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4 years ago

Write an equation in slope-intercept form from the linear inequality graphed in the picture.

Mathematics

1 answer:

stepladder [879]4 years ago

3 0

Answer:

equation: y = x+3
inequality: y < x+3

Step-by-step explanation:

The slope of the line is 1 unit of rise for 1 unit of run, so ...

m = rise/run = 1/1 = 1

The y-intercept is 3 grid lines above the x-axis, so is (0, 3).

Then the equation of the line is ...

y = 1x +3

The inequality has that line as a boundary, but the y-values on the line are not part of the solution space. Only y-values below the line (less than those on the line) are in the solution. The inequality is ...

y < x +3

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Finding the average rate of change of g(z) =4x^2_5 between the points( -2,11) and (2,11

krok68 [10]

Answer:

The average rate of change of g(z) =4x^2_5 between the points( -2,11) and (2,11) is 0.

Step-by-step explanation:

Given a function y, the average rate of change S of $y=g(z)$ in an interval $(z_{s}, z_{f})$ will be given by the following equation:

$S = \frac{g(z_{f}) - g(z_{s})}{z_{f} - z_{s}}$

In this problem, we have that:

$g(z) = 4z^{2} - 5$

Between the points( -2,11) and (2,11).

So $z_{f} = 2, z_{s} = -2$

$g(z_{f}) = g(2) = 4*(2)^{2} - 5 = 11$

$g(z_{s}) = g(-2) = 4*(-2)^{2} - 5 = 11$

$S = \frac{g(z_{f}) - g(z_{s})}{z_{f} - z_{s}} = \frac{11 - 11}{2 - (-2)} = \frac{0}{4} = 0$

The average rate of change of g(z) =4x^2_5 between the points( -2,11) and (2,11) is 0.

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