The position vector from (3, − 8,0) to ( − 9, − 7, − 6) is (-12, 1, -6).
To find the position vector, we need to add this vector to the initial point (3, -8, 0). This gives us:
(3, -8, 0) + (-12, 1, -6) = (-9, -7, -6)
In mathematics, position vector refers to a vector that describes the position of a point relative to an origin point. In this question, we are asked to find the position vector that is equal to the vector from (3, -8, 0) to (-9, -7, -6).
To find the position vector, we need to add the vector from the initial point to the final point to the initial point itself. This gives us the endpoint of the vector, relative to the origin. The position vector is important in many applications, such as physics, engineering, and computer graphics, where it is used to describe the position of an object or point in space.
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Which of the following are quadratic equation 2x² √ 3x 9 0?
Yes, 2x²-√3x+9=0 is a quadratic equation.
A quadratic equation is a type of polynomial equation that can be written in the form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the equation 2x²-√3x+9=0 can be written in the form of ax² + bx + c = 0, where a = 2, b = -√3 and c = 9. Therefore, it is a quadratic equation. Quadratic equations have solutions in the form of x = (-b ± √(b² - 4ac))/2a, which is also known as the quadratic formula. In this case, if we substitute the values of a, b, and c into the quadratic formula, we can find the solutions for x in the equation 2x²-√3x+9=0.
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Complete question:
2x²-√3x+9=0 is it a quadratic equation?
Can a domain be all numbers?
Yes, a domain can be all numbers. This type of domain is called a numerical domain.
A numerical domain is a set of numbers that is used to define a function. It is usually represented by the formula D= {x: x is a real number}. This formula can be used to calculate the domain of a given function by determining which values of x, or the independent variable, produce a valid output. Numerical domains are becoming increasingly popular as they are easier to remember than domains composed of letters and hyphens. They can also be used to represent a business’s contact information, such as a phone number or street address. When registering a numerical domain, it is important to ensure that it is not already taken, as numerical domains are becoming increasingly sought after. For example, if a function is defined as f(x) = x2 + 3, then the domain would be all real numbers, since any real number would produce a valid output.
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Calculate the age of a fossil. If 32% of the initial amount of Carbon 14 in a sample remains, how much time has elapsed?
The age of a fossil can be determined using Carbon 14 dating. Carbon 14 dating is a method of determining the age of an object that is based on the decay of the isotope carbon-14. Carbon-14 has a half-life of approximately 5,730 years, which means that half of the initial amount of carbon-14 in a sample will decay in 5,730 years.
What is carbon dating in simple words?
Simply said, carbon dating is the process of using the presence of carbon 14 to estimate the age of ancient material (such as an archaeological or paleontological specimen).
If 32% of the initial amount of Carbon 14 in a sample remains, we can use the formula:
Age = t = (t1/2) * ln(2) / ln(A0/A)
Where t1/2 is the half-life of carbon-14 (5730 years), A0 is the initial amount of carbon-14 (100%), and A is the remaining amount of carbon-14 (32%).
Age = (5730) * ln(2) / ln(100/32)
Age = (5730) * 0.693 / (-1.51)
Age = 8129 years
So, approximately 8129 years have elapsed since the fossil was formed.
Note that this is an estimate and this method of dating can only be used for fossils that are less than about 60,000 years old. Also, this method assumes that the initial amount of carbon-14 in the sample is known, which can be affected by the environment and other factors that can affect the accuracy of the dating.
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Determine the simple interest on an account paying 5.5% annually interest of an investment of $20,650. a. $1115.65 c. $1135.75 b. $1125.55 d. $1145.45
Elliot added the two equations and the result was 2x = 38. Solve the equation. How many of each type of book does elliot have? fiction books nonfiction books.
For each type of book, Elliott has 19 fiction books and 7 nonfiction books.
To solve for the number of fiction books (x), we can use the first equation of the system: x + y = 26. We know that the number of nonfiction books (y) can be represented by x - 12 (from the second equation of the system: x - y = 12).
So we can substitute x - 12 for y in the first equation:
x + (x - 12) = 26Combining like terms:
2x - 12 = 26Adding 12 to both sides:
2x = 38Dividing both sides by 2:
x = 19Therefore, Elliot has 19 fiction books.
To solve for the number of nonfiction books (y), we can use the first equation of the system: x + y = 26 and input the value of x:
x + y = 26y = 26 - xy = 26 -19y = 7Therefore, Elliot has 7 nonfiction books.
This question is incomplete and should be written as:
Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books and y represent the number of nonfiction books.
This system of equations models the number of books.
x + y = 26x – y = 12Elliot added the two equations and the result was 2x = 38. How many fiction and nonfiction books does Elliot have?
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Jump To The Flag
Bob is trying to reach a flag that's some height above the ground. In his attempt to reach the flag, Bob can make any number of jumps up the rock wall where it's mounted. He can only move up the wall though, and he must end at exactly the height of the flag. There are 2 types of jumps:
1. A jump of height 1.
2. A jump of height j ;
Determine the minimum number of jumps it will take Bob to reach the flag's height exactly
The minimum number of jumps required to reach the flag's height is 3.
Let n be the height of the flag. We can use a recursive approach to determine the minimum number of jumps it takes to reach the flag's height.
For n = 0, it takes 0 jumps to reach the flag's height.
For n = 1, it takes 1 jump to reach the flag's height.
For n > 1, we can calculate the minimum number of jumps using the following equation:
minJumps(n) = 1 + min(minJumps(n-1), minJumps(n-j))
Where minJumps(x) is the minimum number of jumps required to reach the flag's height from ground level x.
For example, if the flag's height is 5 and Bob can jump a height of 2, the minimum number of jumps required to reach the flag's height is 3.
minJumps(5) = 1 + min(minJumps(4), minJumps(3))
= 1 + min(1 + min(minJumps(3), minJumps(2)), 1 + minJumps(2))
= 1 + min(1 + 1, 1 + 1)
= 3
Therefore, the minimum number of jumps required to reach the flag's height is 3.
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What is 20% of 141 thx a lot
Answer:
28.2 percent
Step-by-step explanation:
multiply 1/5 by 141
Which is true about adding and subtracting polynomials?A.In adding and subtracting, we copy the common base, then add or subtract their exponents.B.To add and subtract polynomials, we copy the common variable, then multiply their exponents.C.We can add and subtract terms regardless if they have the same base.D.We can only add and subtract like terms
The correct answer is C. We can add and subtract terms regardless if they have the same base.
To add polynomials, we add the coefficients of the like terms together. For example, to add 2x^3 + 5x^2 + 6x + 3 and 3x^2 + 7x + 8, we would first identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then added together, so 2x^3 + (5+3)x^2 + (6+7)x + (3+8). The result is 2x^3 + 8x^2 + 13x + 11.
To subtract polynomials, we subtract the coefficients of the like terms. For example, to subtract 3x^2 + 7x + 8 from 2x^3 + 5x^2 + 6x + 3, we would identify the like terms, which in this case are x^2 and x. The coefficients of the like terms are then subtracted, so 2x^3 + (5-3)x^2 + (6-7)x + (3-8). The result is 2x^3 + 2x^2 - x - 5.
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What is the formula for scale factor?
The formula for scale factor is: Scale Factor = New Length / Original Length.
What is scale factor?Scale factory the rescue between two corresponding length, area or the volumes of two similar figure it is used to compare the size of one figure to another as well as to the enlarge of reduced to size of a figure the scale factor is expressed as a ratio such as one is to to fit the first number is the original size and the second is the new size.
This is used to determine the factor by which an object has been scaled up or down. For example, if an object was originally 8 inches long and then scaled up to 16 inches long, the scale factor would be 2, as 16 is twice the length of 8.
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What is the tangent ratio for
Check the picture below.
The value of y is 37 times the value of x.
Answer:
y = 37x
Step-by-step explanation:
We know
The value of y is 37 times the value of x, so our equation is
y = 37x
Is this a function or just a relation?
From the given figure, we can say that it is a relation as 0 is input for both -2 and 1.
What is the Onto function ?
Onto function can be defined as the function in which the range is equals to codomain.
We know that relation can be defined as the relationship between sets of values and it is denoted by R.
And Function can be defined as the it is a relation where with only one output to each input.
From the given figure,
(0,-2) (0,1) (1,2) (2,1) (3,4) are the ordered pairs and here 0 is input for both -2 and 1
Hence , From the given figure, we can say that it is a relation as 0 is input for both -2 and 1.
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Are prime numbers only divisible?
No, prime numbers are not divisible by any other number apart from one and number itself.
