determine if 7x^2+y=5 is a linear or nonlinear function
11 answers
This function is nonlinear because it contains an x^2 term. In general, a function is considered linear if it does not contain any variables raised to a power other than 1. Since the term 7x^2 is squared (raised to the power of 2), this function is considered nonlinear.
determine if the given graph is the graph of the function y=-2/3x+3 enter 1 for yes 2 for no
The graph has marks at (0,3) (5,1)
The graph has marks at (0,3) (5,1)
To determine if the given graph is the graph of the function y = -2/3x + 3, we can substitute the given points (0,3) and (5,1) into the equation and check if they satisfy the equation.
1. For point (0,3):
y = -2/3(0) + 3
y = 0 + 3
y = 3
Since the y-value obtained is 3, matches the y-coordinate of the point, (0,3) satisfies the equation.
2. For point (5,1):
y = -2/3(5) + 3
y = -10/3 + 3
y = -10/3 + 9/3
y = -1/3
The y-value obtained is -1/3, which does not match the y-coordinate of the point, (5,1) does not satisfy the equation.
Therefore, since only one of the points satisfy the equation y = -2/3x + 3, the given graph is not the graph of the function y = -2/3x + 3. The answer is 2 (No).
1. For point (0,3):
y = -2/3(0) + 3
y = 0 + 3
y = 3
Since the y-value obtained is 3, matches the y-coordinate of the point, (0,3) satisfies the equation.
2. For point (5,1):
y = -2/3(5) + 3
y = -10/3 + 3
y = -10/3 + 9/3
y = -1/3
The y-value obtained is -1/3, which does not match the y-coordinate of the point, (5,1) does not satisfy the equation.
Therefore, since only one of the points satisfy the equation y = -2/3x + 3, the given graph is not the graph of the function y = -2/3x + 3. The answer is 2 (No).
determine the initial value and the rate of change in the following description
last year josh tomato plant reached maximum height of 2 feet he is growing another tomato plant this year and tracking it growth, the plant height today is 10 inches and it grows 1.7 inches each day.
last year josh tomato plant reached maximum height of 2 feet he is growing another tomato plant this year and tracking it growth, the plant height today is 10 inches and it grows 1.7 inches each day.
In this scenario, the initial value refers to the height of the tomato plant when tracking began. The rate of change is the growth rate of the tomato plant per unit of time.
Initial value:
The initial value is the height of the tomato plant when tracking began. Last year, Josh's tomato plant reached a maximum height of 2 feet. Since the growth of the new tomato plant started this year, we will convert the 2 feet to inches for consistency. 1 foot is equal to 12 inches, so 2 feet is 24 inches. Therefore, the initial value (height) of the plant when tracking began is 24 inches.
Rate of change:
The plant height today is 10 inches, and it grows 1.7 inches each day. The rate at which the plant is growing is 1.7 inches per day.
Hence,
- Initial value: 24 inches
- Rate of change: 1.7 inches per day.
Initial value:
The initial value is the height of the tomato plant when tracking began. Last year, Josh's tomato plant reached a maximum height of 2 feet. Since the growth of the new tomato plant started this year, we will convert the 2 feet to inches for consistency. 1 foot is equal to 12 inches, so 2 feet is 24 inches. Therefore, the initial value (height) of the plant when tracking began is 24 inches.
Rate of change:
The plant height today is 10 inches, and it grows 1.7 inches each day. The rate at which the plant is growing is 1.7 inches per day.
Hence,
- Initial value: 24 inches
- Rate of change: 1.7 inches per day.
determine therate of change and the initial value of the linear function given here as a table of values
TABLE:
(x: 2,8)
(y: 22,25)
TABLE:
(x: 2,8)
(y: 22,25)
To determine the rate of change and initial value of the linear function represented by the table of values:
Given table:
x: 2, 8
y: 22, 25
The rate of change for a linear function is calculated by finding the change in the y-values divided by the change in the x-values.
Rate of change calculation:
Change in y = 25 (y when x = 8) - 22 (y when x = 2) = 3
Change in x = 8 - 2 = 6
Rate of change = Change in y / Change in x
Rate of change = 3 / 6 = 0.5
Therefore, the rate of change for this linear function is 0.5.
Next, to determine the initial value of the linear function, we need to find the y-intercept. The initial value represents the value of y when x = 0.
