Greatest value of xy
x + 2y = 30, x = 30 - 2y
xy = (30-2y)y = 30y-2y^2
so if -2y^2+30y = 100, then we can take out a (-2), so: y^2-15y=-50, y^2-15y+50=0
(y-5)(y-10)=0
y-5=0, y=5
y-10=0, y=10
Now we can "plug n play": plug each into x = 30-2y
x = 30-2(5) = 30-10 = 20
x = 30-2(10) = 30-20 = 10
So if we make x=20, y=5... xy = 100
And if x=10, y=10... xy = 100
Now we need to try other number variations to see if they can make xy > 100
if y=6, then x = 30-2 (6) = 30-12 = 18
xy = (18)(6) = 108. Ooh! there's a better choice, but let's keep going
if y=7, then x = 30-2(7) = 16, xy = 7*16 = 112
Even higher! But let's check others
If y=8, then x = 30-16=14, so xy = 112
But from here, the higher y gets the product of xy starts to decrease again
So the greatest possible value comes from 7*16 and 8*14, in which x*y was the maximum it could be at 112
144+ 18x=360
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The vertex of the function f(x) exists (1, 5), the vertex of the function g(x) exists (-2, -3), and the vertex of the function f(x) exists maximum and the vertex of the function g(x) exists minimum.
<h3>How to determine the vertex for each function is a minimum or a maximum? </h3>
Given:
and
The generalized equation of a parabola in the vertex form exists
Vertex of the function f(x) exists (1, 5).
Vertex of the function g(x) exists (-2, -3).
Now, if (a > 0) then the vertex of the function exists minimum, and if (a < 0) then the vertex of the function exists maximum.
The vertex of the function f(x) exists at a maximum and the vertex of the function g(x) exists at a minimum.
To learn more about the vertex of the function refer to:
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A quadratic equation is an equation with exponents and x's, for example 3x^2+4x+3 is a quadratic. and quadratics usually have two points it can cross the x axis. though that doesn't mean it always crosses twice. some quadratic equations can cross more then twice and some don't at all.
linear equations are simple. they always show a straight line on a graph.
And exponential are kind like quadratics, exponential always have an exponent but don't have multiple x intercepts. exponentials are equations like the equation for compound interest rates (Initial Account Balance * (Interest Rates) ^ Time) it is exponentially growing using exponents.
Answer:
P(even) is 1/2.
Step-by-step explanation:
To get the probability of even numbers, you divide the amount of even numbers by the total amount of numbers. You should get 2 (amount of even numbers) /4 (total amount of numbers.) This simplifies to 1/2. I hope this helps and that you have a marvelous day!! Stay safe!!