MATH SOLVE

4 months ago

Q:
# Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y, the total time that Vlad spent on his homework, and what are the constraints on the values of x and y?

Accepted Solution

A:

The expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.What is domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.We're given that:Time spent by Vlad on history homework = 20 minutesTime spent by Vlad on math homework (x math problems) = 2 minutes on each problemy = time he spent on doing overall homeworkThen we have:y = time on math homework + history homeworky = 2 +2 +2 ... (x times) + 20 minutes[tex]y = 2x + 20[/tex]x is "number of math problems". Thus, x can be 0,1,2,... These numbers are called non-negative integers(or integers greater or equal to 0) or whole numbers. y is the time taken, but we see that y = 2 times (non-negative integer) + 20y = positive integer times non-negative integer + positive integerThus, we have:y = non-negative integer + positive integer = positive integerThus, y assumes positive integral values only (in minutes).Also, y is always going to be at least 20 (as history homework is going to take 20 minutes, even if math homework is nill ).Thus, the expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20Learn more about domain here: