Given that f(8) = 14, it means that the input 8 results in an output of 14. The question asks for the inverse of this function, f^-1(14), which means we need to find the input that results in an output of 14.
To do this, we need to use the fact that f^-1(f(x)) = x for any x in the domain of f(x). In other words, if we apply the inverse function to the output of f(x), we should get back the original input.
So, we can start by finding the inverse function of f(x). If y = f(x), then we have:
y = 2x - 6
x = (y + 6)/2
Therefore, the inverse function of f(x) is f^-1(x) = (x + 6)/2.
Now, we can use this inverse function to find f^-1(14):
f^-1(14) = (14 + 6)/2 = 10
Therefore, the input that results in an output of 14 for the original function f(x) is 10.
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What is the meaning of 2n in math?
The meaning of 2n in mathematics is just a simple series that gives us different values when we put the integral values of n.
Oftentimes we come across a special series in the mathematical problems.
This mathematical series can be simplified into a quite simpler and a shorter form.
The given form 2n is also nothing but just yet another example of the mathematical series.
When we put the values of end to be 1,2,3,4,5,6,7,8...
We get the values of the expression to be 2,4,6,8,10...
This mathematical series makes problem easier for us understand and solve.
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10 POINTS UP FOR GRABS
Answer: Your answer would be 152 cm
Step-by-step explanation:
Outer part of the shape:
Length = 18 cm
width = 12 cm
Area of large rectangle = (18 ⋅ 12)
= 216 cm2------(1)
Inner part of shape:
Length = 6 cm
width = 3 cm
Area of small rectangle = (8 ⋅ 8)
= 64 cm2------(2)
(1) – (2)
= (216 – 164) cm2
= 154 cm2
I hope this helps!
please help me with this question
The distance from the home plate to the 2nd base will be 127.27 ft.
What is Pythagoras theorem?
The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Now using the Pythagoras theorem we can find out the length of the other wall
b²=h²-p²
The distance from home plate to the 2nd base will be
b²=h²-p²
h² = b²+p²
h² = 2*90²
h² = 2*90²
h² = 2*8100
h² = 16200
h = 127.27
Hence The distance from the home plate to the 2nd base will be 127.27 ft.
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does someone mind helping me with this question? Thank you!
Answer:
325 adults and 612 students entered the school play
Step-by-step explanation:
1st equation: x is the number of adults and y the number of students.
2nd equation: Students times what they payed + adults times what they payed:
1st: x + y = 937
2nd: 2x + 0.75y = 1109
x = 937 - y
Now let's replace x for (937 - y) in the 2nd equation, to find out the value of y:
2(937 - y) + 0.75y = 1109
1874 - 2y + 0.75y = 1109
1874 - 1.25y = 1109
-1.25y = 1109 - 1874
-1.25y = -765 (multiply -1)
1.25y = 765
y = 765 / 1.25
y = 612
Now that we found the y value, let's replace it in the 1st equation to find out the value of x:
x + 612 = 937
x = 937 - 612
x = 325
If you want to double check it, you can replace both in the 2nd equation, to make sure:
2 * 325 + 0.75 * 612 = 1109
650 + 459 = 1109 (checked)
What is the formula for an isosceles right triangle?
An isosceles right triangle is a special type of triangle that has two equal sides and one right angle.
It can be described using the Pythagorean Theorem, which states that the sum of the squares of the two legs of a right triangle are equal to the square of the hypotenuse. Mathematically, this can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two legs, and c is the length of the hypotenuse.
In an isosceles right triangle, two of the sides must be equal, so a=b. This means that the Pythagorean Theorem simplifies to 2a^2 = c^2. Solving for a gives a = sqrt(c^2/2). This is the formula for the sides of an isosceles right triangle.
As an example, consider a triangle with a hypotenuse of length 5. Substituting this into the formula gives a = sqrt(25/2), or a = 5/sqrt(2). This means that both of the legs of the triangle have length 5/sqrt(2).
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Pls help!! 20 points!!! Need to finish in an hour!!!!!
Answer:
B
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Please answer
I will give points
Answer:
[C] 3 3/4 Miles
Step-by-step explanation:
Given:
Zoe jogs 3/4 of a mile every 1/5 of an hour.
How many miles does Zoe jog per hour?