As given in the question,
Given numbers are prime numbers,
Condition to be asked :
Prime numbers are divisible.
Prime numbers are those numbers which are only divisible by only two numbers one and number itself.
Prime numbers has only two factors one and number itself.
Example of prime numbers are as follow :
2, 3, 5, 7, 11,.....so on.
If the number has more than two factors then the numbers are considered as composite numbers.
One is neither prime nor composite.
Therefore, prime numbers are not divisible by any other number.
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Find the area of the trapezoid
Step-by-step explanation:
we need Pythagoras for right-angled triangles
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
we also need to remember that the sum of all angles in a quadrilateral (4-sided shape) is 360°.
so, as 3 angles in the main quadrilateral are 90°, so is also the 4th angle. and that makes the quadrilateral a regular rectangle.
we know the length of the rectangle (15 ft).
the width is also the second leg of the attached right-angled triangle.
so, we know
13² = 5² + (leg2)²
169 = 25 + (leg2)²
144 = (leg2)²
leg2 = sqrt(144) = 12 ft
the total area is
the area of the rectangle
+
the area of the triangle
the area of the rectangle is
length × width = 15 × 12 = 180 ft²
the area of the right-angled triangle is
leg1 × leg2 / 2 = 5 × 12 / 2 = 5×6 = 30 ft²
the total area is
180 + 30 = 210 ft²
FYI - a different way is to directly calculate the area of the trapezoid :
(base1 + base2)×height/2
height = the width of the rectangle or leg2 of the right-angled triangle.
so, we have
(15 + (15 + 5))×12/2 = (15 + 20)×6 = 35×6 = 210 ft²
What is the distance from center formula?
From the centre formula the distance is between two points in a plane.
A mathematical calculation known as the distance formula is used to calculate the separation between two points on a plane. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the legs, is the source of the distance formula which is the side opposite the right angle.
The distance formula is frequently shown as: d = √((x2 - x1)² + (y2 - y1)²). The first point's coordinates are x1 and y1, the second point's coordinates are x2 and y2, and d is the distance between the two points. It's crucial to keep in mind that this method only works when the two points are in a 2D plane.
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number of pounds in z ounces
Answer:
0.0625 pounds are in an ounce
Step-by-step explanation:
Hope This Helps!
Answer:
Below
Step-by-step explanation:
There are 16 oz to a pound
if you have 'z' ounces then you have z/16 pounds
z oz / 16 oz/lb = z/16 lb
what is the slope of the line connecting (5,1) and (-1,3)? Please exlplain how you got the answer. I will mark you brainliest.
The slope of the line connecting the points (5,1) and (-1,3) will be - 1/3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are given below.
(5, 1) and (-1, 3)
The slope of the line is given as,
m = (3 - 1) / (- 1 - 5)
m = 2 / (-6)
m = - 1/3
The slope of the line connecting the points (5,1) and (-1,3) will be - 1/3.
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the rate of 2 of 2 pounds of rice for $4 is written
The unit rate of the pound of rice is given by the equation A = $ 2
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the unit rate of the pound of rice be represented as A
Now , the equation will be
The cost of 2 pounds of rice = $ 4
So , the cost of 1 pound of rice = cost of 2 pounds of rice / 2
Substituting the values in the equation , we get
The cost of 1 pound of rice A = 4 / 2
The cost of 1 pound of rice A = $ 2
Therefore , the value of A is $ 2
Hence , the equation is A = $ 2
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Over which of the following is decreasing?
The correct option is C.
Describe Graph?A graph is a visual representation of data or a function, typically shown on a coordinate plane. It can be used to display information in a clear and concise way, and can be used to identify patterns, trends, or relationships within the data. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts. They are used in many different fields, including mathematics, science, engineering, economics, and statistics. A right angled triangle is a type of triangle in which one angle is 90 degrees. The side opposite the right angle is called the hypotenuse and the other two sides are called the legs. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
There are several types of graphs that can be used to represent data and information, including:
Line graphs: these are used to show the change in a variable over time. They are often used to represent continuous data.Bar graphs: these are used to show the frequency or quantity of different categories of data. They are often used to represent discrete data.Pie charts: these are used to show the proportion of different categories of data as a percentage of the whole. They are often used to represent data that is divided into parts of a whole.Scatter plots: these are used to show the relationship between two variables. They are often used to represent data that is spread out over a large range.Histograms: these are used to show the distribution of numerical data. They are similar to bar graphs, but they are used to represent continuous data rather than discrete data.Line plots: A line plot is a way to display data along a number line. It is a graph that shows frequency of data items in specific intervals or ranges along the number line.Dot Plots: A dot plot is a way to display data by using dots. Each dot represents a value.Box and Whisker plots: Box and whisker plots are a way to show the spread of data in a compact form and to identify outliers.To know more about coordinate plane visit:
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How many functions are there from a set with 4 elements to a set with 3 elements?
