1. Let C[0,1] be the space of continuous functions on the interval [0,1]. Show that the map T : C[0,1] →R is linear. [5 Marks]

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

Four equations are shown below. equation 1: y=2*equation 2: y=2x-5equation 3: y=x2 + 6equation 4: tdentify one linear equation and one nonlinear equation from the list. why each equation you identified is linear or nonlinear. nd one nonlinear equation from the list. state a reasonlinear equation

Astudent was asked to find the square of 7x+3. the student quickly wrote (7x+3)^3= 49x^2+9. identify the student's error and provide the correct answer.