Study Guide ACP Review

Front

What is the solution to the equation −5x−4(2x−6)+3=6(5−2x)+11x?

Back

The solution is x = -1/4.

Front

What does it mean for a quantity to vary directly with another quantity?

Back

It means that as one quantity increases, the other quantity increases at a constant rate.

Front

If Arya walks a certain distance each day, how can we express the relationship between the distance walked (y) and the days of therapy (x)?

Back

The relationship can be expressed as a linear equation, typically in the form y = mx + b.

Front

What is the y-intercept in a linear graph?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

If the total cost of gas varies directly with the amount of gas purchased, what is the equation that represents this relationship?

Back

The equation is y = kx, where k is the constant of proportionality.

Front

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

Back

You divide the total cost by the amount of gas purchased.

Front

What is the formula for direct variation?

Back

The formula is y = kx, where k is the constant of variation.

Front

If Raymond spray-painted 25 desks in 5 hours, how many desks can he paint in 1 hour?

Back

He can paint 5 desks in 1 hour.

Front

How do you determine the time it takes to complete a task if you know the rate of work?

Back

You can use the formula: Time = Total Work / Rate of Work.

Front

What is the significance of the slope in a linear equation?

Back

The slope represents the rate of change of y with respect to x.