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Algebra : Radicals and Quadratic Equations

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1.) Find all numbers for which the rational expression is defined: S^3-7s/s^2-25

2.) GCF: -30a^3, 5a^4
(Would it be 5a^3 or -5a^3??)

3.) Use rational expressions to write: x^1/2*y^1/6*z^1/8

4.) Solve: x^2 +6x-4=0

5.: Use rational exponents to simplify: ^4 Sqrt x^12
(Would it be x^3 ??)

6.) Divide: (28b^3 + 27b^2 + 22b + 49) / (4b + 5)

7.) Find the following: ^20 Sqrt (-5) ^20

8.) Divide and Simplify: b^6 / b18

9.) f(x)=1/5 (x+1)^2+2
Vertex:
Line of symmetry:
Maximum/Minimum Value:
Is the value of f(-1) = 2:

10.) Jack usually mows his lawn in 5 hours. Marilyn can mow the same yard in 4 hours. How much time it would take for them to mow the lawn together?

11.) Find the variation constant and an equation of variation where y varies directly as x and y=35 when x=5.

The variation constant is k = _______
The equation of variation is y = ____

12.) (x+5) (x-19) (x+3)> 0
The solution is {x/____}

13.) 2x^2-6x+19 = 0
Value of the discriminate _____
How many solutions does this have: a) Two imaginary solutions
b) One real solution
c) Two real solutions

14.) F(x) = -2x^2 + 2x + 1
X-Coordinate of the vertex:
Y- Coordinate of the vertex:
Line of symmetry:
Maximum/Minimum Value:
Is the value of f(1/2) = 3/2:

15.) 2/v = 8/v-1/5

16.) Multiply: (2*sqrt 2 - 6*sqrt 3)(5*sqrt 2 + 15*sqrt 3) =

17.) Convert to Decimal Notation: 8.49* 10^7 =

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Algebra problems are solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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