Reorder the premises in the argument below to show that the conclusion follows as a valid consequence from the premises. (they are based on tarsky’s world.) it may be to rewrite the statements in if-then form and replace some by their contrapositives. a. every object that is to the right of all the blue objects is above all the triangles. b. if an object is a circle, then it is to the right of all blue objects. c. if an object is not a circle, then it is not gray. ∴ all the gray objects are above the triangles

Acyclist bike x distance at 10 miles per hour .and returns over the same path at 8 miles per hour.what is the cyclist average rate for the round trip in miles per hour ?

What is the product? a-3/15a × 5/a-3

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).