Answer:
- x = ±√3, and they are actual solutions
- x = 3, but it is an extraneous solution
Step-by-step explanation:
The method often recommended for solving an equation of this sort is to multiply by the product of the denominators, then solve the resulting polynomial equation. When you do that, you get ...
... x^2(6x -18) = (2x -6)(9)
... 6x^2(x -3) -18(x -3) = 0
...6(x -3)(x^2 -3) = 0
... x = 3, x = ±√3
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Alternatively, you can subtract the right side of the equation and collect terms to get ...
... x^2/(2(x -3)) - 9/(6(x -3)) = 0
... (1/2)(x^2 -3)/(x -3) = 0
Here, the solution will be values of x that make the numerator zero:
... x = ±√3
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So, the actual solutions are x = ±3, and x = 3 is an extraneous solution. The value x=3 is actually excluded from the domain of the original equation, because the equation is undefined at that point.
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<em>Comment on the graph</em>
For the graph, we have rewritten the equation so it is of the form f(x)=0. The graphing program is able to highlight zero crossings, so this is a convenient form. When the equation is multiplied as described above, the resulting cubic has an extra zero-crossing at x=3 (blue curve). This is the extraneous solution.
Answer:
The slope of this line would be undefined.
Step-by-step explanation:
In order to find the slope of any line, use the slope formula.
m(slope) = (y2 - y1)/(x2 - x1)
m = (3 - -1)/(-6 - -6)
m = (3 + 1)/(-6 + 6)
m = 4/0
Since we cannot divide by 0, then we know the slope is undefined.
Answer
B) x + 20 ≥ 50
Step-by-step explanation:
Answer:
Step-by-step explanation:
pyramid has a height of 5 inches and a volume of 60 cubic inches. Select all figures that could be the base for this pyramid.
A:
a square with side length 6 inches
B:
a 3 inch by 4 inch rectangle
C:
a 4 inch by 9 inch rectangle
D:
a circle with radius 4 inches
E:
a right triangle with one side 5 inches and the hypotenuse 13 inches
F:
a hexagon with an area of 36 square inches
Answer:Let P = initial investment
r = annual interest rate (decimal form)
t = number of years
A(t) = amount after t years
Then, A(t) = Pert
A(12.5) = 800e(0.0265)(12.5)
= 800e0.33125
= $1114.17
Step-by-step explanation: