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inessss [21]
3 years ago
8

How do you know when a term is defined or undefined

Mathematics
1 answer:
lord [1]3 years ago
5 0
In geometry, definitions are formed using known words or terms to describe a new word. There are three words in geometry that are not formally defined. These three undefined terms are point, line and plane. 

<span>POINT (an undefined term) </span>
<span>In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, (x,y). </span>

<span>LINE (an undefined term) </span>
<span>In geometry, a line has no thickness but its length extends in one dimension and goes on forever in both directions. A line is depicted to be a straight line with two arrowheads indicating that the line extends without end in two directions. A line is named by a single lowercase written letter or by two points on the line with an arrow drawn above them. </span>

<span>PLANE (an undefined term) </span>
<span>In geometry, a plane has no thickness but extends indefinitely in all directions. Planes are usually represented by a shape that looks like a tabletop or wall. Even though the diagram of a plane has edges, you must remember that the plane has no boundaries. A plane is named by a single letter (plane m) or by three non-collinear points (plane ABC). </span>

<span>Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the end point, and all points extending infinitely to one side of the end point. </span>

<span>Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single end point. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them. </span>

<span>Everything else builds on these and adds more information to this base. Those added things include all the theorems and other "defined" terms like parallelogram or acute angle. </span>
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Which type of geometry best describes the following statement?
oksian1 [2.3K]

Answer:

answer C

Hyperbolic geometry

The sum of the angles of a hyperbolic triangle is less than 180°.

6 0
3 years ago
The Students' Conjectures Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Po
noname [10]

Complete Question:

Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Polynomial product B: (x2 + x – 2)(4x2 – 8x) They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.

Answer:

A = B

Step-by-step explanation:

<em>See comment for complete question</em>

Given

A: (4x^2 - 4x)(x^2 - 4)

B: (x^2 + x - 2)(4x^2 - 8x)

Required

Determine how they can show if the products are the same or not

To do this, we simply factorize each polynomial

For, Polynomial A: We have:

A: (4x^2 - 4x)(x^2 - 4)

Factor out 4x

A: 4x(x - 1)(x^2 - 4)

Apply difference of two squares on x^2 - 4

A: 4x(x - 1)(x - 2)(x+2)

For, Polynomial B: We have:

B: (x^2 + x - 2)(4x^2 - 8x)

Expand x^2 + x - 2

B:(x^2 + 2x - x - 2)(4x^2- 8x)

Factorize:

B:(x(x + 2) -1(x + 2))(4x^2- 8x)

Factor out x + 2

B:(x -1) (x + 2)(4x^2- 8x)

Factor out 4x

B:(x -1) (x + 2)4x(x- 2)

Rearrange

B: 4x(x - 1)(x - 2)(x+2)

The simplified expressions are:

A: 4x(x - 1)(x - 2)(x+2) and  

B: 4x(x - 1)(x - 2)(x+2)

Hence, both polynomials are equal

A = B

3 0
3 years ago
Find the distance between y=4x+2,y=4x-3
KonstantinChe [14]
Pay attention in class and you would know
7 0
3 years ago
12x -20=n (3x-5)<br><br> I need help I don’t get it please help me.
Salsk061 [2.6K]

Answer:

The value of n = 4 and  

The value of x = \frac{5}{3}

Step-by-step explanation:

Method I:

As given, 12x -20=n (3x-5)      .........(1)

Firstly , take 12x - 20

As 12x - 20 can be written as 4(3x - 5)

∴ equation (1) becomes

4(3x - 5) = n (3x-5)

Divide the equation by (3x-5) , we get

4 = n

Method II:

As given, 12x -20=n (3x-5)

⇒12x - 20 = 3nx - 5n

⇒12x - 3nx = 20 - 5n

⇒3x(4 - n) = 5( 4 - n)

Divide the equation by (4-n) , we get

3x = 5

⇒ x = \frac{5}{3}

∴ we get

n = 4 and  x = \frac{5}{3}

Now, check that value of n and x satisfies the equation or not

12(\frac{5}{3}) - 20 = 4( 3(\frac{5}{3}) - 5)

⇒4(5) - 20 = 4(5 - 5)

⇒20 - 20 = 4(0)

⇒ 0 = 0

Hence , we get

The values of x and n satisfies the equation

so, we get

n = 4 and  x = \frac{5}{3}

5 0
3 years ago
What is the slope of the line that passes through the points (2,3) and (-2,6)?
Kobotan [32]

Answer:

-3/4

Step-by-step explanation:

To find the slope of the line, use the slope formula:

m = \frac{y_2-y_1}{x_2-x_1} = \frac{6-3}{-2-2} =\frac{3}{-2+-2}=\frac{3}{-4}

The slope of the line is -3/4.

3 0
3 years ago
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