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Area of ABC : AB*AC/2
the maximum of the parabola is reached at x=-4/(2*(-1))=2 hence A is at (2,0) and B is at (2,(-2)^2+4*2+C)=(2,12+C)
C is the second root (x-intersect), which we can find :
determinant1 : D=16-4*(-1)*C=4(4+C) thus the second root is at x=
Hence the area of the triangle is
hence 
.
We remark that
Hence 4+C=16 thus C=12
the maximum of the parabola is reached at x=-4/(2*(-1))=2 hence A is at (2,0) and B is at (2,(-2)^2+4*2+C)=(2,12+C)
C is the second root (x-intersect), which we can find :
determinant1 : D=16-4*(-1)*C=4(4+C) thus the second root is at x=
Hence the area of the triangle is
We remark that
Hence 4+C=16 thus C=12
Answer:
B. Angle X is the largest angle.
C. Angle Z is greater than angle Y.
E. Line segment X Z is the shortest side.
Step-by-step explanation:
YZ = 2n, XZ = n - 2, XY = n + 4 and n ≥ 5.
YZ - XZ = 2n - (n - 2) = n + 2. but n ≥ 5, hence YZ - XZ = n + 2 ≥ 7.
YZ > XZ
YZ - XY = 2n - (n + 4) = n - 4. but n ≥ 5, hence YZ - XY = n - 4 ≥ 1
YZ > XY
XY - XZ = n + 4 - (n - 2) = 6: XY > XZ
Therefore:
YZ > XY > XZ
The angles are proportional to their opposite sides, hence:
∠X > ∠Z > ∠Y
A. Line segment XY is the longest side.
This is wrong because YZ is the longest side.
B. Angle X is the largest angle.
This is correct. ∠X is the largest angle because it is opposite to the longest side (YZ)
C. Angle Z is greater than angle Y.
This is correct. ∠Z is opposite to the side XY while ∠Y is opposite to the side XZ
D. Line segment XZ is opposite the largest angle.
This is wrong. ∠X is the largest angle which is opposite to the longest side (YZ)
E. Line segment X Z is the shortest side.
This is correct
