Solve for x 3/4 x + 5/8 = 4x

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

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.

The ratio of the perimeters of two similar triangles is 4: 3. what are the areas of these triangles if the sum of their areas is 130cm2?