Q5 The net income y in millions of dollars of Pet Products U

Q5. The net income y (in millions of dollars) of Pet Products Unlimited from 1997 to 1999 is given by the equation y = 9x² + 15x + 52, where x represents the number of years after 1997. Assume this trend continues and predict the year in which Pet Products Unlimited\'s net income will be $598 million.
   a. 2005
   b. 2004
   c. 2003
   d. 2006

Q6. Solve the equation x² + 144 = 0 in the complex number system.
   a. {-12, 12}
   b. {12}
   c. {12i}
   d. {-12i, 12i}

Q7. Find the real solutions of the equation 24x + 48 = x + 8.
   a. {-4}
   b. {6}
   c. {-3}
   d. {4}

Q8. Solve P-5Q/3=(P+7)/2+1 for P.
   a. P = (15 - 10Q)/3
   b. P = (27 + 10Q)/3
   c. P = (27 - 10Q)/3
   d. P = (15 + 10Q)/3

Q9. Tracy can wallpaper 2 rooms in a new house in 8 hours. Together with her trainee they can wallpaper the 2 rooms in 6 hours. How long would it take the trainee working by herself to do the job?
   a. 8 hr
   b. 30 hr
   c. 22 hr
   d. 44 hr

Q10. Solve x² - 2x - 24 = 0 by using completing the square.
   a. {5, -1}
   b. {-6, 4}
   c. {-20, -4}
   d. {6, -4}

Solution

Answer 5: d (As shown below)

9x² + 15x + 52 = 598

9x² + 15x - 546 = 0

x = 7 satisfies the above equation:

9(7²) + 15(7) - 546 = 9(49) + 135 - 546 = 441 +135 - 546 = 0

1999 + 7 = 2006

Answer 6: d (As shown below)

x² + 144 = 0

x² = -144

x² = (-1)(144)

x² = (-1^1/2)²(12)²

x² = (i)²(12)²

x = +12 or x = -12

Answer 7: d (As shown below)

(24x + 48)^1/2 = x + 8

Squaring both sides, we get:

24x + 48 = x² + 16x + 64

x² + 8x + 16 = 0

(x - 4)² = 0

x = 4

Answer 8: b (As shown below)

P - 5Q / 3 = (P + 7) / 2 + 1

(3P - 5Q) / 3 = ((P + 7) + 2) / 2

2 (3P - 5Q) = 3 (P + 7 + 2)

6P - 10Q = 3P + 27

3P = 10Q + 27

P = (27 + 10Q) / 3