1.) Which of the following points contained within the feasible region corresponding to the system of inequalities? 3x + 6y < 12 and 5x + 7y > 8 2.)Find the minimum and maximum value of the objective quantity. Objective Quantity C = 2x + y, constraints: x ≥ 0, y ≥ 2, 2x + y ≤ 10 , x - 3y ≥ - 3 3.)For each unit of a product made by process A, you make P50 profit. For each unit of a product made by process B, you make P55 profit. How many units should you make by each process to obtain a maximum profit? Assembly Hours Process A Process B Maximum Hours Unskilled 1 6 2700 Machine 3 1 1500 Skilled 1 1 700

Samantha is growing a garden in her back yard. she spend $90 setting up the garden bed and buying the proper garden supplies. in addition, each seed she plants cost $0.25. a. write the function f(x) that represents samantha's total cost on her garden. b. explain what x represents. c. explain what f(x) represents. d. if samantha plants 55 seeds, how much did she spend in total?

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).

The measurement of one angle of a right triangle is 42° what is the measurement of the third angle? (there is no picture)