Solve the linear inequality. Other than ?, use interval notation to express the solution set and graph the solution set on a number line.
? 
+ 4
A. [10, ?)
B. (10, ?)
C. [-10, ?)
D. (-?, 10]
Answer: A
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Evaluate the expression.
A. 6
B. 
C. 2!
D. 30
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.
Evaluate the expression for the given value or values.- 
, for y = -45, z = 5
A. -5 B. 9 C. 5 D. -9
Use the method of natural frequencies to find the indicated probability.In one town, 10% of 18-29 year olds own a home, as do 35% of 30-50 year olds and 65% of those over 50. According to a recent census taken in the town, 27.3% of adults in the town are 18-29 years old, 36.8% are 30-50 years old, and 35.9% are over 50. If an adult is selected at random from the town and found to be a home-owner, what is the probability that they are aged between 30 and 50?
A. 0.331 B. 0.368 C. 0.129 D. 0.35