Expert: Lynn Houston - 1/10/2009

Question
22. Solve the system for (c,d):  
   d = 2 - 6c
  0.5 d - c =1

a.) (-4,2)      b.) (0,2)

c.) (0,-4)      d.) (2,0)




23. Solve the system:  
x + y = 4 (y + 2)

x - y = 2 (y +4 )

a.) Infinite solutions         b.) (3,8)

c.) No solution                d.) (8,3)


24. Solve the system to find (u,v).  
Hint:  x = 1/u and y = 1/v. Use x and y in the equations to solve. Once you solve for x and y, set those solutions equal to 1/u and 1/v, respectively, to find (u,v):

3 + 4 = 1
-   -
u   v

6 - 2 = 1
-   -
u   v

a.) (5,10)              b.) (1 / 5,1 / 10)

c.) (1 / 3,7 / 5)       d.) (10,5)



25. Megan has twice as many quarters as half-dollars. The total value is $5.00. How many of each type of coin are there?

a.) 5 quarters; 10 half-dollars
b.) 10 quarters; 5 half-dollars
c.) 20 quarters; 2 half-dollars  
d.) 2 quarters; 20 half-dollars



26. A chemist has one solution containing 20% acid, and a second containing 30% acid. How many liters of each solution must be combined to obtain 80 liters of a mixture that is 28% acid?

a.) 70L of 20%,10L of 30%      b.) 16L of 20%,64L of 30%

c.) 15L of 20%, 65L of 30%     d.) 60L of 20%, 20L of 30%



27. The measure of the larger of two complementary angles is twice the measure of the smaller. Find the measure of each angle.

a.) 40, 80        b.) 30, 60

c.) 20, 40        d.) 50, 100




28. Simplify: (9 - 5t)(5t - 9)

a.) -25t^2 + 90t - 81        b.) 25t^2 + 90t - 81

c.) -25t^2 + 81              d.) -25t^2 - 81



29. Simplify: (y^2 - 2y + 1)(y^2 + y +1)

a.) 2y^2 - y + 2          b.) y^4 - y + 2

c.) y^4 - y^3 + y + 1     d.) y^4 - y3 - y + 1



30. Simplify: (a + b)^2

a.) a^3 + b^3          b.) a^2 + 2ab + b^2

c.) 3a^3 + 3b^3        d.) a^3 + 2ab^2 + b^2  

Answer
22. Solve the system for (c,d):  
  d = 2 - 6c
 0.5 d - c =1

b.) (0,2)


23. Solve the system:  
x + y = 4 (y + 2)

x - y = 2 (y +4 )

a.) Infinite solutions


24. Solve the system to find (u,v).  
Hint:  x = 1/u and y = 1/v. Use x and y in the equations to solve. Once you solve for x and y, set those solutions equal to 1/u and 1/v, respectively, to find (u,v):

3 + 4 = 1
-   -
u   v

6 - 2 = 1
-   -
u   v

a.) (5,10)            



25. Megan has twice as many quarters as half-dollars. The total value is $5.00. How many of each type of coin are there?

b.) 10 quarters; 5 half-dollars



26. A chemist has one solution containing 20% acid, and a second containing 30% acid. How many liters of each solution must be combined to obtain 80 liters of a mixture that is 28% acid?

b.) 16L of 20%,64L of 30%


27. The measure of the larger of two complementary angles is twice the measure of the smaller. Find the measure of each angle.

b.) 30, 60


28. Simplify: (9 - 5t)(5t - 9)

a.) -25t^2 + 90t - 81  


29. Simplify: (y^2 - 2y + 1)(y^2 + y +1)

d.) y^4 - y3 - y + 1



30. Simplify: (a + b)^2

b.) a^2 + 2ab + b^2