Terry paid $22.50 for 3 games, so the cost per game for Terry is $22.50 / 3 = $7.50.
Tommy paid $15 for 2 games, so the cost per game for Tommy is $15 / 2 = $7.50.
Therefore, the rate of change for the cost of each game at the bowling alley is $7.50.
At the bowling alley, Terry paid $22.50 and bowled 3 games while Tommy bowled 2 games and paid $15. Interpret the rate of change by identifying the cost of each game. (1 point
7 answers
A spring has a length of 12 inches when a 2-pound weight is attached, and a length of 18 inches when a 5-pound weight is attached. Use rate of change to find the length of the spring when no weights are attached.
We are given that the length of the spring is 12 inches when a 2-pound weight is attached and 18 inches when a 5-pound weight is attached. Let's define the length of the spring when no weights are attached as "L inches".
To find the rate of change, we can calculate the change in length of the spring per pound of weight added.
For the first scenario with the 2-pound weight attached:
Rate of change = (change in length) / (change in weight) = (18 - L) / (5 - 0)
For the second scenario with the 5-pound weight attached:
Rate of change = (change in length) / (change in weight) = (12 - L) / (2 - 0)
Since the rate of change is constant regardless of the weight added, we can set the two rates of change equal to each other and solve for L:
(18 - L) / (5 - 0) = (12 - L) / (2 - 0)
(18 - L) / 5 = (12 - L) / 2
2(18 - L) = 5(12 - L)
36 - 2L = 60 - 5L
3L = 24
L = 8
Therefore, the length of the spring when no weights are attached is 8 inches.
To find the rate of change, we can calculate the change in length of the spring per pound of weight added.
For the first scenario with the 2-pound weight attached:
Rate of change = (change in length) / (change in weight) = (18 - L) / (5 - 0)
For the second scenario with the 5-pound weight attached:
Rate of change = (change in length) / (change in weight) = (12 - L) / (2 - 0)
Since the rate of change is constant regardless of the weight added, we can set the two rates of change equal to each other and solve for L:
(18 - L) / (5 - 0) = (12 - L) / (2 - 0)
(18 - L) / 5 = (12 - L) / 2
2(18 - L) = 5(12 - L)
36 - 2L = 60 - 5L
3L = 24
L = 8
Therefore, the length of the spring when no weights are attached is 8 inches.
A graph of the cost of gas purchased depending on the number of gallons pumped has the points (4, 15) and (8, 30). What is the rate of change in the cost of the gas as each gallon is pumped? (1 point)
To find the rate of change in the cost of gas as each gallon is pumped, we first need to find the slope of the line passing through the points (4, 15) and (8, 30).
The formula for calculating the slope of a line passing through two points (x1, y1) and (x2, y2) is:
Slope = (y2 - y1) / (x2 - x1)
Given the points (4, 15) and (8, 30), we can plug these values into the formula:
Slope = (30 - 15) / (8 - 4)
Slope = 15 / 4
Slope = 3.75
Therefore, the rate of change in the cost of the gas as each gallon is pumped is $3.75.
The formula for calculating the slope of a line passing through two points (x1, y1) and (x2, y2) is:
Slope = (y2 - y1) / (x2 - x1)
Given the points (4, 15) and (8, 30), we can plug these values into the formula:
Slope = (30 - 15) / (8 - 4)
Slope = 15 / 4
Slope = 3.75
Therefore, the rate of change in the cost of the gas as each gallon is pumped is $3.75.
A linear graph of the cost of broccoli in dollars per pound has the points (3, 8.25) and (6, 16.50). What is the rate of change in the purchase price in dollars per pound? (1 point)
To find the rate of change in the purchase price in dollars per pound, we need to calculate the slope of the line passing through the points (3, 8.25) and (6, 16.50).
The formula for calculating the slope of a line passing through two points (x1, y1) and (x2, y2) is:
Slope = (y2 - y1) / (x2 - x1)
Given the points (3, 8.25) and (6, 16.50), we can plug these values into the formula:
Slope = (16.50 - 8.25) / (6 - 3)
Slope = 8.25 / 3
Slope = 2.75
Therefore, the rate of change in the purchase price in dollars per pound is $2.75.
The formula for calculating the slope of a line passing through two points (x1, y1) and (x2, y2) is:
Slope = (y2 - y1) / (x2 - x1)
Given the points (3, 8.25) and (6, 16.50), we can plug these values into the formula:
Slope = (16.50 - 8.25) / (6 - 3)
Slope = 8.25 / 3
Slope = 2.75
Therefore, the rate of change in the purchase price in dollars per pound is $2.75.
40 answers