If x is the hypotenuse then
hyp^2 = 4^2 + 5^2
hyp^2 = 41
hypotenuse =
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6.403124
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if x is a leg then
leg^2 = 5^2 - 4^2
leg^2 = 25 - 16
leg^2 = 9
leg =3
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].
Approximately 186in^3 was released from the water balloon
Answer:
-8 + 14n
Step-by-step explanation:
-2(4-4n)+6n
Distribute the -2
-8 +8n+6n
Combine like terms
-8 + 14n
A graph shows the solutions to be
(x, y) = (-6, 312) or (6, 312)To solve algebraically, remove a factor of 2 from the second equation and use that expression to substitute for y in the first equation.
10x^2 -(8x^2 +24) = 48
2x^2 = 72
x = ±√(72/2) = ±6
y = 8*36 +24 = 312
