because writing a negative symbol with a denominator and numerator makes the sense same. Because the negative is as a whole not only the numerator and not only the denominator. As it is a fraction which is a whole single identity.
3/4= 0.75, Therefore in each above three always the
-0.75= -0.75= -0.75 will give same value in each.
The table shows the number of points scored by a basketball team in their first seven games.
Answer:
15
Step-by-step explanation:
the range is the largest number take away the smallest number
56-41=15
3
Each side of a cube is 2.5 cm long. Find the volume of the cube.
7.5 cm3
6.25 cm3
15.625 cm3
5 cm3
The volume of a cube is 15.625 cubic cm.
What is the volume of a cube?
A cube is a three-dimensional shape having 6 square faces, all the faces are of equal length, breadth, and height.
The volume of the cube is given by side * side * side.
The volume of a cube is given by:
V = a³,
where a is the side length of the cube.
Each side of a cube is 2.5 cm long.
Then, the volume of the cube will be:-
V = (2.5)³,
= 15.625
Hence, the volume of a cube is 15.625 cubic cm.
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suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same. what is the probability that one of the first three golfers that registered for the tournament will win?
The correct answer c. 0.300
All the golfers have similar skill levels, which means that they are equally as likely to win the tournament.
The sum of all 10 golfers probability to win the tournament is 100/10 = 10%.
What is the probability that one of the first three golfers that registered for the tournament will win?
Each one of them has a 10% probability of winning
3*10% = 30% = 0.3
So the correct answer is:
c. 0.300
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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Full Question :Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same. What is the probability that one of the first three golfers that registered for the tournament will win?
a. 0.111
b. 0.001
c. 0.300
d. 0.9
e. 0.850
19. On the grid below, graph the following functions:
(a) y = 2 · (x − 6) 2 − 10
(b) y = − x 2 + 4
Answer:
это будет 1000000000000
P(A)=0.2 and P(B)=0.4 are independent events. P(B|A)= 0.8.
What is P(A and B) ?
a) .40
b) .16
c) .48
d) .32
e) .60
The probability P(A and B) has a value of 0.08
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Event A has probability 0.2Event B has probability 0.4These mean that
P(A) = 0.2
P(B) = 0.4
From the question, we have
The events are independent events
The probability A and B is calculated as
P(A and B) = P(A) * P(B)
Substitute the known values in the above equation, so, we have the following representation
P(A and B) = 0.2 * 0.4
Evaluate
P(A and B) = 0.08
Hence, value is 0.08
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Given the function:
y = 3x2 − 10
What can replace y?
What is the range if the domain value is 3?
It derives its name from the famous rock on the Capitoline Hill in Rome from where prisoners were hurled to their deaths in ancient times.
What is a domain in the function?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. Range = {12, 3, 0}Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.A domain is a particular field of thought, activity, or interest, especially one over which someone has control, influence, or rights.To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y).
This question isn't history; it's mathematics.
However, the solution is as follows:
Given
f(x) = 3x²
Domain = {-2, -1, 0}
Required
Calculate the Range
To calculate the range, we simply plug in the values of the domain in the given function
Let the domain be represented by x; such that
x = {-2, -1, 0}
When x = -2
f(x) = 3x²
f(-2) = 3 * (-2)²
f(-2) = 3 * 4
f(-2) = 12
When x = -1
f(x) = 3x²
f(-1) = 3 * (-1)²
f(-1) = 3 * 1
f(-1) = 3
When x = 0
f(x) = 3x²
f(0) = 3 * 0²
f(0) = 3 * 0
f(0) = 0
The range are the values of f(-2), f(-1) and f(0)
Hence, Range = {12, 3, 0}
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-2+x=22 one step equations
Answer:
x = 24
Step-by-step explanation:
-2+x=22 one step equations
just add 2 to 22
-2 + x = 22
x = 24
----------------------
check
-2 + 24 = 22
22 = 22
the answer is good
Answer:
x = 24
Step-by-step explanation:
- 2 + x = 22 ( isolate x by adding 2 to both sides )
x = 22 + 2 = 24
A line passes through the points A(–1, 7) and B(1, 3). b Write an equation
Answer:
y=-2x+5
Step-by-step explanation:
First, find the slope:
m=(y2-y1)/(x2-x1) ==> slope formula where m is the slope
(–1, 7), (1, 3) ==> (x1=-1, y1=7), (x2=1, y2=3)
m=(3 - 7)/(1 - (-1)) ==> plugin y2=3, y1=7, x2=1, and x1=-1 into the slope formula
m=(-4)/(1 + 1) ==> simplify
m=(-4)/2
m=-2 ==> the slope is -2
y=mx+b ==> slope-intercept equation
3=(-2)(1)+b ==> plugin the slope(m=-2) and point B(1, 3) ==> (x=1, y=3)
3=-2+b ==> solve for b
3+2=-2+2+b ==> add 2 on both sides to isolate b
b=5 ==> simplify
y=-2x+5 ==> plugin the slope and b=5 into the equation
What is the roots of 3x² 10x 8 0?
The roots of equation in quadratic form 3[tex]x^{2}[/tex]- 10x + 8 = 0 are: x= -2/3 , -4 .. A polynomial equation of the second degree can be used to define quadratics.
what is a quadratic equation ?A quadratic issue in mathematics involves multiplying a variable by itself, often known as "squaring," which is a mathematical operation. This vocabulary is based on the fact that a square's area is equal to the product of its side length and itself. Quadratum, the Latin word for square, is the source of the word "quadratic."
here
= 3[tex]x^{2}[/tex] - 10x + 8 = 0
= 3[tex]x^{2}[/tex]+ 2x - 12x + 8 = 0
= 2 ( x + 4 ) + 3x( x + 4 )
= ( x + 4 )( 3x + 2 )
x = -4 and x = -2/3
The roots of equation in quadratic form 3[tex]x^{2}[/tex]- 10x + 8 = 0 are: x= -2/3 , -4 .