The total number of functions from a set with 4 elements to a set with 3 elements is 333 × 3 = 64.
There are a total of 4³ = 64 functions from a set with 4 elements to a set with 3 elements.
A function from a set A to a set B is a rule or a correspondence that assigns to each element of A exactly one element of B. Set A is called the domain of the function and set B is called the co-domain.
Since there are 4 elements in the domain and 3 elements in the co-domain, each element in the domain can be mapped to any of the 3 elements in the co-domain.
So for the first element in the domain, there are 3 options to map it to in the co-domain. Similarly, for the second element, there are 3 options, and so on.
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What are bases Grade 7?
Bases are chemical compounds that can accept hydrogen ions (H+) when added to water. Bases have a pH higher than 7 on the pH scale. Common bases include baking soda (sodium bicarbonate), lye (sodium hydroxide), ammonia (NH3), and calcium hydroxide (CaOH2).
The Importance of Understanding Bases in Grade 7 ChemistryBases are an important concept to understand in Grade 7 Chemistry. They are chemical compounds that have a pH higher than 7 on the pH scale and are capable of accepting hydrogen ions (H+) when added to water. Knowing the basics of bases can help students in a variety of ways, from understanding the properties of solutions to being able to identify and use different bases in lab experiments.
To begin with, understanding the properties of bases is essential in order to properly identify and use them in experiments. Bases can be divided into two categories: alkalis and acids. Alkalis are bases that are soluble in water, while acids are bases that are insoluble in water. Each type of base has its own unique properties and uses. For example, baking soda (sodium bicarbonate) is a common alkali that can be used for baking, cleaning, and even as an antacid. Meanwhile, lye (sodium hydroxide) is an acid that is used in many industrial processes, such as soap and textiles manufacturing.
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A rectangular solid (with a square base) has a surface area of 181. 5 square centimeters. Find the dimensions that will result in a solid with maximum volume.
The maximum volume is 63.75 cubic cm. The rectangular is kind of shape that has lenght and width.
To find the dimensions of the rectangular solid that will result in a maximum volume, we can use the formula for the surface area of a rectangular solid, which is:
Surface Area = 2lw + 2lh + 2wh
where l is the length, w is the width (which is the same as the base of the square), and h is the height.
We can set up an equation using this formula, with the given surface area:
181.5 = 2lw + 2lh + 2wh
To find the maximum volume, we can take the derivative of the volume equation and set it equal to 0, then solve for the value of the variable.
The volume of the rectangular solid is V = lwh
The derivative of V with respect to l is : dV/dl = wh
The derivative of V with respect to w is : dV/dw = lh
The derivative of V with respect to h is : dV/dh = lw
Therefore, the maximum volume occurs when dV/dl = 0, dV/dw = 0 and dV/dh = 0
Since the base of the rectangular solid is a square, we know that l = w
If we substitute this value into the equation for the surface area, we get:
181.5 = 2l^2 + 2lh
Solving for h in terms of l, we get:
h = (181.5 - 2l^2) / (2l)
We can now differentiate this equation with respect to l, and set it equal to 0, then solve for l:
[tex]\frac{dV}{dl} = (2lh + l^2h - 2l^3) / l = 0\\2l(181.5 - 2l^2) + l^3 = 0\\2l(181.5 - 2l^2) = -l^3\\2(181.5 - 2l^2) = -l^2\\363 - 4l^2 = -l^2\\l^2 = 181.5 / 2\\l = \sqrt{\frac{181.5}{2} } \\I = \sqrt{90.75} \\I = 3.5[/tex]
So the dimensions that will result in a maximum volume are:
length (l) = 3.5 cm
width (w) = 3.5 cm
height (h) = (181.5 - 23.53.5) / (2*3.5) = 5 cm
The maximum volume is V = lwh = 3.53.55 = 63.75 cubic cm
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Give a algebra equation to represent this pattern
In January, the number of days shown by the equation m = 4w + 3.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A pattern shown in the image.
