
Which real numbers are equal to their cubes?
Solution on Video

Write 4×10^{2} as a decimal.
Solution on Video

Write 0.12×10^{3} as a decimal.

Write 2 log_{3} x + log_{3} 5 as a single logarithmic expression.

Factor the algebraic expression 6x^{2}  21 x y + 8 x z  28 y z.
Solution on Video

Factor the algebraic expression (x  1)^{2}  (y  2)^{2}.
Solution on Video

Factor the algebraic expression x^{2}  z^{4}.

Evaluate the algebraic expression 2 x  y + 3 for x = 3 and y = 5

Simplify the algebraic expression 2(x  3) + 4(2 x + 8)

Expand and simplify the algebraic expression (x + 3)(x  3)  (x  9)

Which property is used to write a(x + y) = a x + a y

Simplify ( 8 x^{3} ) / ( 2 x^{3})

Simplify (a^{2}b^{3})^{2}(c^{2})^{0}

For what value of k is the point (2, k) on the line with equation 3 x + 3 y = 4?

For what value of a will the system given below have no solutions?
2 x + 6 y = 2
3 x + a y = 4

Which equation best describes the relationship between x and y in this table?
x 
y 
0 
4 
4 
20 
4 
12 
8 
36 
A) y =  x/4  4
B) y =  x/4 + 4
C) y =  4x  4
D) y =  4x + 4

Which equation best represents the area of the rectangle below?
.
A) area = 2(x+1) + 2(x1)
B) area = 4(x+1)(x1)
C) area = 2x^{2}
D) area = x^{2}  1

Which line given by its equation below contains the points (1, 1) and (3, 5)?
A) 2y 6x = 0
B) 2y = 6x  8
C) y = 3x + 4
D) y = 3x + 4

Solve the equation 23x  2  3 = 7.

Solve for x the equation (1/2)x^{2} + mx  2 = 0.

For what values of k the equation x^{2} + 2kx  4 = 0 has one real solution?

For what values of b the equation x^{2}  4x + 4b = 0 has two real solutions?

Function f is described by the equation f (x) = x^{2} + 7. What is the set of values of f(x) corresponding to the set for the independent variable x given by {1, 5, 7, 12}?

Find the length and width of a rectangle whose perimeter is equal to 160 cm and its length is equal to triple its width.

Simplify:  x + 3 x   2 x + 3x

If (x^{2}  y^{2}) = 10 and (x + y) = 2, find x and y.
Answers to the Above Questions
 0 , 1 , 1 are all equal to their respective cubes.
 0.04
 0.00012

= log_{3} x^{2} + log_{3} 5 = log_{3}(5x^{2})
 = 3x(2x  7y) + 4z(2x  7y) = (2x  7y)(3x + 4z)
 = [(x  1) (y  2)][(x  1)+ (y  2)] = (x  y + 1)(x + y  3)

= (x + z^{2})(x  z^{2}) = (x + z^{2})(x + z)(x  z)
 = 2(3)  (5) + 3 = 8 = 8
 = 2x + 6 8x + 32 = 10x + 38

= x^{2}  9 + x + 9 = x^{2} + x
 distributivity

4 x^{6}

a^{4}b^{6}
 k = 2/3
 a = 9
 C. y =  4x  4

D. area = (x + 1)(x  1) = x^{2}  1
 B. 2y = 6x  8
 solution set : {7/3 , 1}

solution set : {m + sqrt(m^{2} + 4) , m  sqrt(m^{2} + 4)}
 k = 2 , k = 2

all values of b less than 1
 {6 , 18 , 42 , 137}
 width = 20 cm and length = 60 cm
 x + 3x  2x + 3x = 5x
 x = 7 / 2 , y =  3 / 2
