Everything Solving - STAAR Practice

Front

What is the formula to determine the number of small boxes sent when given the total number of boxes and their capacities?

Back

Let x be the number of small boxes and y be the number of large boxes. The equations are: x + y = total boxes and 20x + 45y = total capacity.

Front

How do you calculate the constant of variation in a direct variation problem?

Back

The constant of variation (k) is calculated by dividing the dependent variable by the independent variable (k = y/x).

Front

What does it mean for a system of linear equations to have infinitely many solutions?

Back

It means that the equations represent the same line, and thus every point on the line is a solution.

Front

In a direct variation problem, if the number of miles driven varies directly with the number of gallons used, how is the constant of variation interpreted?

Back

The constant of variation represents the number of miles driven per gallon of fuel.

Front

What is the significance of the constant of variation in a real-world context, such as pricing or rates?

Back

It indicates the rate at which one quantity changes in relation to another, such as cost per item.

Front

How can you set up an equation to solve for the number of items when given total cost and cost per item?

Back

Use the equation: total cost = number of items × cost per item.

Front

What is the relationship between the number of boxes and the total capacity in a packing problem?

Back

The total capacity is the sum of the capacities of all boxes used, which can be expressed as an equation.

Front

What is the process for solving a system of linear equations graphically?

Back

Graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

How do you interpret the slope in a direct variation scenario?

Back

The slope represents the constant of variation, indicating how much the dependent variable changes for a unit change in the independent variable.

Front

What is the formula for calculating the total number of items based on the number of boxes and their individual capacities?

Back

Total items = (number of small boxes × capacity of small box) + (number of large boxes × capacity of large box).