We can verify this with the graph
(-6, 3) NO
(-3, 3) NO
(-5, 0) NO
(-4, 2) YES
(0,0) NO
(-6, 6) YES
(-3, -6) NO
(-4.0) YES
the area where the solutions are in the yellow area
Simplify, assume the variable represents a positive real number
1 answer:
The simplification of the given expression will be equal to
The process of reducing the complex mathematical expressions into the simplest form is called as the simplification.
The simplification of the given expression will be:
hence the simplification of the given expression will be equal to
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To find the gradient of the tangent, we must first differentiate the function.
The gradient at x = 0 is given by evaluating f'(0).
The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.
The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so
Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).
So the point (0, -1) lies on the tangent. Substituting into the tangent equation:
Those points you can see on the graph.
The first one refers to the x value and the second, to y value. If you notice, when you have x = 0, y = 3. When x = -5, y = 0.
When the line intercepts one of the axis, means the other coordinate is = 0.
3 is y intercept, it means the x value of that point is 0. The same happens to the x intercept - 5. It means the y value of that point is 0.
A ( -5 | 0 )
B ( 0 | 3 )
m = Delta y / Delta x.
Delta y is the variation over the x-axis. Delta x, the x axis.
Be safe!
The first one refers to the x value and the second, to y value. If you notice, when you have x = 0, y = 3. When x = -5, y = 0.
When the line intercepts one of the axis, means the other coordinate is = 0.
3 is y intercept, it means the x value of that point is 0. The same happens to the x intercept - 5. It means the y value of that point is 0.
A ( -5 | 0 )
B ( 0 | 3 )
m = Delta y / Delta x.
Delta y is the variation over the x-axis. Delta x, the x axis.
Be safe!