(10 - 5) + 5^2 - 2 =
1 answer:
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Answer: sqrt(2)/2 which is choice D
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Explanation
(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).
The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle
180-135 = 45
Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2
sine is positive in quadrant 2
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Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2
Recall that y = sin(theta).
The solutions to the systems of equations are:
1. (2, 3) (see attachment below). [one solution]
2. no solution
3. (3, 13) [one solution]
<h3>Solution to a System of Equations?</h3>The solution to a system of equations is the x-value and y-value that will make both equations true. It can be found either using a graph, by elimination method, or substitution method as explained below.
1. Using graph to solve y = 2x - 1 and y = 4x - 5:
The solution is the point where both lines intersect which is: (2, 3) (see attachment below). [one solution]
2. Solving using substitution method:
x = -5y + 4 ---> eqn. 1
3x + 15y = -1 ---> eqn. 2
Substitute x = -5y + 4 into eqn. 2
3(-5y + 4) + 15y = -1
-15y + 12 + 15y = -1
-15y + 15y = -1 - 12
0 = -13 (this shows that there is no solution)
3. Using elimination method:
14x = 2y + 16 ---> eqn. 1
5x = y + 2 ---> eqn. 2
1(14x = 2y + 16)
2(5x = y + 2)
14x = 2y + 16 ----> eqn. 3
10x = 2y + 4 -----> eqn. 4
Subtract
4x = 12
x = 12/4
x = 3
Substitute x = 3 into eqn. 2
5(3) = y + 2
15 = y + 2
15 - 2 = y
13 = y
y = 13
The solution is: (3, 13).
Learn more about the solution of a system of equations on:
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