The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2, the fraction is now equal to . If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

a 3n = 5d and 3n + 6 = 2d + 4
b 5n = 3d and 3n + 6 = 2d + 4
c 5n = 3d and 4n + 4 = 3d + 6

"how does lena finally defeat the robots? ” this question will best be used to describe the story’s exposition. rising action. climax. falling action.

(a) (8%) compute the probability of an even integer among the 100 integers 1! , 2! , 3! , until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100

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.