Question
use the table to awnser the question
x y
2 22
8 25
Determine the ROC and IV of the linear function given here as a table of values
x y
2 22
8 25
Determine the ROC and IV of the linear function given here as a table of values
Answers
GPT 3.5
To determine the Rate of Change (ROC) of the linear function, we need to calculate the change in y divided by the change in x.
Change in y = 25 - 22 = 3
Change in x = 8 - 2 = 6
ROC = Change in y / Change in x = 3 / 6 = 0.5
Therefore, the Rate of Change (ROC) of the linear function is 0.5.
To determine the Initial Value (IV) of the linear function, we can substitute the values of x=2 and y=22 into the equation of the linear function.
Using the formula for the equation of a line (y = mx + b), we can plug in the values of x=2 and y=22:
22 = 0.5(2) + b
22 = 1 + b
b = 21
Therefore, the Initial Value (IV) of the linear function is 21.
Change in y = 25 - 22 = 3
Change in x = 8 - 2 = 6
ROC = Change in y / Change in x = 3 / 6 = 0.5
Therefore, the Rate of Change (ROC) of the linear function is 0.5.
To determine the Initial Value (IV) of the linear function, we can substitute the values of x=2 and y=22 into the equation of the linear function.
Using the formula for the equation of a line (y = mx + b), we can plug in the values of x=2 and y=22:
22 = 0.5(2) + b
22 = 1 + b
b = 21
Therefore, the Initial Value (IV) of the linear function is 21.
STAN STRAY KIDS <3
are you sure
GPT 3.5
Let's double-check the calculations.
To find the Rate of Change (ROC):
Change in y = 25 - 22 = 3
Change in x = 8 - 2 = 6
ROC = Change in y / Change in x = 3 / 6 = 0.5
The Rate of Change (ROC) is indeed 0.5.
To find the Initial Value (IV):
We will use the point (2, 22) and the formula y = mx + b:
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the Initial Value (IV) of the linear function is 21.
Yes, the calculations provided earlier were correct.
To find the Rate of Change (ROC):
Change in y = 25 - 22 = 3
Change in x = 8 - 2 = 6
ROC = Change in y / Change in x = 3 / 6 = 0.5
The Rate of Change (ROC) is indeed 0.5.
To find the Initial Value (IV):
We will use the point (2, 22) and the formula y = mx + b:
22 = 0.5(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the Initial Value (IV) of the linear function is 21.
Yes, the calculations provided earlier were correct.
STAN STRAY KIDS <3
Determine the inital value and the ROC of the linear function as given in the graph round the answer to three decimal places as needed
graph points:
(6, 1), (3, 2), (0, 3), (-3, 4)
graph points:
(6, 1), (3, 2), (0, 3), (-3, 4)
GPT 3.5
To find the Initial Value (IV) and Rate of Change (ROC) of the linear function given the graph points, we will use the formula y = mx + b, where m is the Rate of Change and b is the Initial Value.
Step 1: Calculate the Rate of Change (ROC) using two points from the graph.
Let's choose two points: (3, 2) and (0, 3).
m = (y2 - y1) / (x2 - x1)
m = (3 - 2) / (0 - 3)
m = 1 / -3
m = -0.333 (rounded to three decimal places)
Step 2: Calculate the Initial Value (IV) using the Rate of Change (ROC) and one of the points.
Using point (3, 2):
2 = -0.333 * 3 + b
2 = -1 + b
b = 3
Therefore, the Initial Value (IV) is 3.
So, the Rate of Change (ROC) is approximately -0.333 and the Initial Value (IV) is 3.
Step 1: Calculate the Rate of Change (ROC) using two points from the graph.
Let's choose two points: (3, 2) and (0, 3).
m = (y2 - y1) / (x2 - x1)
m = (3 - 2) / (0 - 3)
m = 1 / -3
m = -0.333 (rounded to three decimal places)
Step 2: Calculate the Initial Value (IV) using the Rate of Change (ROC) and one of the points.
Using point (3, 2):
2 = -0.333 * 3 + b
2 = -1 + b
b = 3
Therefore, the Initial Value (IV) is 3.
So, the Rate of Change (ROC) is approximately -0.333 and the Initial Value (IV) is 3.
STAN STRAY KIDS <3
A pan with four eggs weighs 18 oz. A pan with 8 eggs weighs 24 ounces. what is the weight of the pan
GPT 3.5
Let's denote the weight of the pan as P (in ounces).
Given:
- Weight of a pan with 4 eggs: 18 oz
- Weight of a pan with 8 eggs: 24 oz
Let's first find the weight of each egg by subtracting the weight of the pan from the total weight of each pan:
Weight of an egg = (Weight of the pan with eggs) - (Weight of the pan)
Weight of an egg in the pan with 4 eggs = 18 oz - P
Weight of an egg in the pan with 8 eggs = 24 oz - P
Since each egg has the same weight, we can set up a proportion:
(Weight of an egg in the pan with 4 eggs) / 4 = (Weight of an egg in the pan with 8 eggs) / 8
(18 - P) / 4 = (24 - P) / 8
Now, we can solve for P:
Cross multiply:
8(18 - P) = 4(24 - P)
144 - 8P = 96 - 4P
Solve for P:
144 - 96 = 8P - 4P
48 = 4P
P = 48 / 4
P = 12
Therefore, the weight of the pan is 12 ounces.
Given:
- Weight of a pan with 4 eggs: 18 oz
- Weight of a pan with 8 eggs: 24 oz
Let's first find the weight of each egg by subtracting the weight of the pan from the total weight of each pan:
Weight of an egg = (Weight of the pan with eggs) - (Weight of the pan)
Weight of an egg in the pan with 4 eggs = 18 oz - P
Weight of an egg in the pan with 8 eggs = 24 oz - P
Since each egg has the same weight, we can set up a proportion:
(Weight of an egg in the pan with 4 eggs) / 4 = (Weight of an egg in the pan with 8 eggs) / 8
(18 - P) / 4 = (24 - P) / 8
Now, we can solve for P:
Cross multiply:
8(18 - P) = 4(24 - P)
144 - 8P = 96 - 4P
Solve for P:
144 - 96 = 8P - 4P
48 = 4P
P = 48 / 4
P = 12
Therefore, the weight of the pan is 12 ounces.