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Rational Numebers: a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example: 1,2,3,-1,-2,-3
Irrational Numbers: an irrational number is a real number that cannot be expressed as a ratio of integers. For example: 1/3, 1/7 , 1/9
Real Numbers: a real number is a value that represents a quantity along a continuous line. For example: all rational and irrational numbers.
Whole Numbers: A member of the set of positive integers and zero. A positive integer. An integer. For example: 142, 20, 1
The geometric features of objects are the objects features that are constructed by the aid of elements of geometry
The definition of the geometrical features are as follows
- A ray is a line having a single starting point and a straight extension, having no end point
- A vertex is the meeting point of two or more lines
- An angle is formed by two rays that have a common vertex
- Parallel lines are two lines that are always the same distance from each other
- Parallel planes are two planes that have equal distance from each other
- Coplanar points are points on the same plane
- Collinear points are points on the same line
- Segment addition postulate states that segment AC can include a third point B, when AB + BC = AC
- Perpendicular lines are two lines that intersect at 90°
Based on the above definitions, the values in the table are as follows;
![\begin{array}{lcl} \mathbf{Feature}&& \mathbf{Denoted \ in \ diagram (s)}\\ \\Ray&&\\\\Vertex&&\\\\Angle&&\\\\Parallel \ lines &&\\\\Parallel \ planes &&\\\\Coplanar \ points&&\mathbf{C, \ F, A, N, B}\\\\Collinear \ points&&\mathbf{A, N, B}\\\\Segment \ addition \ postulate&&\mathbf{AN + NB} = AB\\\\Perpendicular \ lines&&\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Blcl%7D%20%5Cmathbf%7BFeature%7D%26%26%20%5Cmathbf%7BDenoted%20%5C%20in%20%5C%20diagram%20%28s%29%7D%5C%5C%20%5C%5CRay%26%26%5C%5C%5C%5CVertex%26%26%5C%5C%5C%5CAngle%26%26%5C%5C%5C%5CParallel%20%5C%20lines%20%26%26%5C%5C%5C%5CParallel%20%5C%20planes%20%26%26%5C%5C%5C%5CCoplanar%20%5C%20points%26%26%5Cmathbf%7BC%2C%20%5C%20F%2C%20A%2C%20N%2C%20B%7D%5C%5C%5C%5CCollinear%20%5C%20points%26%26%5Cmathbf%7BA%2C%20N%2C%20B%7D%5C%5C%5C%5CSegment%20%5C%20addition%20%5C%20postulate%26%26%5Cmathbf%7BAN%20%2B%20NB%7D%20%3D%20AB%5C%5C%5C%5CPerpendicular%20%5C%20lines%26%26%5Cend%7Barray%7D%5Cright%5D)
The features in the diagram are;
Coplanar points: C, F, A, N, B
Collinear points: A, N, B
Segment addition postulate: AN + NB = AB
Learn more about geometric features here:
brainly.com/question/11672333
Answer:
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Answer:
The term
for (x²-4x+8) and for (x²+4x+8) is negative.
Step-by-step explanation:
The x intercepts are the values of x in which the function is equal to zero. So if x⁴+64=(x²-4x+8)(x²+4x+8), the x intercepts are the values of x that satisfy:
(x²-4x+8) = 0 or (x²+4x+8) = 0
Then, the values of x that satisfy (ax²+bx+c) = 0 are calculated as:
or
![x=\frac{-b-\sqrt{b^{2}-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b-%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%7B2a%7D)
So, if the term
is negative the graph of the function has no x-intercepts.
Then, for (x²-4x+8) = 0, we get:
![b^{2} - 4ac = (-4)^{2}-4(1)(8)=16-32=-16](https://tex.z-dn.net/?f=b%5E%7B2%7D%20-%204ac%20%3D%20%28-4%29%5E%7B2%7D-4%281%29%288%29%3D16-32%3D-16)
At the same way, for (x²+4x+8) = 0, we get:
![b^{2} - 4ac = (4)^{2}-4(1)(8)=16-32=-16](https://tex.z-dn.net/?f=b%5E%7B2%7D%20-%204ac%20%3D%20%284%29%5E%7B2%7D-4%281%29%288%29%3D16-32%3D-16)