Complete the square:
F(x) = -3x² - 6x - 5
F(x) = -3 (x² + 2x) - 5
F(x) = -3 (x² + 2x + 1 - 1) - 5
F(x) = -3 ((x + 1)² - 1) - 5
F(x) = -3 (x + 1)² + 3 - 5
F(x) = -3 (x + 1)² - 2
The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :
F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5
The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.
The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from
(x + 1)² ≥ 0 ⇒ -3 (x + 1)² ≤ 0 ⇒ -3 (x + 1)² - 2 ≤ -2
This is to say, every point on the parabola has a y-coordinate no greater than -2.
As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.
Answer:
Length: 14 feet Width: 1 foot
Step-by-step explanation:
This is the only way to have a rectangle that has a perimeter of 30 feet, and an area of 14 feet.
For perimeter:
14 + 14 = 28
1 + 1 = 2
2 + 28 = 30
These dimensions have a perimeter of 30.
For area:
14 x 1 = 14
These dimesnions also have an area of 14.
So, 14 and 1 are the correct dimensions!
Answer:
4x + 9. Given f(x) = 2x + 3 and g(x) = –x2 + 5, find (g o g)(x). (g o g)(x) = g(g(x)) ... Given f (x) = sqrt(x) and g(x) = x – 2, find the domains of ( f o g)(x) and (g o f )(x). Since f (x) involves a square root, the inputs have to be non-negative. ... Given h(x) = (x + 1)2 + 2(x + 1) – 3, determine two functions f (x) and g(x
Step-by-step explanation:
Answer:
86 books
Step-by-step explanation:
A stack of books is 43 inches tall.
Each book is 
inch thick.
To find the number of books in tha stack, divide the height of the stack by the height of the book:
The division by the fraction is equivalent to the multiplication by the fraction 
so
