Because the vertex of the parabola is at (16,0), its equation is of the formy = a(x-10)² + 15
The graph goes through (0,0), thereforea(0 - 10)² + 15 = 0100a = -15a = -0.15
The equation is y = f(x) = -0.15(x - 10)² + 15
The graph is shown below.
Part A
Note that y = f(x).
The x-intercepts identify values where the function or y=0. The x-intercepts occur at x=0 and x=20, or at (0,0) and (20,0).
The maximum value of y occurs at the vertex (10, 15) because the curve is down due to the negative leading coefficient of -0.15.
The curve increases in the interval x = (-∞, 10) and it decreases in the interval x = (10, ∞).
Part B
When x=12, y = -0.15(12 - 10)² + 15 = 14.4When x=15, y = -0.15(15 - 10)² + 15 = 11.25
The average rate of change between x =12 to x = 15 is(11.25 - 14.4)/(15 - 12) = -1.05
This rate of change represents the slope of the secant line from A to B. It approximates the rate at which f(x) decreases in the interval x =[12, 15].
Circumference
C = pi d
C = 3.14 x 10
C = 31.4 cm
Area
A = pi r^2
A = 3.14 x 5^2
A = 78.5 cm^2
Answer:
x=-11, y=0. (-11, 0).
Step-by-step explanation:
x-12y=-11
x-y=-11
-------------
x=y+(-11)
x=y-11
y-11-12y=-11
-11y=-11+11
-11y=0
y=0/-11=0
x-0=-11
x=-11+0=-11
<h3>
Answer: 0</h3>
Explanation:
The single digits are {0,1,2,3,4,5,6,7,8,9}
So naturally 0 is the first thing to test.
The number 270 is a multiple of 9 because 9*30 = 270. The digits of 270 add to 2+7+0 = 9 showing that it's a multiple of 9. Refer to the "divisibility by 9 rule".
The next possible value of y will be 9 units higher than y = 0, so we go for y = 9. Meaning that 279 is also a multiple of 9 (because 2+7+9 = 18 is a multiple of 9).
