Using Similar Triangles On a coordinate plane, a line goes through (0, 3) and (x, y). A triangle has a rise of 2 and run of 3. A larger triangle has a rise of 5 and run of 7. Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3). What is the ratio of the rise to the run in the smaller triangle in the diagram? What is the ratio of the rise to the run in the larger triangle in the diagram? What is the equation of the line in slope-intercept form?

Evaluate cos2θ for cosθ = square root of 3/2

Alocal hamburger shop sold a combined total of 601 hamburgers and cheeseburgers on friday. there were 51 more cheeseburgers sold than hamburgers. how many hamburgers were sold on friday? a local hamburger shop sold a combined total of hamburgers and cheeseburgers on friday. there were more cheeseburgers sold than hamburgers. how many hamburgers were sold on friday?

Based on the situation in part a, the width of a rectangular garden is x feet, and its length is 5 feet more than twice its width. the right side of the equation, g(x) = 2x2 − 13x + 6, can be factored to g(x) = (2x − 1)(x − 6). this function could represent an inner region of the garden from the first equation, such as a vegetable garden with a border around it. the length of this inner garden would be 2x − 1 feet, and the width would be x − 6, which would leave a 3-foot border around the garden. part d what is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?