Late at night, in a castle far away, the king could not sleep. so he got up and at 1/4 of the mangoes from a bowl in the kitchen. the queen got up and ate 1/3 of the mangoes that were left. the prince at 1/2 of the mangoes that the queen did not eat. there were 12 mangoes left in the bowl when she was done. how many mangoes were in the bowl at the beginning?

Mr. walker gave his class the function f(x) = (x + 3)(x + 5). four students made a claim about the function. each student’s claim is below. jeremiah: the y-intercept is at (15, 0). lindsay: the x-intercepts are at (–3, 0) and (5, 0). stephen: the vertex is at (–4, –1). alexis: the midpoint between the x-intercepts is at (4, 0). which student’s claim about the function is correct?

Which equations represents circles that have a diameter of 12 units and a center that lies on the y-axis? check all that apply

Describe the relationship between the angles of similar triangles and the sides of similar triangles