Let m is the number of days in a month.
And w represents the number of days in the weeks.
So, algebraic equation,
m = 4w + 3.
Therefore, the equation is m = 4w + 3.
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What are the 2 methods of solving equations?
There are many methods for solving equations, but the two main methods are algebraic method and graphic method.
Algebraic methods: These methods involve using algebraic manipulation to isolate the variable on one side of the equation and find its value. This can include using operations such as addition, subtraction, multiplication, and division, as well as the use of inverse operations (e.g. undoing addition with subtraction) and properties of equality (e.g. transitive property).
Graphic methods: These methods involve using graphs to represent the equation and find the solution. This can include plotting the equation on a coordinate plane and finding the points of intersection, or using a graphing calculator or software to plot the equation and find the solution.
It's worth noting that the method used to solve an equation will depend on the complexity of the equation and the information available. Some equations can be easily solved using algebraic methods, while others may require a combination of algebraic and graphic methods or an entirely different approach.
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h(x)= 1/8 x^3 − x^2
Over which interval does h have a positive average rate of change?
A positive average rate of change over any interval [a,b] such that b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).
What is average rate?Average rate is a term used to describe the mean value of a set of data points or the mean rate of change of a function. It is calculated by adding all the values in a set and then dividing the sum by the total number of values.
The average rate of change of a function over an interval [a,b] is given by the formula (f(b) - f(a))/(b - a). Therefore, for h to have a positive average rate of change over an interval, we must have f(b) - f(a) > 0.
Substituting h(x) into this formula, we get (1/8b^3 - b^2 - 1/8a^3 + a^2) / (b - a) > 0.
Solving for b, we get b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).
Therefore, h has a positive average rate of change over any interval [a,b] such that b > a + (1/8a^3 - a^2)/(1/8a^3 - a^2).
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What is an example of a perpendicular bisector?
A perpendicular bisector is a line that passes through the midpoint of two points, and is perpendicular to the line connecting the two points.
An example of a perpendicular bisector is the line between points A(2,4) and B(4,6). The midpoint of A and B is (3,5), and the equation of the line perpendicular to A and B is y= -x+10. To verify that the equation is perpendicular to A and B, we can calculate the slope of the line connecting A and B. The slope of A and B is (6-4)/(4-2) which is equal to 2. The slope of a perpendicular line is the negative reciprocal of 2, which is -1/2. Therefore, the equation of the perpendicular line is y = -(1/2)x + 10. This equation passes through the midpoint (3,5) which verifies that it is a perpendicular bisector of A and B.
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i need the answer to this simplifying radicals
Answer:
9√6
Step-by-step explanation:
3√2 × 3√3
3√2×3 ×3
3√6×3
9√6
Triangle ABC is congruent to Triangle PDF. Side AC corresponds to what side in Triangle PDF?
Triangle ABC and Triangle are congruent, but PF is the corresponding side.
What are triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.
The vertex is the intersection of two straight lines. The triangle therefore has three vertices.
According to our question-
The matching parts of two figures that are congruent are identified by their respective vertices in the same order.
The side PF of PDF corresponds to the side AC of ABC (the first and last letters of the name or vertices) (corresponding letters in the name).
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What is the exponential of 7?
Answer:
1096.63316
Step-by-step explanation:
Is it possible to define all terms in geometry?
No, it is not possible to define all terms in geometry. The point, line, and plane are only a few of the many undefined terms in geometry. All other concepts in geometry may be defined from these three undefined terms.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.
The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
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No, it is practically not possible to define all terms in geometry. Points, lines, and planes are just a few of the many terms not defined in geometry.
Which term is not defined in geometry?The point, line, and plane are only adequately described by examples and descriptions, hence they are regarded as undefined words in geometry. Give the points, lines, and planes a name. Points that are on the same line are known as collinear points.
A legal document's definitions are often located at the outset, or at the start of a standalone portion like a schedule or section.
The study of different mathematical or real-world shapes, sizes, and figures is known as Geometry. You will learn about points, lines, planes, angles, parallel lines, triangles, similarity, quadrilaterals, transformations, circles, and area in geometry.
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