Answer:
A system of equations that represents the situation is:
3x + 2y = 315..... Equation 1
2x + 4y = 450...... Equation 2
Step-by-step explanation:
Let the number of
Haircuts = x
Hair dyes = y
Hence:
Alexandra finds that she can give:
3 haircuts and 2 hair dyes in 315 minutes.
3x + 2y = 315..... Equation 1
Giving 2 haircuts and 4 hair dyes takes 450 minutes
2x + 4y = 450...... Equation 2
Therefore:
a system of equations that represents the situation is:
3x + 2y = 315..... Equation 1
2x + 4y = 450...... Equation 2
anything multiplied by one is itself, anything multiplied by zero is zero
Y=-2(x-5)^2+7
y=-2(x^2-10x+25)+7
y=-2x^2+20x-50+7
y=-2x^2+20x-43
dy/dx=-4x+20, d2y/dx2=-4
Since acceleration, d2y/dx2 is a constant negative, when dy/dx, velocity, equals zero, it represent the absolute maximum for y...
dy/dx=0 only when 4x=20, x=5
y(5)=7 so the vertex is at the point (5, 7). It has an absolute maximum at that point and decreases without bound on either side of x=5. So the parabola opens downward.