Math 027 Exam #2

  1. Given the points (2,-3) and (-5,6), Find the slope of the line connecting them.

    2. ANS: M= (-3-6)/(2--5) = -9/7

  2. Give the equation of the line passing thru (2,-3) and having a slope of -2.

    3. ANS: y --3 = -2(x-2) or y + 3 = -2x + 4 or y = -2x + 1

  3. Joe sells 10 computers at $2000 or 17 computers at $1300. Assume a linear relationship between the number of computers C that Joe can sell and the price P that Joe charges.

    4. ANS: m=(2000-1300)/(10-17) = -100 then P - 2000 = -100(C - 10) so P = -100C + 3000

  4. Given a graph:

 

How Much were sales in march?

ANS: 3000

When are sales increasing?

ANS: FEB-MAR and JUN to JULY

When is the minimum?

ANS: FEB

5. Solve the system of equations: 5x - y = 18 and x + 2y = -3

ANS: 5x - y = 18 (times 2) 10x - 2y = 36 add to x + 2y = -3 to get 11x = 33. So x = 3. Then 3 + 2y = -3 so y = -3

6. Simplify

ANS: ( 2x 4 - 2 y 2 - 5 ) 4 = ( 2 x 2 y -3 ) 4 = 16 x 8 / y 12

7. Simplify ( r 2 s - 2 ) - 1 ( r - 1 s 2 ) 3

ANS: r - 2 s 2 r - 3 s 6 then r -5 s 8 or s 8 / r 5

 

  1. Convert 0.000000035 to scientific notation

    2. ANS: 3.5 x 10 -8

    Convert 3.26 x 10 5 to scientific notation

    ANS: 326000

  2. Multiply and simplify 5x2 y ( xy - y ) - 2x ( x 2y 2 - x y 2 )

    3.  

    ANS: 5 x3 y2 - 5 x2 y2 - 2 x3 y2 + 2 x2 y2 or 3 x3 y2 - 3 x2 y2

     

  3. ( 2 a b - c ) ( 3 a b + 5 c)

    4.  

    ANS: 6 a2 b2 + 7 a b c - 5 c2

     

  4. Use AC method to solve 6 a2 - 7 a - 10

    5. ANS: AC = -60 that factors to -12 and 5 so 6 a2 - 12a + 5a - 10 then factor by grouping to get (6a + 5) ( a - 2)

  5. Solve the quadratic equations: 12 x2 + 36 x - 120 = 0

    6. ANS: 12 ( x2 + 3x - 10) = 0 becomes 12 ( x - 2) ( x + 5) = 0 so x = 2 or -5

  6. Perform and simplify:

    7. ANS: LCD: 6r2 ( r - 6) so the problem becomes 5 (r-6)/ 6r2 ( r - 6) + 6r/6r2 ( r - 6) and

    Then (5r - 30 + 6r)/ 6r2 ( r - 6) = (11r - 30) /6r2 ( r - 6)

ANS: FACTOR