Question 1

1. AC = AB + BC

   BC = AC - AB

   BC = (6/3) - (4/-0.5)

   BC = (2/3.5)

2. AD = AC+CD

   DC = -(8/-1)

   AD = (6/3) + -(8/-1)

   AD = -2/4

3. ?

Question 2

1. t+2c+b = 160

   t+b-c = 70

   t+2c+b = 160

   -t-b+c = -70

   3c = 90

   c = 30

Question 3

1. 3/5

2. 3/5 → 3/10, 2/3

3. (2/5) x (3/10) = 3/25

   (3/5) x (2/3) = 2/5

   (3/25) + (2/5) = 13/25

4. (3/25) / (13/25) = 3/13

5. 3/25, 1/5

Question 4

1. -2 = klog3 (10-1)

   -2 = k log39

   -2 = log3 3^2k

   3^-2 = 3^2k

   k = -1

2. d = fx-gx

   d = log3 (5x+7) - -log3 (x-1)

   d = log3 (5x+7)(x-1)

   d = log3 (5x^2 - 5x + 7x - 7)

   d = log3 (5x^2 +2x - 7)

3. d = log3 (5(4)^2 +2(4) - 7)

   d = 4

4. 0 = log3 (5x^2 +2x - 7)

   1 = 5x^2 +2x - 7

   5x^2 +2x - 8 = 0

   (-b ± √b^2 - 4ac) / 2a

   (-2 ± √2^2 - 4(5)(-8) / 2(5)

   x = 1.08, 1.1

Question 5

1. d = st

   d = 500 x 2.33

   d = 1,165 = 1170km

2. t = d/s

   t = 5760/900

   t = 6.4 x 60

   t = 384