To find the equation of the line using the given values, we use the point-slope formula:
y - y₁ = m(x - x₁)
Using the point (2, 22) for (x₁, y₁):
y - 22 = 0.5(x - 2)
Expanding the equation:
y - 22 = 0.5x - 1
y = 0.5x + 21
Comparing this equation to y = mx + b (standard form of a linear equation), the initial value (y-intercept) of the linear function is 21.
Therefore,
- Rate of change: 0.5
- Initial value: 21
Given table:
x: 2, 8
y: 22, 25
The rate of change for a linear function is calculated by finding the change in the y-values divided by the change in the x-values.
Rate of change calculation:
Change in y = 25 (y when x = 8) - 22 (y when x = 2) = 3
Change in x = 8 - 2 = 6
Rate of change = Change in y / Change in x
Rate of change = 3 / 6 = 0.5
Therefore, the rate of change for this linear function is 0.5.
Next, to determine the initial value of the linear function, we need to find the y-intercept. The initial value represents the value of y when x = 0.
To find the equation of the line using the given values, we use the point-slope formula:
y - y₁ = m(x - x₁)
Using the point (2, 22) for (x₁, y₁):
y - 22 = 0.5(x - 2)
Expanding the equation:
y - 22 = 0.5x - 1
y = 0.5x + 21
Comparing this equation to y = mx + b (standard form of a linear equation), the initial value (y-intercept) of the linear function is 21.
Therefore,
- Rate of change: 0.5
- Initial value: 21
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.
GRAPH:
(-3,4)(0,3)(3,2)(6,1)
GRAPH:
(-3,4)(0,3)(3,2)(6,1)
To determine the initial value and the rate of change of the linear function represented in the graph with the given points:
The rate of change (slope) of a linear function can be calculated using any two points on the line. By calculating the rate of change between any two points, we can determine the rate of change of the linear function.
Using the points (0,3) and (3,2) from the graph to calculate the rate of change:
Rate of change (slope) = (y2 - y1) / (x2 - x1)
Rate of change = (2 - 3) / (3 - 0)
Rate of change = -1 / 3
Rate of change ≈ -0.333 (rounded to three decimal places)
The initial value of a linear function corresponds to the y-intercept, which is the y-value when x equals zero. In this case, we can see that the point (0,3) is provided in the data:
Initial value (y-intercept) = 3
Therefore, for the linear function represented by the graph:
- Rate of change: -0.333 (rounded to three decimal places)
- Initial value: 3
The rate of change (slope) of a linear function can be calculated using any two points on the line. By calculating the rate of change between any two points, we can determine the rate of change of the linear function.
Using the points (0,3) and (3,2) from the graph to calculate the rate of change:
Rate of change (slope) = (y2 - y1) / (x2 - x1)
Rate of change = (2 - 3) / (3 - 0)
Rate of change = -1 / 3
Rate of change ≈ -0.333 (rounded to three decimal places)
The initial value of a linear function corresponds to the y-intercept, which is the y-value when x equals zero. In this case, we can see that the point (0,3) is provided in the data:
Initial value (y-intercept) = 3
Therefore, for the linear function represented by the graph:
- Rate of change: -0.333 (rounded to three decimal places)
- Initial value: 3
the graph shows the elevation of a deep sea diver in relation to mins passed.Using any two points on the graph what is the rate of change in the diver elevation
GRAPH: begins at 0,0 ends at 6,-110
GRAPH: begins at 0,0 ends at 6,-110
To determine the rate of change in the diver's elevation using the two given points on the graph (0,0) and (6,-110), we can calculate the rate of change (slope) using the coordinates of these points.
Given points:
Point 1: (0,0)
Point 2: (6,-110)
The rate of change (slope) can be calculated using these points:
Rate of change (slope) = (y2 - y1) / (x2 - x1)
Rate of change = (-110 - 0) / (6 - 0)
Rate of change = -110 / 6
Rate of change = -18.3333.... (rounded to three decimal places)
Therefore, the rate of change in the diver's elevation, based on the graph points (0,0) and (6,-110), is approximately -18.333.
Given points:
Point 1: (0,0)
Point 2: (6,-110)
The rate of change (slope) can be calculated using these points:
Rate of change (slope) = (y2 - y1) / (x2 - x1)
Rate of change = (-110 - 0) / (6 - 0)
Rate of change = -110 / 6
Rate of change = -18.3333.... (rounded to three decimal places)
Therefore, the rate of change in the diver's elevation, based on the graph points (0,0) and (6,-110), is approximately -18.333.
1 answer