1) Taking in account that the function is f(x)= -(2/3) |x+4|-6, I enclose a file with the graph.
That helps you to conclude:
a) The graph of f(x) has a vertex on (-4, -6)
b) When you multiply a function times 2/3 it is vertically compressed which is equivalent to horizontally streched.
c) The graph of f(x) opens downward
d) The domain of f(x) is all the real values (the absolute function accepts any value of x either positive or negative)
Answer: the graph of f(x) is horizontally stretched.
Answer:
See explanations below
Explanation:
Vertex of a graph is the lowest point on the curve. The vertex occurs at (1.75, -2.5)
The axis of symmetry is the point on the x axis of the line that cuts through the minimum point. The axis of symmetry occurs at x = 1.75
x intercept is the point where the curve cuts the x axis. The x intercept occurs at x = 0 and x = 2.5
To get the minimum, we will use the formula;
c - b^2/4a
The equation of the curve is expressed as;
(x-0)(x-2.5)
= x (x-2.5)
= x^2 - 2.5x
a = 1, b = -2.5, c = 0
minimum = 0 - (-2.5)^2/4(1)
minimum = -6.25/4
minimum = -1.5625
Minimum value occurs at the base of the parabola. The minimum value of the function is -2.5
y intercept is the point where the curve cuts the y axis. The y-intercept occurs at y = 0.
Step-by-step explanation:
1. y=(x-2)²-9
Using Formula (a-b)²=a²-2ab=b²
y=(x²-4x+4)-9
y=x²-4x-5
Using Mid term Break
y=x²-5x+x-5
y=x(x-5)+1 (x-5)
y=(x+1)(x-5)
2. y= -(x-5)²+16
Using the same formula as above
y= -(x²-10x+25)+16
y= -x²+10x-25+16
y= -x²+10x -9
Taking (-) as Common
y= -(x²-10x+9)
y= -(x²-9x-x+9)
y= -[x(x-9)-1(x-9)]
y= -(x-1)(x-9)
Answer:
.
Step-by-step explanation:
Total number of cards in a deck = 52
number of black cards in a deck = 26
Find the probability that both cards are black (without replacement).
Therefore, both events are dependent.
The probability of first card is black = 
the probability of second card is black = 
× 
= 
× 
=
The probability that both cards are black is .
