Recall that example 1.1.7 represented the following sentences by word vectors w = (ncat, ndog, nmat; nat, n. cratched). 1. "the cat and dog sat on the mat" is summarized by the vector a = (1,1,1,1,0). 2. "the dog scratched" is summarized by the vector b = (0,1,0,0,1). 3. "the dog sat on the mat; the cat scratched the dog." is summarized by the vector c= (1,2,1,1,1). (a) (1 credit) find the similarity between pairs of these sentences by calculating the angle between each pair of word vectors. to receive full credit show all your work. (b) (1 credit) what is the most similar pair of sentences? о 1 and 2 0 1 and 3 o 2 and 3

How can you solve an equation with a variable on both sides? complete the explanation. you can solve the equation by using *(blank)* operations to get the variable terms on one side of the equal sign and the constant terms on the *(blank)* side. then *(blank)* both sides by the coefficient of the resulting variable term.

What is the sum of the first 8 terms of the geometric series

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.