(3, 5)
Determine if the given graph is the graph of the function y = - 2/5x + 3. Enter 1 for yes. Enter 2 for no.
2
Determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places as needed.
The initial value is __, and the rate of change is __.
The initial value is 3, and the rate of change is -2/5.
A pan with four eggs weighs 18 ounces. A pan with eight eggs weighs 24 ounces. What is the weight of the pan?
To find the weight of the pan, we need to determine the weight of one egg by subtracting the weight of the eggs from the total weight of the pan.
The weight of one egg can be found by taking the difference between the total weight of the pan with eight eggs and the total weight of the pan with four eggs:
24 ounces - 18 ounces = 6 ounces
Since each egg weighs 6 ounces, we can find the weight of the pan by subtracting the weight of one egg from the total weight of the pan:
Total weight of the pan - Weight of one egg = Weight of the pan
24 ounces - 6 ounces = 18 ounces
Therefore, the weight of the pan is 18 ounces.
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.
Linear Function 1: y = x + 8
Linear Function 2:
(4,10)
(2,6)
Linear Function __ has the greater rate of change.
To find the rate of change for each linear function, we need to calculate the difference in y-values divided by the difference in x-values for two points on each line.
For Linear Function 1:
(2, 10) and (4, 12)
Rate of change = (12 - 10) / (4 - 2) = 2 / 2 = 1
For Linear Function 2:
(4, 10) and (2, 6)
Rate of change = (6 - 10) / (2 - 4) = -4 / -2 = 2
Comparing the rates of change, we see that Linear Function 2 has the greater rate of change, so we choose Linear Function 2.
Therefore, Linear Function 2 has the greater rate of change.
Day of the Week Number of Children in the Car
Sunday 2
Monday 4
Tuesday 4
Wednesday 3
Thursday 4
Friday 3
Saturday 0
Describe the meaning of the word function in math. Then consider the table. Why does this table show a function?
simple and short version
In mathematics, a function is a relationship or rule that assigns each input value (or element from a set called the domain) to a single output value (or element from another set called the range). A function can be thought of as a machine that takes an input and produces a corresponding output.
The given table shows a function because for each day of the week (input value), there is a unique and specific number of children in the car (output value). In other words, each day of the week is associated with only one value in the table. This characteristic, known as "uniqueness of output," is one of the fundamental properties that define a function.