[A] 3/20 Miles
[B] 4/15 Miles
[C] 3 3/4 Miles
[D] 6 2/3 Miles
Solve:
Since, Zoe jogs 3/4 of a mile every 1/5 hour. And 5/5 = 1 hour.(Also known as 60 minutes) Which means 1/5 is 12 minutes. In order to find how much Zoe jogs per hour, we have to multiply.
Knowing that;
1/5 = 12 minutes
2/5 = 24 minutes
3/5 = 36 minutes
4/5 = 48 minutes
5/5 = 60 minutes (1 Hour)
Hence, 3/4 Multiply by 5.
3/4 × 5 = 3.75 = 15/4 = 3 3/4
As a result, Zoe jogs 3 3/4 miles per hour.
RevyBreeze
On Monday you ran to a playground 2 1/4 mi from your house. It took you 22 min to run there and 25 min to run back home. on Tuesday you ran the entire 4 1/2 mi at a constant speed of 6 1/4. What must you do to compare the times it took to go to and from the playground each day
You can conclude that it took you less time on Tuesday to run to and from the playground than it did on Monday.
What is the distance?Distance is defined as the product of speed and time.
To compare the times it took to go to and from the playground each day, you need to calculate the total time for each day.
On Monday, it took 22 minutes to run to the playground and 25 minutes to run back home, for a total time of 47 minutes.
On Tuesday, you ran the entire 4 1/2 miles at a constant speed of 6 1/4 miles per hour, so you can use the formula:
distance / speed = time.
In this case, 4.5 miles / 6.25 mph = 0.72 hours or 43.2 minutes.
Therefore, you can see that it took you 47 minutes on Monday, and 43.2 minutes on Tuesday to run to and from the playground.
Hence, you can conclude that running to and from the playground took you less time on Tuesday than it did on Monday.
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Which of the following are quadratic equations? (i) x^ 2 + 6 x − 4 = 0 (ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0 (iii) x^ 2 + 1/ x^ 2 = 5 (iv) x − 3/ x = x ^ 2 (v) 2 x^ 2 − √ 3 x + 9 = 0 (vi) x ^ 2 − 2 x − √ x − 5 = 0 (vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3 (viii) x + 1 x = 1 x+1x=1
Answer:
A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is a variable.
The equations that are quadratic equations are:
(i) x^ 2 + 6 x − 4 = 0
(v) 2 x^ 2 − √ 3 x + 9 = 0
The equations that are not quadratic equations are:
(ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0
(iii) x^ 2 + 1/ x^ 2 = 5
(iv) x − 3/ x = x ^ 2
(vi) x ^ 2 − 2 x − √ x − 5 = 0
(vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3
(viii) x + 1 x = 1
In (ii) √ 3 x^ 2 − 2 x + 1/ 2 = 0 the coefficient of x^2 is not a real number.
In (iii) x^ 2 + 1/ x^ 2 = 5 the equation is not in the form of ax^2 + bx + c = 0
In (iv) x − 3/ x = x ^ 2 the equation is not in the form of ax^2 + bx + c = 0
In (vi) x ^ 2 − 2 x − √ x − 5 = 0 the equation is not in the form of ax^2 + bx + c = 0
In (vii) 3 x ^ 2 − 5 x + 9 = x 2 − 7 x + 3 both sides are not equal
In (viii) x + 1 x = 1 the equation is not in the form of ax^2 + bx + c = 0
So, the equations that are quadratic equations are (i) and (v).
Step-by-step explanation:
In parallelogram ABCD, AB = 6x-4, CD = 5x + 1, and BC = 2x.
What is the perimeter of ABCD?
D
Perimeter
A
units
The perimeter of the parallelogram is 16x - 8
How to determine the perimeter of the parallelogramThe properties of a parallelogram are;
Opposite sides are said to be parallelOpposite sides of a parallelogram are equalOpposite angles of a parallelogram are equalInterior angles are supplementaryEach diagonal of a parallelogram separates it into two equal or equivalent trianglesThe diagonals of a parallelogram divide each otherThe formula for perimeter of a parallelogram is;
Perimeter = 2(a + b)
substitute the values
Perimeter = 2(6x - 4 + 2x)
collect like terms
Perimeter = 2(8x - 4)
expand the bracket
Perimeter = 16x - 8
Hence, the value is 16x - 8
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The population of Brownsville, Texas increased by 41 thousand
people from 1990 to 2000. In 2000, the population of Brownsville
was 140 thousand people. Write an equation to find the population
of Brownsville in 1990. Then use mental math to solve the equation.
