is 25=x2+y2 Linear or Nonlinear
15 answers
The equation 25 = x^2 + y^2 represents a circle centered at the origin with a radius of 5. A circle is a nonlinear equation, so 25 = x^2 + y^2 is a nonlinear equation.
is it a Function or Not a Function
The equation 25 = x^2 + y^2 is not a function because for a given x-value, there are multiple y-values that satisfy the equation. In other words, there are multiple outputs (y-values) for a single input (x-value).
wat bout (y+7)=3(x−2) Linear or Nonlinear and Function or Not a Function
The equation (y+7) = 3(x−2) is a linear equation because it can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
To determine if it is a function or not, we can rewrite the equation in the form y = f(x).
Expanding the equation, we get y + 7 = 3x - 6.
Rearranging the equation, we have y = 3x - 13, which is in the form of y = f(x).
Since, for every input x, there is a unique output y, the equation (y+7) = 3(x−2) represents a function.
To determine if it is a function or not, we can rewrite the equation in the form y = f(x).
Expanding the equation, we get y + 7 = 3x - 6.
Rearranging the equation, we have y = 3x - 13, which is in the form of y = f(x).
Since, for every input x, there is a unique output y, the equation (y+7) = 3(x−2) represents a function.
Linear or Nonlinear
The equation (y+7) = 3(x−2) is a linear equation because it is in the form y = mx + b, where m is the slope (3 in this case) and b is the y-intercept (-7 in this case). Therefore, it is a linear equation.
is this table Linear or Nonlinear
Time (hours) 3, 6, 9, 12
Temperature (degree Celsius) 5, 0, -5, -10
Time (hours) 3, 6, 9, 12
Temperature (degree Celsius) 5, 0, -5, -10
To determine whether the table represents a linear or nonlinear relationship between time and temperature, we can find the rate of change between each pair of values.
For the given table:
Time (hours): 3, 6, 9, 12
Temperature (degree Celsius): 5, 0, -5, -10
To find the rate of change, we can calculate the difference in temperature divided by the difference in time for consecutive pairs of values.
The rate of change between the first and second pair is: (0 - 5) / (6 - 3) = -5 / 3
The rate of change between the second and third pair is: (-5 - 0) / (9 - 6) = -5 / 3
The rate of change between the third and fourth pair is: (-10 - (-5)) / (12 - 9) = -5 / 3
Since the rate of change is consistent for each pair, the table represents a linear relationship between time and temperature.
For the given table:
Time (hours): 3, 6, 9, 12
Temperature (degree Celsius): 5, 0, -5, -10
To find the rate of change, we can calculate the difference in temperature divided by the difference in time for consecutive pairs of values.
The rate of change between the first and second pair is: (0 - 5) / (6 - 3) = -5 / 3
The rate of change between the second and third pair is: (-5 - 0) / (9 - 6) = -5 / 3
The rate of change between the third and fourth pair is: (-10 - (-5)) / (12 - 9) = -5 / 3
Since the rate of change is consistent for each pair, the table represents a linear relationship between time and temperature.
is this table Function or Not a Function
Time (hours) 3, 6, 9, 12
Temperature (degree Celsius) 5, 0, -5, -10
Time (hours) 3, 6, 9, 12
Temperature (degree Celsius) 5, 0, -5, -10
The given table represents a function because for each input value (time), there is only one corresponding output value (temperature). In other words, there are no repeated x-values with different y-values.
is the table Linear or Nonlinear
x 1,2,3,4,5,6,7
y 1,8,27,64,125,216,?
x 1,2,3,4,5,6,7
y 1,8,27,64,125,216,?
To determine if the table represents a linear or nonlinear relationship, we can examine the pattern of the outputs (y-values) relative to the inputs (x-values).
If we take the square root of each y-value, we get:
√1 = 1
√8 ≈ 2.83
√27 ≈ 5.20
√64 = 8
√125 ≈ 11.18
√216 ≈ 14.70
From this pattern, we can observe that the outputs are not increasing or decreasing at a constant rate. Instead, they are increasing at a faster and faster rate.
Therefore, the table does not represent a linear relationship.
If we take the square root of each y-value, we get:
√1 = 1
√8 ≈ 2.83
√27 ≈ 5.20
√64 = 8
√125 ≈ 11.18
√216 ≈ 14.70
From this pattern, we can observe that the outputs are not increasing or decreasing at a constant rate. Instead, they are increasing at a faster and faster rate.
Therefore, the table does not represent a linear relationship.
but is it a Function or Not a Function
The given table represents a function because for each input value (x), there is exactly one corresponding output value (y). In other words, there are no repeated x-values with different y-values.