Expert: Richard J. Raridon - 7/25/2010

Question
1.   Solve the system:
z + 3x + y = 3

2x + 3y = 10

2y = 8

  (-1, 2, 2)      (1, 4, 2)
  (-1, 4, 2)      (-3, 2, 4)
2.   Solve the system:
2x + 5y + 2z = -5

-3x + 3y + 5z = 2

x + 4y - z = 3

  (-3, 1, -2)      (3, -1, -2)
  (-3, 1, 2)      (-3, 1, 4)
3.   Solve the system:
2x + 2y + z = -3

3x + 2y - 2z = -1

5x - 2y - 6z = 17

  (-5, 5, 3)      (5, -5, -3)
  (2, -3.5, 0)      (2, 3.5, 0)
4.   Solve the system:
a + 3b + 4c = 6

a - 2b + c = 10

2a + 3b - c = 0

  (4, -2, 2)      (4, 2, -2)
  (-4, 2, -2)      (-4, -2, 4)
5.   Solve the system:
1   +   3   -   2   =   1
r    s    t
2   +   3   -   4   =   1
r    s    t
1   -   6   -   6   =   0
r    s    t
  (1, -3, 2)      (-1, 3, 2)
  (1, 3, -2)      (-1, 3, -2)
6.   David paid $9.50 for some 15 cent, 25 cent, and 45 cent stamps. He bought 38 stamps and the number of 25 cent stamps was 8 more than twice the number of 45 cent stamps. How many of each type did David buy?
  10 15-cent; 22 25-cent; 8 45-cent      12 15-cent; 20 25-cent; 6 45-cent
  10 15-cent; 20 25-cent; 8 45-cent      12 15-cent; 10 25-cent; 8 45-cent
7.   The sum of the length, width, and height of a rectangular box is 75 cm. The length is twice the sum of the width and height. The width exceeds the height by 5 cm. Find the dimensions.
  50 cm by 10 cm by 15 cm      40 cm by 10 cm by 25 cm
  45 cm by 15 cm by 15 cm      45 cm by 10 cm by 15 cm
8.   Simplify:
27 1/3

  9      3
  
1
3
  
1
9
9.   Simplify:
25-3/2

  
1
125
  125
  75      -75
10.   Simplify:
4      -3/2
9
  
12
13
  
2
3
  
27
8
  27
11.   Simplify:
-(93/2)

  -27      -6
  -18      No solution
12.   Simplify:
7-2/3      3
  14      
1
49
  49      -14
13.   Simplify:
(274)-1/12

  8      -9
  3      
1
3
14.   Simplify:
(82/3 - 81/3)3

  8      24
  256      16
15.   Choose the correct exponential form for:
The cube root of (p to the fourth power times q)

pe="radio" value="162455" name="Q56688">   p to the 4 thirds power times q to the one third power      p to the 3 fourths power times q cubed
  p to the twelfth power times q cubed      p to the fourth power times q cubed
16.   Choose the correct exponential form for:
The cube root of (x to the sixth power times y to the negative four power)

  x to the eighteenth power times y to the negative 12 power      x to the one half power times y to the negative three fourths power
  x squared times y to the four thirds power      x squared times y to the negative four thirds power
17.   Solve:
125    =    (x3)    /        1       -3
                        3          
  7      14
  15      9
18.   Solve:
(9t)-2/3 = 4

  
1
144
  
1
72
  72      144
19.   Solve:
(3n-1)-2/3 = 1/4

  3      27
  6      9
20.   (x2 + 9)1/2 = 5
  ±4      16
  4      
Ö   34
21.   Simplify:
The cube root of four to the six y power

  16y      32y
  64y      4y
22.   Simplify:
(six to the square root of two power times 6 to the square root of eight power) divided by

(6 to the 3 times the square root of 2 power)

  2      6 to the square root of eight power divided by 6 cubed
  1      0
23.   Simplify:
The square root of 3 to the square root of 2 power times the square root of 3 to the negative square root of 2 power.

  3-1      1/3
  1      3
24.   Simplify:
The square root of 2 to the square root of 2 power all to the square root of 2 power.

  4      2
  4 to the square root of 2 power      -2
25.   Simplify:
252.4
55.8
  2      
2   60
29
  
1
5
  5
26.   Simplify:  
(The square root of 2 minus 1 to the 2 plus y power) all divided by (the square root of 2 minus 1 to the y power).

  
Ö   2
  
3 - 2Ö   2
  1      
3 + 2Ö   2
27.   Simplify:
The square root of 2 to the negative 9 plus 3 power

  2 square root of 3 divided by 2      8
  1/2      1/8
28.   
5x = Ö    125
  
2
3
  3
  
1
3
  
3
2
29.   Solve:
41-x = 8

  
-5
2
  
-1
2
  
1
2
  2
30.   
49x-2 = 7Ö    7
  
-5
4
  
5
4
  
11
4
  
-11
4

31.   
Suppose f(x) = x/2, g(x) = x - 3, and h(x) = Ö    x
Simplify:   h(f(32))


32.   
Suppose f(x) = x/2, g(x) = x - 3, and h(x) = Ö    x
Simplify: g(h(9))


33.   Write the equation for:
Ellipse with x-intercepts ± the square root of 6 and y-intercepts ± 2


34.   Write the equation for:
The circle having center (-3, 4), a radius of length 5, and passing through the origin


35.   Solve the system:
x - 3y = 5

4x + y = 7

Answer
You need to write exponents as x^2 or y^1/3                                                     1. (-1,4,2)
2. (-3,1,-2)
3. (2,-3.5,0)
4. (4,-2,2)
6. 12, 20, 6
7. 50*10*15
8. 3
9. 1/125
10. 27/8
11. -27
14. 8
15. p^4/3q^1/3
16. x^2y^-4/3
19. n=3
20. x = +/-4
21. 16^y
22. 6^(8^1/2)/6^3
23. 3
24. 2
28. 5^1/2
33. x^2/6 +y^2/4 = 1
34. (x+3)^2 +(y-4)^2 = 25
I would have worked a few more if I could have figured out what you meant.