P = 140,000 - 41,000
P = 99,000
The population of Brownsville in 1990 was 99,000 people.
Please Help!!!
What is the volume of the box in the picture? (Volume= Length x Width x Height)
Answer: 72cm i think
Step-by-step explanation: L=6cm, W=2cm, H=6cm
6x2x6=72cm
What should be taken away from 3x² 4y² 5xy 20 obtain X² y²+ 6xy 20?
The expression that should be subtracted is 4x² - 3y² - xy.
An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
We will be using the concept of addition and subtraction of algebraic expressions to solve the given question.
Let us assume the missing part is X.
Therefore according to the question,
(3x² - 4y² + 5xy + 20) - (X) = - x² - y² + 6xy + 20
Let us shift the terms to find the value of X
X = 3x² - 4y² + 5xy + 20 - (- x² - y² + 6xy + 20)
X = 3x² - 4y² + 5xy + 20 + x² + y²- 6xy - 20
X = 4x² - 3y² - xy
Thus, the expression that should be subtracted is 4x² - 3y² - xy.
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It is given that y varies directly as x. If y = 5 when x = 4 determine the constant of variation.
When y changes directly as x, the variation constant is 5/4.
What is constant of variation?In a direct variation, the ratio of two variables; in an inverse variation, the product of two variables. The constant of variation k is used in the direct variation equations = k and y = kx, as well as the inverse variation equations xy = k and y =. A constant of variation (k) is a ratio that shows the connection between the independent and dependent variables (x and y) (y). If both variables have known values, it may be determined by dividing y by x. The constant of variation is the number that connects two variables that are either directly or inversely proportional to each other.
Here,
When one thing varies to another there is always a constant of variation. direct variation it is; y = kx
use the x,y values to find k
5 = 4k
5/4 = k
The constant of variation when y varies directly as x is 5/4.
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Nya mapped a quadrilateral on a coordinate plane. If she plots one segment from (−3,−3) to (3, 9) and another segment from (−5, 12) to (1, 0) are the segments parallel? Justify your reasoning.
We checked the equation of lines are not parallel to each other.
What are parallel lines?
The two lines when located at the same plane and equidistance from each other are called parallel lines. The properties of parallel lines as shown in equation is that both have same slope but different y intercept.
Two parallel lines never intersect.
Does the two lines parallel?equation of line passes through the point (- 3, -3) and (3, 9)
is given by the formula [ y - y₁] = [(y₂- y₁) / (x₂- x₁)] [x - x₁}
[ y- (-3)] = [9 - (-3) / 3- (-3)] [x - (-3)]
(y +3) = [(9+3)/ (3+3)] (x+3)
y+ 3 = 12/ 6 (x+3)
y+3 = 2 (x+3)
y+3 = 2x+6
y = 2x+3 this is the first line.
equation of line passes through (-5, 12) and (1, 0)
[y - 12] = [(0 - 12) / 1 - (-5)] [x - (-5)]
y -12 = -12/ 6 (x+5)
y - 12 = -2 x - 10
y = - 2x + 2
the above is the equation of second line.
the above two equation have same slope but different sign. Hence, the lines are not parallel to each other.
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Me need help please and thanks
The set of points that represents a relation and a function are given as follows:
{(-3, -2), (6, -2)}.{(-4, -3), (4,3)}.When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
Hence the desired relations are given as follows:
{(-3, -2), (6, -2)}.{(-4, -3), (4,3)}.As they both have different inputs, hence each input is mapped to a single output and they are functions.
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Identify whether the following problems are looking for the percentage, rate, or bas Then, solve for the unknown.
1. 250% of 200 85% of P78.00 is what amount?
2. 45% of 70 is what number?
3. 7 is 35% of what number?
4. 110% of what amount is P660.00? 5.P120.00 is 180% of what amount?
6. 125 is 250% of what number?
7. What percent of 16 is 64?
8. 85 is what percent of 340?
9. 13/11 13-is 1 is 26²/4 3 30.
10.
0.5% of what number is 2.5? 26% of what number?
