So the easiest method to find the vertex (the minimum in this case) to do this is to find the axis of symmetry, then plug it into the function.
Firstly, the equation to find the axis of symmetry is 
, with b = x coefficient and a = x^2 coefficient. The equation equation can be solved as such:
Since the vertex falls on the axis of symmetry, we know that the x-coordinate of the vertex is -2.5. Now to solve for the y-coordinate, plug in x with -2.5 and solve as such:
Now putting it all together, our minimum value (vertex) is (-2.5,-12.25).
Answer:
The degrees of freedom for this problem are 21
Step-by-step explanation:
Degrees of freedom:
When testing an hypothesis involving two samples, the number of degrees of freedom is given by:
In which 
is the size of the first sample and 
is the sample of the second sample.
In this question:
Samples of 9 and 14, so 
The degrees of freedom for this problem are
The degrees of freedom for this problem are 21
The number is 42.
Let xy be the number. x is the tens digit, y is the units digit. The ratio of the units digit to the tens digit, y/x, is 1/2. This gives us the proportion
y/x = 1/2
The tens digit is 2 more than the units digit; x = y+2; substituting in our proportion we have
y/(y+2) = 1/2
Cross multiply:
y*2 = (y+2)*1
2y = y+2
Subtract y from each side:
2y - y = y+2-y
y = 2
x = y+2
x = 2+2
x =4
xy = 42
Answer:
y = 5x - 5
Step-by-step explanation:
It appears that the graph intersects the y-axis at (0, -5). This point is the y-intercept of the line.
As we move from (0, -5) to the point (2, 5), x increases by 2 and y increases by 10. Thus, the slope of the line through these two points is
m = rise / run = 10 / 2 = 5.
The slope-intercept form of the equation of a straight line, y = mx + b, becomes y = 5x - 5
Answer:
2?
Step-by-step explanation:
7-5 is equal to 2
