5-2 Direct Variation Quiz

Explanation
If m varies directly as a, it means that m is directly proportional to a. This can be represented as m = ka, where k is the constant of variation. To find the value of k, we can use the given information that when a is 36, m is 6. Plugging these values into the equation, we get 6 = k * 36. Solving for k, we find that k = 1/6. Therefore, the constant of variation is 1/6.

Explanation
The number of calories varies directly as the weight of the cheese, which means that as the weight of the cheese increases, the number of calories also increases proportionally. Since there are about 200 calories in 50 grams of Swiss cheese, we can set up a proportion to find the number of calories in 70 grams.

50 grams / 200 calories = 70 grams / x calories

Cross-multiplying, we get:

50x = 70 * 200
50x = 14000
x = 280

Therefore, the cheese that Willie ate had approximately 280 calories.

Explanation
The variable A varies directly as the variable C, which means that as C increases, A also increases proportionally. In the given equation A12xC3y15, we can see that when x = 5 and y = 6, the equation holds true. If we substitute these values into the equation, we get A12xC3y15 = A12x5C3y6 = A60C18 = 15, which matches the given equation. Therefore, x = 5 and y = 6 is the correct answer.

Explanation
The constant of variation can be found by dividing the pressure by the temperature. In this case, the pressure is given as 7 lb per square inch and the temperature is denoted as F. Therefore, the constant of variation is 7/F.

Explanation
In the given equation 3x + 5y = 0, we can rewrite it as 5y = -3x. To find the constant of variation, we need to isolate y. By dividing both sides of the equation by 5, we get y = (-3/5)x. Comparing this equation with the general form of direct variation y = kx, we can see that k = -3/5. Therefore, the constant of variation for the given equation is -3/5.