A certain company's Mixed Cereal for Baby contains, in each serving, 75 calories and 10 grams of carbohydrates. The same company's Mango Tropical Fruit Dessert contains, in each serving, 45 calories and 7 grams of carbohydrates. You want to provide your child with at least 240 calories and at least 34 grams of carbohydrates. Draw the feasible region that shows the number of servings of cereal and number of servings of dessert that you can give your child. (Place the Mixed Cereal for Baby on the x-axis and the Mango Tropical Fruit Dessert on the y-axis.)

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x)

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).

Tom travels between the two mile markers shown and then finds his average speed in miles per hour. select the three equations that represent this situation.