The ratio of golf balls to tennis balls in the coach's bag is 20 to 5. If there are 100 golf balls in the bag, how many tennis balls are in the bag?

golf balls ---- 20x

tennis balls -- 5x

20x+5x = 100
25x = 100
x = 4

so 80 golf balls and 20 tennis balls

A coach has `72` tennis balls for the school's tennis team. The coach will give each player `6` tennis balls. The graph shows the linear relationship between `y`, the number of tennis balls remaining for the team, and `x`, the number of players on the team.

The coach will use no more than `8` players on the school's tennis team. Which set best represents the range of the function for this situ

ation?

The initial number of tennis balls is 72, and the coach will give 6 tennis balls to each player. If there are x players total, then the total number of tennis balls given to players is 6x. Therefore, the remaining number of tennis balls y can be represented by the function y = 72 - 6x.

To find the range of this function for 1 to 8 players, we can substitute x = 1 to x = 8 into the function and evaluate y.

When x = 1, y = 72 - 6(1) = 66. So there are 66 tennis balls remaining if there is only one player.

When x = 8, y = 72 - 6(8) = 24. So there are 24 tennis balls remaining if there are eight players.

Therefore, the range of the function for this situation is {y | 24 ≤ y ≤ 66}.

The set {30, 36, 42, 48, 54, 60, 66, 72} represents the possible initial numbers of tennis balls, not the range of the function.

Answer: {y | 24 ≤ y ≤ 66}.

A part of linear function `f` is graphed on the grid.

Which inequalities best describe the domain and range of the part shown?

The domain of a function represents the set of all possible input values, while the range represents the set of all possible output values.

Looking at the graph, we can see that the graph is a line segment that starts at the point (-2, 4) and ends at the point (3, 1).

To describe the domain of the part shown, we can use the x-coordinates of these two points as the endpoints. Therefore, the domain is the set {x | -2 ≤ x ≤ 3}.

To describe the range of the part shown, we can use the y-coordinates of these two points as the endpoints. Therefore, the range is the set {y | 1 ≤ y ≤ 4}.

So the inequalities that best describe the domain and range of the part shown are:

Domain: -2 ≤ x ≤ 3

Range: 1 ≤ y ≤ 4

To find the number of tennis balls in the bag, we can use the given ratio between golf balls and tennis balls. The ratio is 20 to 5, which simplifies to 4 to 1.

To solve the problem, follow these steps:

Step 1: Set up a proportion using the known values:
20 (golf balls) / 5 (tennis balls) = 100 (golf balls) / x (tennis balls)

Step 2: Cross-multiply and solve for x:
20x = 5 * 100
20x = 500

Step 3: Divide both sides of the equation by 20 to isolate x:
x = 500 / 20
x = 25

Therefore, there are 25 tennis balls in the coach's bag.