Simplify
1 answer:
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Answer:
1. ∠1 = 120°
2. ∠2 = 60°
3. ∠3 = 60°
4. ∠4 = 60°
5. ∠5 = 75°
6. ∠6 = 45°
Step-by-step explanation:
From the diagram, we have;
1. ∠1 and the 120° angle are corresponding angles
Corresponding angles are equal, therefore;
∠1 = 120°
2. ∠2 and the 120° angle are angles on a straight line, therefore they are supplementary angles such that we have;
∠2 + 120° = 180°
∠2 = 180° - 120° = 60°
∠2 = 60°
3. Angle ∠3 and ∠2 are vertically opposite angles
Vertically opposite angles are equal, therefore, we get;
∠3 = ∠2 = 60°
∠3 = 60°
4. Angle ∠1 and angle ∠4 an=re supplementary angles, therefore, we get;
∠1 + ∠4 = 180°
∠4 = 180° - ∠1
We have, ∠1 = 120°
∴ ∠4 = 180° - 120° = 60°
∠4 = 60°
5. let the 'x' and 'y' represent the two angles opposite angles to ∠5 and ∠6
Given that the two angles opposite angles to ∠5 and ∠6 are equal, we have;
x = y
The two angles opposite angles to ∠5 and ∠6 and the given right angle are same side interior angles and are therefore supplementary angles
∴ x + y + 90° = 180°
From x = y, we get;
y + y + 90° = 180°
2·y = 180° - 90° = 90°
y = 90°/2 = 45°
y = 45°
Therefore, we have;
∠4 + ∠5 + y = 180° (Angle sum property of a triangle)
∴ ∠5 = 180 - ∠4 - y
∠5 = 180° - 60° - 45° = 75°
∠5 = 75°
6. ∠6 and y are alternate angles, therefore;
∠6 = y = 45°
∠6 = 45°.
Functions, equations and tables can be represented using graphs
- The x-intercepts are: 0, 0.35 and 1.53
- The local maximum is at point (0.17, 0.08), and the local minimum is at point (1.13, -1.07)
The expression is given as:
Rewrite the expression as a function
See attachment for the graph of the function.
<h3>The x-intercepts</h3>This is the point where the graph cross the x-axis.
From the attached graph, the x-intercepts are: 0, 0.35 and 1.53
<h3>The local maximum</h3>From the attached graph, the local maximum is at point (0.17, 0.08)
<h3>The local minimum</h3>From the attached graph, the local minimum is at point (1.13, -1.07)
<h3>Intervals</h3>- The graph increases at interval (-1.30, 0) and (1,13, infinity)
- The graph decreases at interval (- infinity, 1.30) and (0.35, 1.13)
Read more about graphs and functions at:
The answer is r=16 you have to square everything
