Given DEF D'E'F', describe a sequence of transformations that maps DEF to D'E'F'.
TA
Rotation of 90° about the origin, translation
of 6 units down, translation of 6 units left
Reflection across the x-axis, translation of
6 units left, translation of 6 units up
Translation of 6 units down, translation of 6
units right, reflection across the y-exis
Reflection across the y-axis, reflection
across the x-axis, translation of 6 units left

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?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 7 5 11 14 which of the following is a scatter diagrams accurately represents the data? what does the scatter diagram developed in part (a) indicate about the relationship between the two variables? try to approximate the relationship betwen x and y by drawing a straight line through the data. which of the following is a scatter diagrams accurately represents the data? develop the estimated regression equation by computing the values of b 0 and b 1 using equations (14.6) and (14.7) (to 1 decimal). = + x use the estimated regression equation to predict the value of y when x = 4 (to 1 decimal). =