A girl has a pen that is of length 12 cm, measured to the nearest centimetre. Her pencil case has a diagonal of length 12.5 cm, measured to the nearest millimetre. Explain why it might not be possible for her to fit the pen in the pencil case.

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?

Formulate alisha has a number in mind. if she adds three to her number the result is less than five. use this information to write and solve an inequality about alisha's number. then graph the solution set.

Percy rides his bike 11.2 miles in 1.4 hours at a constant rate. write an equation to represent the proportional relationship between the number of hours percy rides, x,and the distance in miles, y, that he travels.