Darius is considering renting an apartment or buying a house. The apartment he likes is $1,175 per month. The house would have a mortgage of $1,200. If the mortgage lasts for 20 years, how much money will he spend on either the apartment or the house in those 20 years? If Darius were to buy the house, how long would it take for him to start saving money after he pays it off compared to if he chose to rent the apartment all that time?

Let r = 3. what is the value of r + 58?

The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)