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emmasim [6.3K]
3 years ago
12

Which statement best explains whether the table represents a linear or nonlinear function? Input (x) Output (y) 2 5 4 10 6 15 8

20
A It is a linear function because the input values are increasing.

B It is a nonlinear function because the output values are increasing.

C It is a linear function because there is a constant rate of change in both the input and output.

D It is a nonlinear function because there is a constant rate of change in both the input and output.
Mathematics
1 answer:
Vinil7 [7]3 years ago
5 0

Answer:

C It is a linear function because there is a constant rate of change in both the input and output.

Step-by-step explanation:

With the values, you can see that the Y value is always 2.5 times the value of X.  That's a constant rate of change.

Answers A and B make no sense, because the fact that the input or output values are increasing or decreasing have no impact to determine if a function is linear or not, can be linear or non-linear in all cases.

Answer D gives the definition of a linear function, but applies it to a non-linear function.

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Option A: \frac{1}{3} is the dilation factor

Explanation:

The Coordinates of the square ABCD are A(-21,18), B(-12,18), C(-12,9), D(-21,9)

Also, the coordinates of the square A'B'C'D' are A'(–7, 6), B'(-4,6), C'(-4,3), D'(-8,3)

Now, we shall determine the scale factor in the dilation if the coordinates A' and C'.

Since, the dilation is the enlargement of the image in the same shape but different size.

To determine the scale factor, let us divide A'C' by AC

Thus, we have,

\begin{aligned}A^{\prime} C^{\prime} &=\sqrt{(-4+7)^{2}+(3-6)^{2}} \\&=\sqrt{3^{2}+(-3)^{2}} \\&=\sqrt{9+9} \\&=\sqrt{18}\\&=3\sqrt{2} \end{aligned}

Also,

\begin{aligned}A C &=\sqrt{(-12+21)^{2}+(9-18)^{2}} \\&=\sqrt{9^{2}+(-9)^{2}} \\&=\sqrt{81+81} \\&=\sqrt{162}\\&=9\sqrt{2} \end{aligned}

Dividing A'C' by AC, we have,

\frac{A'C'}{AC} =\frac{3\sqrt{2} }{9\sqrt{2}} =\frac{1}{3}

Thus, \frac{1}{3} is the dilation factor

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