Answer:
center: (0,0)
vertices: (-4,0) and (4,0)
foci: (-10.8,0) and (10.8,0)
asymptotes: y = -5/2*x and y = 5/2*x
Step-by-step explanation:
Hyperbola with center as origin general equation is:
x²/a² - y²/b² = 1
Our equation is:
25x² - 4y² = 400
Dividing each term by 400:
25x²/400 - 4y²/400 = 400/400
x²/16 - y²/100 = 1
which matches the general equation. Then, the center is (0,0)
a² = 16
a = 4
b² = 100
b = 10
c² = a² + b²
c = √(16+100) = 10.8
General vertices formula: (±a,0). Replacing, the vertices are: (-4,0) and (4,0)
General foci formula: (±c,0). Replacing, the foci are: (-10.8,0) and (10.8,0)
General asymptotes formula: y = ±b/a*x. Replacing, the asymptotes are:
y = -10/4*x = -5/2*x
y = 10/4*x = 5/2*x
Let 
be the most the manager can pay the suppliers.
Then, we know from the information given in the question that the manager needs a 30% markup based on cost.
Therefore, the guiding equation will be:
because $10 is the most people will pay for a neck warmer.
Thus, the above equation will become:
Thus, the most a manager can pay the suppliers for neck warmers and still keep the selling price at $10 is $7.69
solid line. we shade above the line
the dotted line. shadow above the line
Answer in the attachment (the first graph).
f(x)=4x^3 - 6x^2 + 2x - 5
f(-2)
Replace X with -2:
4(-2)^3 - 6(-2)^2 + 2(-2) - 5 =
Calulate the powers:
4(-8) - 6(4) +(-4) -5=
Multiply:
-32 - 24 -4 -5=
Subtract
-65
