If f(x)=5x-2 and g(x)=2x1 find (f+g)(x)
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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
The cost of one drink is $2.50 and cost of one popcorn is $3.75
<u><em>Explanation</em></u>
Suppose, the cost of one drink is dollar and cost of one popcorn is
dollar.
Given that, total cost for 2 drinks and 2 popcorns is $12.50 and total cost for 6 drinks and 5 popcorns is $33.75
So, the system of equations will be......
Multiplying equation (1) by -3 , we will get.....
Now, adding equation (2) and equation (3) , we will get ............
Plugging this into equation (1) ......
So, the cost of one drink is $2.50 and cost of one popcorn is $3.75