Flashcard (Review)

Front

What does it mean for a quantity to be directly proportional to another quantity?

Back

A quantity is directly proportional to another if it increases or decreases at the same rate. This means that the ratio of the two quantities remains constant.

Front

How do you solve an inequality like 6(n + 2) < -72?

Back

To solve the inequality, first distribute the 6: 6n + 12 < -72. Then, subtract 12 from both sides: 6n < -84. Finally, divide by 6: n < -14.

Front

What is the formula to find pay based on hours worked when pay is directly proportional to hours?

Back

The formula is Pay = k * Hours, where k is the constant of proportionality. You can find k by using known values.

Front

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

Back

To find the constant of proportionality (k), divide the pay by the number of hours worked: k = Pay / Hours.

Front

What is the solution to the inequality -2(x + 2) < 14?

Back

First, distribute -2: -2x - 4 < 14. Then, add 4 to both sides: -2x < 18. Finally, divide by -2 (remember to flip the inequality): x > -9.

Front

What does the domain of a function represent?

Back

The domain of a function represents all the possible input values (x-values) for which the function is defined.

Front

How do you express the domain of a function in interval notation?

Back

In interval notation, the domain is expressed as a range of values, such as [-4, 2] for the domain {-4 ≤ x ≤ 2}.

Front

What is the relationship between actual distance and scaled distance on a map?

Back

The relationship is a direct proportion, where a certain distance on the map represents a specific actual distance.

Front

How do you set up a proportion to find the scaled distance on a treasure map?

Back

Set up the proportion as: (actual distance / scaled distance) = (15 miles / 3 cm). Then, use this to find the scaled distance for 135 miles.

Front

What is the process to solve for the scaled distance if 15 miles is represented by 3 centimeters?

Back

Set up the proportion: 15 miles / 3 cm = 135 miles / x cm. Cross-multiply and solve for x.