Unknown numbers are 68, 31.50, 20, 600, 150, 50, 400%, 25%, 50, and 500 as percentages or rates.
what is percentage ?A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.
given
1. percentage
p = base x rate
= 80 x 85%
= 68
2. percentage
= 70 x 45%
= 31.50
3. base
b = percentage ÷ rate
= 7 ÷ 35%
= 20
4. base
= 660 ÷ 110%
= 600
5. base
= 120 ÷ 80%
= 150
6. base
= 125 ÷ 250%
= 50
7. rate
= 64 ÷ 16 x 100
= 400%
8. rate
= 85 ÷ 340 x 100
= 25%
9. base
= 13 ÷ 26%
= 50
10. base
= 2.5 ÷ 0.5%
= 500
Unknown numbers are 68, 31.50, 20, 600, 150, 50, 400%, 25%, 50, and 500 as percentages or rates.
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Which expression and quotient does the diagram model?
The diagram models the expression of option D: (x² + x - 2)/(x - 1) = x + 2.
What is an 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.
The given image is the dissection of an expression.
From the image it can be obtained that -
The area of the shadow of the fourth quadrant is equal to the width of the first quadrant multiplied by the length of the third quadrant.
So, the expression for the statement will be -
x² + x + x - x - 1 - 1 = (x + 1 + 1)(x-1)
x² + x - 2 = (x + 2) (x - 1)
(x² + x - 2)/(x - 1) = x + 2
Therefore, the expression obtained is (x² + x - 2)/(x - 1) = x + 2
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Need help with this question
On solving the provided question, we can say that equality of given trapezium we find, y=13/10 and x=21
What in mathematics is a trapezium?A convex quadrilateral with exactly one pair of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. A quadrilateral is a polygon in Euclidean geometry that has four sides and four vertices.
Since ABCD~PQRS
then, on comparing
5y-3/4 = 7/8
y=13/10
On comparing angle,
3x+24=87°
3x=63°
x=21
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Can someone help me? Picture attached
Answer:
6 units
Step-by-step explanation:
You want the length of the hypotenuse of a right triangle with legs 5 and √11.
Pythagorean theoremThe Pythagorean theorem tells you the relation between the legs a, b, and the hypotenuse c of a right triangle is ...
c² = a² +b²
c² = 5² +(√11)²
c² = 25 +11 = 36
c = √36 = 6
The length of the third side is 6 units.
Consider the triangles FGH and IJH where FGH ~ IJH
step one: find x
The values of x = 14 and y = 6.
What are Similar Triangles?Triangles that resemble one another but may not be exactly the same size are said to be similar triangles. When two objects have the same shape but different sizes, they can be said to be similar.
If ΔABC and ΔPQR are two similar triangles
=> AB/PQ = BC/QR = AC/PR
Here we have
ΔFGH and ΔIJH are two similar triangles
FG/IJ = GH/JH = FH/HI
From the given data,
6/3 = 12/y = x/7
Take 6/3 = x/7
Do cross multiplication
=> 3x = 42
=> x = 14
Take 6/3 = 12/y
Do cross multiplication
=> 6/3 = 12/y
=> 6y = 36
=> y = 6
Therefore,
The values of x = 14 and y = 6.
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15 more than twice a number is 37 What is the number?
Answer: 11
Step-by-step explanation:
Let the number be N.
Let's set up the equation.
2N + 15 = 37
Let's subtract 15 from both sides.
2N = 22
Divide both sides by 2, and you get
N = 11
Final Answer : 11
Explain the meaning of the expression p + 0.08p.
Answer:
The expression p + 0.08p can be interpreted as "p plus 8% of p". Mathematically, this expression is equal to 1.08p, which is the same as saying "p multiplied by 1.08".
3.1=x=-2
What is x
Three point one equals x equals negative two.
What is the answer to x
Answer: x = 6.2
Step-by-step explanation: don't ask how I know
What are the zeros of the function y = 2x*2 +7x + 1?
The zeros of the function y = 2x²+7x+1 are -0.35 and -3.35
What are zeros of a quadratic function?The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis.The zeros are often called the roots, solutions, or x-intercepts of the function.
Therefore when y = 0
2x²+7x+1 = 0
using formula method
a= 2, b= 7 and c = 1
x = (-b ± √b²-4ac )/2a
x= -7± √ -7²-4×2×1)/2×2
x= (-7± √ 49-8)/4
x= (-7± √41)/4
x= (-7+√41)/4 or (-7-√41)/4
x =( -7+6.4)/4
or (-7-6.4)/4
x = -1.4/4 or -13.4/4
x = -0.35 or -3.35
therefore the zeros of the function are -0.35 and -3.35
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Write the number 60 as a product of its prime factors in the same way. Write the factors in order, from smallest to largest
The prime factorization of 60 from smallest to largest is 2×2×3×5.
