Which proportion would you set up to change 6 cups to pints?
2 answers:
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Answer: Angle A = 60°, angle B = 120°, angle C = 60°, angle D = 120°
Step-by-step explanation: Please refer to the attached diagram for further details.
The question has given the parallelogram ABCD as having side AB measuring 6 units, side AK measuring 3 units and line BK has been drawn perpendicular to line AD. This means line AK forms a right angle at the point where it meets line AD. From the information provided and the figure derived from that, we have right angled triangle ABK with the right angle at point K, line AB equals 6 units and line AK equals 3 units.
Using angle A as the reference angle, line AK is the opposite (side facing the reference angle), line AB is the hypotenuse (line facing the right angle) and line AK is the adjacent (side that lies between the right angle and the reference angle).
Hence, using the trigonometric ratios,
Cos A = adjacent/hypotenuse
Cos A = 3/6
Cos A = 0.5
Checking with the calculator, (that is second function of Cos 0.5)
A = 60
The opposite sides of a parallelogram are equal (that is line AD is parallel to line BC) and therefore opposite angles are equal (that is angle A is equal to angle C).
Similarly, angle B is equal to angle D. However, angles in a quadrilateral equals 360 degrees.
Therefore, angles in parallelogram ABCD is derived as;
A + B + C + D = 360
60 + B + 60 + D = 360
120 + B + D = 360
Subtract 120 from both sides of the equation
B + D = 240
Having known that angle B equals angle D, angles B and D is derived as each half of the value 240
Angle B = 240/2
Angle B = 120
and angle D = 120
Therefore, the angles are;
A = 60, B = 120, C = 60, D = 120
Answer:
This equation has 2 solutions.
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The point of intersection is the point where lines intersect.
<em>There will be 595 intersections for 35 lines, where no 3 lines are concurrent.</em>
<em />
Given
<em /><em> --- the number of lines</em>
<em /><em> --- no three lines are concurrent</em>
<em />
When no three line are concurrent, it means that no three lines meet at the same point.
<u>So, the sequence of intersection is:</u>
- <em>0 intersection for 1 line</em>
- <em>1 intersection for 2 lines</em>
- <em>3 intersections for 3 lines</em>
- <em>6 intersections for 4 lines</em>
<em />
Following the above sequence, the number of intersections for n lines is:
In this case,
So, we have:
<em>Hence, there will be 595 intersections for 35 lines, where no 3 lines are concurrent.</em>
<em />
Read more about lines of intersections at: