vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2…

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?\no y = 2x + 20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.\no y = 2x + 20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.\no y = 20x + 2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.\no y = 20x + 2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.

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?\no y = 2x + 20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.\no y = 2x + 20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.\no y = 20x + 2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.\no y = 20x + 2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.

Answer

Explanation:

Step1: Calculate total math - time

Time for math problems is 2 minutes per problem. If he solved $x$ math problems, time for math problems is $2x$ minutes.

Step2: Calculate total homework - time

He spent 20 minutes on history homework. So total time $y$ on homework is $y = 2x+20$.

Step3: Determine constraints on $x$

The number of math problems $x$ must be a non - negative integer because you can't have a fraction of a problem. So $x\geq0$ and $x\in\mathbb{Z}$.

Step4: Determine constraints on $y$

Since $x\geq0$, when $x = 0$, $y=2\times0 + 20=20$. So $y\geq20$ and $y\in\mathbb{Z}$.

Answer:

$y = 2x+20$; $x$ is any integer greater than or equal to 0, and $y$ is an integer greater than or equal to 20.