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Mnenie [13.5K]
3 years ago
7

Which undefined term is used to define an angle? line plane point ray

Mathematics
2 answers:
grigory [225]3 years ago
9 0

The undefined term is used to define an angle is the \boxed{{\mathbf{point}}}.

Further explanation:

A ray

It is straight line that has one fixed point and can be extended from another point.

The best example of the ray of sunlight as it does not extend from both the points and proceed in one direction.

Angle

An angle can be drawn with the union of two rays that has common endpoint.

The rays are the sides of the angle and the common end point is the vertex of the angles.

The symbol to represent the angle is “\angle”.

It can be better explained through an explain as,

\angle ABC{\text{ and }}\angle PQR    

The middle alphabet always represents the vertex of the angle.

The angle \angle ABC{\text{ }} can also be called as \angle B and \angle PQR can also be called \angle Q.

The angle \angle ABC read as ABC and \angle PQR read as PQR.

The angle is measured with the use of protractor.

Procedure to measure an angle with protractor:

Place the mid point of the protractor on the vertex of the angle.

Placed the protractor in such a way that one side of the angle match with the zero line of the protractor.

Now read the degree as per the required problem.

Thus, the undefined term is used to define an angle is the {\text{point}}.

Learn more:  

  1. Learn more about the cost of   coffee cans brainly.com/question/1576882
  2. Learn more about the whole value of   for which the solution of the equation brainly.com/question/11744034
  3. Learn more about total number of pictures does Jennifer and Luisa has brainly.com/question/862216

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Line, rays and angles.

Keywords: Angle, rays, lining, vertex, line, segment, line segment, mid point, degrees, zero line, protractor, scale

Afina-wow [57]3 years ago
4 0

The Undefined term that is used to define an angle is a point.

<h2>Further Explanation: </h2><h3>Angle</h3>
  • An angle is defined as the union of two rays with a common endpoint.
  • The common end point is known as the vertex of the angle while the rays are known as the sides of the angle.
<h3>A ray  </h3>

It is a part of a line with one end point and proceeds on in one direction.

<h3>Naming of angles</h3>
  • Angles can be named in three different ways;
  1. Using three Capital letters such as ∠ PQR, or ∠BCD. The middle letter represents the vertex of the angle. Therefore, the angles above are read as "angle PQR" and angle BCD.
  2. Using the Vertex of the angle. For example, in the case of ∠PQR, can also be called angle Q, while ∠BCD can be called angle C.
  3. Angles can also be named by placing any number or symbol at the vertex in the interior of the angle. Such that angles can be called angle 1 or angle 3 , or angle 5, and so on.
  • Angles are measured using a tool known as a protractor
<h3>Measuring of an angle using a protractor</h3>
  • To measure the angle, the mid-point of a protractor is placed on the vertex of the angle.  
  • Then lining up one side of the angle with the zero line of the protractor.  
  • Then read the degrees where the other side crosses the number scale.

Keywords: Rays, angles, properties of angles, measurement of angles

<h3>Learn more about;</h3>
  • Angles: brainly.com/question/1745042
  • Rays: brainly.com/question/1745042
  • Units used to measure angles: brainly.com/question/8812311
  • Methods of naming angles: brainly.com/question/1594009
  • Measuring angles: brainly.com/question/1594009

Level: Middle school  

Subject: Geometry

Topic: Angles  

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f(x) = 2<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class="latex
loris [4]

Answer:

No answer is possible

Step-by-step explanation:

First, we can identify what the parabola looks like.

A parabola of form ax²+bx+c opens upward if a > 0 and downward if a < 0. The a is what the x² is multiplied by, and in this case, it is positive 2. Therefore, this parabola opens upward.

Next, the vertex of a parabola is equal to -b/(2a). Here, b (what x is multiplied by) is 1 and a =2, so -b/(2a) = -1/4 = -0.25.

This means that the parabola opens upward, and is going down until it reaches the vertex of x=-0.25 and up after that point. Graphing the function confirms this.

Given these, we can then solve for when the endpoints of the interval are reached and go from there.

The first endpoint in -2 ≤ f(x) ≤ 16 is f(x) = 2. Therefore, we can solve for f(x)=-2 by saying

2x²+x-4 = -2

add 2 to both sides to put everything on one side into a quadratic formula

2x²+x-2 = 0

To factor this, we first can identify, in ax²+bx+c, that a=2, b=1, and c=-2. We must find two values that add up to b=1 and multiply to c*a = -2  * 2 = -4. As (2,-2), (4,-1), and (-1,4) are the only integer values that multiply to -4, this will not work. We must apply the quadratic formula, so

x= (-b ± √(b²-4ac))/(2a)

x = (-1 ± √(1-(-4*2*2)))/(2*2)

= (-1 ± √(1+16))/4

= (-1 ± √17) / 4

when f(x) = -2

Next, we can solve for when f(x) = 16

2x²+x-4 = 16

subtract 16 from both sides to make this a quadratic equation

2x²+x-20 = 0

To factor, we must find two values that multiply to -40 and add up to 1. Nothing seems to work here in terms of whole numbers, so we can apply the quadratic formula, so

x = (-1 ± √(1-(-20*2*4)))/(2*2)

= (-1 ± √(1+160))/4

= (-1 ± √161)/4

Our two values of f(x) = -2 are (-1 ± √17) / 4 and our two values of f(x) = 16 are (-1 ± √161)/4 . Our vertex is at x=-0.25, so all values less than that are going down and all values greater than that are going up. We can notice that

(-1 - √17)/4 ≈ -1.3 and (-1-√161)/4 ≈ -3.4 are less than that value, while (-1+√17)/4 ≈ 0.8 and (-1+√161)/4 ≈ 2.9 are greater than that value. This means that when −2 ≤ f(x) ≤ 16 , we have two ranges -- from -3.4 to -1.3 and from 0.8 to 2.9 . Between -1.3 and 0.8, the function goes down then up, with all values less than f(x)=-2. Below -3.4 and above 2.9, all values are greater than f(x) = 16. One thing we can notice is that both ranges have a difference of approximately 2.1 between its high and low x values. The question asks for a value of a where a ≤ x ≤ a+3. As the difference between the high and low values are only 2.1, it would be impossible to have a range of greater than that.

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