Prove that a positive integer is divisible by 3 if and only if the sum of digits is divisible by 3. be sure to prove it forward and backwards. as in prove knowing an integer is divisible by 3 and find that the sum of its digits is then divisible by 3. then, assume the sum of its digits is divisible by 3 and prove that the integer is then divisible by 3. if you cannot prove both ways, do not try and solve this problem.

Acar traveling at 65 mph leaves 25 foot skid mark what is the ratio of the speed to length of skid mark (feet) in the simplest form

An object is translated by (x + 4, y - 2). if one point in the image has the coordinates (5, -3), what would be the coordinates of its pre-image? (9, -5) (1, -5) (9, -1) (1, -1)

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).