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How do you make the discontinuous classes as continuous classes explain with an example?
Discontinuous classes can be made continuous by using interpolation, which expression values between known points. For example, a discontinuous class of heights can be made continuous by using interpolation to estimate heights between known points.
Discontinuous classes can be made continuous by using interpolation. Interpolation is a mathematical process that estimates values between known points. This can be done in a variety of ways, such as linear interpolation which estimates values using the slope between two known points, or polynomial interpolation which uses a polynomial equation to estimate the values between known points. For example, if you have a discontinuous class of heights, you can use interpolation to estimate values between the known heights. This would result in a continuous class of heights, which may be more useful than the discontinuous class. Interpolation can also be used to estimate other types of values, such as temperature, pressure, or any other type of value that can be represented on a continuous scale.
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What are the 3 linear formulas?
Basic Formula: ax + by = c
where a 0 and a, b, and c are all real numbers. m ...
Form of the Slope Intercept: y = mx + b
where (x,y) is a line connecting the points y and x.
In two-point form, y y 1 = m (x x 1) y y 1 = m (x x 1)
In the case where (x1,y1) (x 1, y 1) and (x2,y2) (...
Form of Intercept:
x/ x0 x 0 and y/ y0 y 0 equal 1.
where y0 y 0 = y-in and x0 x 0 = x-intercept...
What are the two types of two-variable linear equations?Different forms of a two-variable linear equation are possible, including standard form, intercept form, and point-slope form. For instance, the equation 2x+3y=9 may be expressed using either of the following forms: 2x+3y-9=0 (standard form), y = (-2/3)x + 3, and Form of the Intercept: y - 5/3 = -2/3(x + (-2)) (point-slope form).
How are linear equations solved?Find the value of the variable that causes the equation to be true in order to solve linear equations. Utilize the inverse of the variable's multiplier and divide or multiply both sides by it. To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.
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thanks and 20 points
How many elves are helping Santa?
There are a total of 58 reindeer and elves helping Santa get ready for Christmas. Each reindeer has 4 legs and each elf has 2 legs. Frosty the Snowman, who doesn’t have any legs, counted 158 legs when all the reindeer and elves were in Santa’s workshop helping Santa. How many elves are helping Santa? Enter your answer as a number only
Santa's workshop staff traditionally consists of six elves with names. His elves construct the toys, wrap the presents, and craft the magic.
How many elves help Santa?Manufacturing toys for Christmas presents, caring for the reindeer, baking cookies, making sweets, setting up Santa's sleigh, and helping Santa with other jobs are all responsibilities of a Christmas elf. Making toys all year long is one of the main responsibilities of Christmas elves.
They numbered 144 in total. Twelve became their base number and 144 their greatest number as all elves were discovered in groups of twelve (for a long time). There was no common name for a larger number in any of the later Elvish languages.
The typical image of a Christmas elf is one who is dressed in green or red, has big, pointy ears, and a pointy cap. They are frequently shown as humanoids, yet occasionally as fuzzy, tail-equipped mammals.
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Find a set of vectors spanning the null space of A= 1 1 2 -1 2 3 6 -2 -2 1 2 2 0 -2 -4 0
The set of vectors spanning the null space of A is {(0,0,z)}.
A set of vectors spanning the null space of a matrix A is a set of vectors that, when multiplied by the matrix A, result in the zero vector. In other words, these vectors are in the null space of A because they are mapped to the zero vector under the transformation represented by A.
To find a set of vectors spanning the null space of matrix A, you can use the following steps:
Write the matrix A in row-reduced echelon form.Identify the pivot columns in the matrix. These are the columns that contain the leading 1's in the row-reduced echelon form.For each pivot column, assign a variable to the corresponding pivot row.For each pivot column, set the variables corresponding to all other rows in the column equal to 0.For each non-pivot column, set the variables corresponding to the rows in the column equal to a free variable.The set of vectors formed by the values of the variables is a set of vectors spanning the null space of A.To find a set of vectors spanning the null space of the matrix A= 1 1 2 -1 2 3 6 -2 -2 1 2 2 0 -2 -4 0:
Write the matrix A in row-reduced echelon form:
1 1 2 | -1
0 0 0 | 0
0 0 0 | 0
The pivot columns are the first and second columns, which contain the leading 1's.
Assign variables x and y to the pivot rows:
1 1 2 | -1
0 0 0 | 0 x
0 0 0 | 0 y
Set the variables corresponding to all other rows in the pivot columns equal to 0:
1 1 2 | -1
0 0 0 | 0 0
0 0 0 | 0 0
Set the variables corresponding to the rows in the non-pivot column equal to a free variable z:
1 1 2 | -1
0 0 0 | 0 0 z
0 0 0 | 0 0 z
The set of vectors spanning the null space of A is {(0,0,z)}.
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How do you read a limit on a graph?
The limit of a graph can be read by a function is said to have a limit if the value of the function is less than or equal to a particular value.
Limit
One way to think about the limit of a function at a number at x = an is as the value that the function begins to take as it gets closer to that value. Approaching the location where x = a can be done from either the left or the right side.
From a limx to a f (x)
As an illustration, if f(x) is defined as the limit of x, then x is the highest value that f can take. A function is said to have a limit if the value of the function is less than or equal to a particular value. For a given function, there can be multiple limits, but only one of them can be larger than the others.
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