Which represents the solution(s) of the system of equations, y = -x2 + 6x + 16 and y = - 4x + 37? Determine the solution set
1 answer:
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1) From the picture, we see that we have two vertical angles:
2) Now, because of the<em> "Vertical Angles Postulate"</em> from geometry, we know that angles A and B are equal, so equalling the angles and replacing by their expression from above, we get the following equation in terms of x:
3) We must solve the last equation for x, doing that we find:
Steps to solve the equation
0) We have the equation:
1) We want all the terms with x on one side, and the other on the other one. So we pass the term +3x to the right as -3x:
2) Now we pass the term -10 to the left as +10:
3) We sum the terms on each side:
4) We pass the 3 that multiplies the x on the right, dividing the 60 on the left:
5) Finally we make the division and we get:
Answer
x = 20