Direct/Joint Variation
Inverse/Combined Variation
Rational Exponents & Radical Expressions
Multiplying & Dividing Rational Expressions
Solving Radical Equations
100
If y varies directly with x, what is the constant of variation, k, when y = 8 and x = 4?
k = 2
100
If y varies inversely as to x, what is k when y= 8 and x = 2?
k = 16
100
Evaluate 8^(1/3)
2
100
Simplify: (6x^3)/(3x)
2x^2
100
SQRT (x + 1) = 4
x = 17
200
If y varies directly with x and y = 12 when x = 4, what is x when y = 9?
x = 3
200
If y varies inversely with x, and y = 9 when x = 2, what does y equal when x = 3?
y = 6
200
Evaluate the cubed root of 27^2
9
200
Simplify (x^2 + 4x + 3) / (x^2 - 2x - 3)
(x + 3) / (x - 3)
200
SQRT (2x - 6) = SQRT (4x)
x = -3
300
If A varies jointly with B and C, and k = 3, B = -1, C= 4, what is A?
A = -12
300
Do the following points represent an inverse relationship? If so, what is k? x: -2 3 0 6 y: -6 4 - 2
Yes, k = 12
300
Evaluate 2^-5
1/32
300
Simplify: (x^2 - 4x - 12) / (2x^2 + 4x)
(x - 6) / 2x
300
2 (x -4)^1/3 = (2x -2)^1/3
x = 5
400
If A varies jointly with B and C, and A = 16 when B = 4 and C = 2, find A when B = 6 and C = 2.
A = 24
400
If A varies inversely with B and directly with C, and A = 20 when B = 2 and C = 4, find the value of A when B = 3 and C = 15.
A = 50
400
(x^4 * y * z^3)^(1/3)
x^(4/3) * y^(1/3) * z
400
Simplify: [(x + 3) / (x-1)] * [(x^2 -1) / (x^2 + 7x + 12)]
(x + 1) / (x + 4)
400
SQRT (-14x + 2) = x - 3
No solution
500
Interest, I, earned on a certificate of deposit (CD) at a certain rate varies jointly as the principal, P, and time, T (in years). If the CD earned an interest of $12.50 with a principal of $2500 over 3 months, how much would it earn in 6 months on a $3000 CD?
I = $30
500
The time it takes to clean up after a party, T, varies directly with the number of guests, G, and inversely with the number of helpers, H. If it takes 3 hours to clean up after a party with 50 guests and only 2 people helped, how much time will it take to clean up after a party of 75 people if 5 people help?
T = 9/5 hours or 1.8 hours
500
Simplify the fourth root of (16x^2)^3
8x^(3/2)
500
Simplify: [(x^2 - 6x - 27)/(3x^2 - 27x)] / [(x^2 + 4x + 3)/(x^2 + x)
1/3
500
SQRT (-9x + 28) = (-x + 4)
x = -4 AND 1
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