Which statements are true regarding the sides and angles of the triangle? Select three options. Line segment X Y is the longest
2 answers:
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
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Answer:
1) w₁=4 - i w₂= -4 + i
2) w₁= 3 - i w₂= -3 + i
3) w₁= 1 + 2i w₂= - 1 - 2i
4) w₁= 2- 3i w₂= -2 + 3i
5) w₁= 5 - 2i w₂= -5 + 2i
6) w₁= 5 - 3i w₂= -5 + 3i
Step-by-step explanation:
The root of a complex number is given by:
where:
r: is the module of the complex number
θ: is the angle of the complex number to the positive axis x
n: index of the root
1) z = 15 − 8i ⇒ r=17 θ= -0.4899 rad
w₁==4-i
w₂==-1+i
2) z = 8 − 6i ⇒ r=10 θ= -0.6435 rad
w₁== 3 - i
w₂== -3 + i
3) z = −3 + 4i ⇒ r=5 θ= -0.9316 rad
w₁== 1 + 2i
w₂== -1 - 2i
4) z = −5 − 12i ⇒ r=13 θ= 0.4426 rad
w₁== 2- 3i
w₂== -2 + 3i
5) z = 21 − 20i ⇒ r=29 θ= -0.8098 rad
w₁== 5 - 2i
w₂== -5 + 2i
6) z = 16 − 30i ⇒ r=34 θ= -1.0808 rad
w₁== 5 - 3i
w₂== -5 + 3i