For each of these three equations, determine whether there are any solution(s). If there are solutions, say what they are and show how you found them. If there aren't solutions, explain why not. (a) $\textcolor{white}.~~\frac x3+\frac x4+\frac x5 ~=~ \frac{2x}3 + \frac{2x}4 + \frac{2x}5$

(b) $\textcolor{white}.~~\frac y3+\frac y4+\frac y5 ~=~ \frac y3+\frac y4+\frac y5+1$

(c) $\textcolor{white}.~~\frac z3+\frac z4+\frac z5 ~=~ \frac z4+\frac z5+\frac z6+1$

The test scores of 32 students are listed below. construct a boxplot for the data set and include the values of the 5-number summary. 32 37 41 44 46 48 53 55 57 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 81 82 83 86 89 92 95 99

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Guys i need ! graded assignment grade 8 checkpoint 2, part 2 answer the questions below. when you are finished, submit this assignment to your teacher by the due date for full credit. total score: of 9 points (score for question 1: of 4 points) 1. the cost of renting a car for a day is $0.50 per mile plus a $15 flat fee. (a) write an equation to represent this relationship. let x be the number of miles driven and y be the total cost for the day. (b) what does the graph of this equation form on a coordinate plane? explain. (c) what is the slope and the y-intercept of the graph of the relationship? explain.