Determine if 7x2+y=5 is a linear or nonlinear function.
y=−25x+3. Enter 1 for yes. Enter 2 for no.
Is the slope of the line in the equation y = -25x + 3 negative?
1. Yes
2. No
Determine the initial value and the rate of change in the following description.
Last year, Joshua’s tomato plant reached a maximum height of 2 feet. He is growing another tomato plant this year, and he is tracking its growth. The plant’s height today is 10 inches, and it grows 1.7 inches each day.
Initial value: 2 feet = 24 inches (since the maximum height reached by Joshua's tomato plant last year was 2 feet)
Rate of change: 1.7 inches per day (since the plant grows 1.7 inches each day)
x y
2 22
8 25
Determine the rate of change and the initial value of the linear function given here as a table of values.
To determine the rate of change and the initial value of the linear function, we need to find the slope and y-intercept.
First, let's find the slope using the two points given (2, 22) and (8, 25):
slope = change in y / change in x
= (25 - 22) / (8 - 2)
= 3 / 6
= 1/2
So the slope is 1/2.
Next, we can use one of the points and the slope to find the y-intercept. Let's use the point (2, 22):
y = mx + b (where m is the slope and b is the y-intercept)
22 = (1/2)(2) + b
22 = 1 + b
b = 21
So the y-intercept is 21.
Therefore, the linear function is:
y = (1/2)x + 21
The rate of change is 1/2 and the initial value is 21.
(-3,4) (0,3) (3,2) (6,1)
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.
To determine the initial value and rate of change of the linear function, we need to first find the slope, which is the rate of change.
Using the two points (3, 2) and (6, 1):
slope = change in y / change in x
= (1 - 2) / (6 - 3)
= -1/3
So the slope is -1/3.
Next, we can use any of the points and the slope to find the y-intercept. Let's use point (0, 3):
y = mx + b (where m is the slope and b is the y-intercept)
3 = (-1/3)(0) + b
3 = b
So the y-intercept is 3.
Therefore, the linear function is:
y = (-1/3)x + 3
The rate of change is -1/3 and the initial value is 3.
A pan with four eggs weighs 18 ounces. A pan with eight eggs weighs 24 ounces. What is the weight of the pan?
We can start the problem by using algebra. Let "p" be the weight of the pan, in ounces.
According to the problem, a pan with four eggs weighs 18 ounces. This means that the weight of the eggs is 18 - p ounces. Similarly, a pan with eight eggs weighs 24 ounces, which means that the weight of the eggs is 24 - p ounces.
We can set up an equation based on the above information:
24 - p = 2(18 - p)
In words, this equation says that the weight of the eight-egg pan (24 - p) is twice the weight of the four-egg pan (2 * (18 - p)).
Now we can solve for "p":
24 - p = 36 - 2p
p = 12
Therefore, the weight of the pan is 12 ounces.