Assume that A = {2, 3, 5, 6} and that U is the universal set of natural numbers less than 11. Find  figure 1.png)
.
a. {2, 3, 5, 6}
b. {1, 4, 7, 8, 9, 10}
c. {1, 4, 7, 8, 9, 10, 11}
d. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
e. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
b. {1, 4, 7, 8, 9, 10}
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Decide if an Euler circuit exists for the graph.
A. No B. Yes
Decide whether or not the points are the vertices of a right triangle.Consider the three points A = (-3, 3), B = (-1, 7), C = (1, 6). Determine whether the triangle ABC is a right triangle. Explain your reasoning.
A. The side lengths of triangle ABC are d(A, B) = 3
, d(A, C) = 5, d(B, C) = 
.
[d(A, B)]2 + [d(B, C)]2 = (3
)2 + (
)2 = 18 + 5 = 23
[d(A, C)]2 = 52 = 25
Since [d(A, C)]2 ? [d(A, B)]2 + [d(B, C)]2, triangle ABC is not a right triangle.
B. The side lengths of triangle ABC are d(A, B) = 2
, d(A, C) = 2
, d(B, C) = 2.
[d(A, B)]2 + [d(B, C)]2 = (2
)2 + 22 = 20 + 4 = 24
[d(A, C)]2 = (2
)2 = 24
Since [d(A, C)]2 = [d(A, B)]2 + [d(B, C)]2, triangle ABC is a right triangle.
C. The side lengths of triangle ABC are d(A, B) = 2
, d(A, C) = 5, d(B, C) = 2.
[d(A, B)]2 + [d(B, C)]2 = (2
)2 + 22 = 20 + 4 = 24
[d(A, C)]2 = 52 = 25
Since [d(A, C)]2 ? [d(A, B)]2 + [d(B, C)]2, triangle ABC is not a right triangle.
D. The side lengths of triangle ABC are d(A, B) = 2
, d(A, C) = 5, d(B, C) = 
.
[d(A, B)]2 + [d(B, C)]2 = (2
)2 + (
)2 = 20 + 5 = 25
[d(A, C)]2 = 52 = 25
Since [d(A, C)]2 = [d(A, B)]2 + [d(B, C)]2, triangle ABC is a right triangle.
Convert to a logarithmic equation.
2 = 
A. log8/3
= 2
B. log8/32 = 
C. log2
= 
D. 
= 
Solve the problem.Classify the number as rational, irrational, or imaginary.-
A. imaginary B. irrational C. rational