What is prime factorization?Prime factorization is the technique of expressing a number as the product of prime numbers. The only two components in prime numbers are the number itself and the number itself. Prime numbers include, for instance, 2, 3, 5, 7, 11, 13, 17, 19, and so forth. Any number can be represented as a sum of prime numbers using prime factorization.
The prime factorization of the number 60 is,
60 = 6×10.
60 = 2×3×2×5.
60 = 2×2×3×5.
60 = 2²×3×5.
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Triangle BMS has vertices B(-1, 0), M(-1, 1), and S(1, -6). Triangle BMS is dilated
by a scale factor of 4.5 with the origin as the center of dilation. What are the
new coordinates of the vertices of B'M'S'?
a B'(4.5, 0), M'(-4.5, 4.5), S'(-4.5, 0)
bB'(-4.5, 0), M'(-4.5, 4.5), S'(4.5, -27)
cB'(4.5, 0), M'(-4.5, 4.5), S'(4.5, 0)
dB'(-4.5, 0), M'(4.5, 4.5), S'(4.5, 0)
Using the provided coordinates and the scaling factor, The answer is option b. B'(-4.5, 0), M'(-4.5, 4.5), S'(4.5, -27).
What do you mean by transformation?In mathematics, a transformation refers to a function or a mapping that takes an input and produces an output. The input and output can be geometric shapes, vectors, or functions, and the transformation can change their position, size, or shape. Examples of transformations include translation, rotation, scaling, and reflection. In physics and engineering, transformation also refer to mathematical operations used to change a system's variables from one set of coordinates to another set of coordinates.
What do you mean by scaling?Scaling refers to the process of enlarging or reducing an object in size, either uniformly or non-uniformly. In mathematics, scaling is often represented by a scaling factor, which is a number used to multiply the coordinates of the object. Scaling can be applied to geometric shapes, vectors, and functions, and it can be done in one or multiple dimensions. Uniform scaling means that the object is scaled by the same factor in all dimensions. Non-uniform scaling means that the object is scaled by different factors in different dimensions.
B(-1, 0), M(-1, 1), and S(1, -6)
scaling factor (k) = 4.5
after scaling,
B'(-4.5, 0), M'(-4.5, 4.5), S'(4.5, -27)
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Consider the two linear functions reprsented by the table and the equations
Find the rise and run to determine the slope. Look up the y-intercept (the point where the line crosses the y-axis) Insert the value into the formula f(x)=mx+b.
How do you solve if an equation is a function?For any input, a function will only have one or no outputs. The equation does not define a function if a given input has more than one output. Each value of x must have a maximum of one output value of y in order to be considered a function. To determine the slope of a graphed function, use the average rate of change formula.
The average rate of change from a to some other value x is what determines the instantaneous rate of change at some time[tex]x_{0} =a[/tex]. The average rate of change from x=a+h to x=a is y x = f(x) f(a) x a =f (a + h) f( a ) h if h = 0 and a = f ( a + h ) f (a) h are set.
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In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 16 feet of fence for the shortest side and 20 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
The total perimeter of fencing that is needed for the entire animal pen is equal to 48 feet.
How to determine the feet of fencing that is needed for the entire animal pen?In order to determine the feet of fencing that is needed for the entire animal pen, we would have to calculate the third side of this right triangle pen by applying Pythagorean's theorem:
a² + b² = c²
Where:
a, b, and c represents the side lengths of a right triangle.
16² + b² = 20²
b² = 400 - 256
b = √144
b = 12 feet.
How to calculate the perimeter of this triangle?Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:
Perimeter of a triangle = a + b + c
Where:
a, b, and c represents the length of sides of a triangle.
Perimeter of a triangle = 16 + 20 + 12
Perimeter of a triangle = 48 feet.
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How do you work out a 1/3 of something?
By dividing any number 3 to simplify the expression.
What is simplifying an expression?
To simplify an expression, create a similar expression devoid of any similar terms. Therefore, we will rewrite the expression using the fewest number of terms possible.
When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.
One third is one part of three equal parts. When you split an object or number into thirds, you divide it by three.
Thirds are calculated by dividing by 3.
For example: One third of 24 =1/3 of 24 = 24/3 = 8.
Hence, by dividing any number 3 to simplify the expression.
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