Simplify the following expression (2x^2y^5)^3
1 answer:
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The answers are
focus: (−2,3)
directrix: y=7
vertex: (−2,5)
The vertex is at the point (−2,5), the focus is at the point (−2,3), and the directrix is the line at y=7.
Hope this helps
9514 1404 393
Answer:
x = -2, x = -1
Step-by-step explanation:
A graphing calculator solves this nicely, as shown in the attachment.
x = -2, x = -1
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The given equation resolves to two equations.
<u>x+3 < 0</u>
-(x +3) -1 = (x +2)^2
x^2 +5x +7 = 0
Checking the discriminant, we find ...
b^2 -4ac = (5)^2 -4(1)(7) = 25 -28 = -3
There are only complex solutions to this equation.
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<u>x+3 ≥ 0</u>
x +3 -1 = (x +2)^2
(x +2)^2 -(x +2) = 0 . . . .subtract x+2
(x +2)(x +2 -1) = 0 . . . . . factor
Solutions are values of x that make these factors zero.
x +2 = 0 ⇒ x = -2
x +1 = 0 ⇒ x = -1
<em>Domain Check</em>
x +3 = -2 +3 = 1 > 0 . . . . as required.
