Question 1

1. m = (y2-y1) / (x2-x1)

   mAB = (10-4) / (9- -3)

   mAB = 6/12 = 1/2

   mAD = (-4 - 4) / (1- -3)

   mAD = -8/4 = -2

   They -2 is the negative reciprocal of 1/2 and therefore the two lines are perpendicular to each other

2. 6/12 = (2- -4) / (x-1)

   6/12 = 6/x-1

   1/2x -0.5 = 6

   1/2x = 6.5

   x = 13

3. d = √(x1-x2)^2 + (y1-y2)^2

   = √(-3-9)^2 + (4-10)^2

   = √144+36

   = √180

   = 6√5

4. m = (x1+x2) / 2 , (y1+y2) / 2

   m = (1+9)/2 , (-4+10) / 2

   = (5, 3)

Question 2

1. 6x + 3y = 12

   y = 4 - 2x

   6x + 8x + 4y = 19

   14x + 4y = 19

   14x + 4(4-2x) = 19

   14x + 16 - 8x = 19

   6x = 3

   x = 1/2

   6(1/2) + 3y = 12

   3y = 12-3

   3y = 9

   y = 3

2. 3+14+5+8+7+9+12+4 = 62km

3. ABDECBA

   3+4+12+7+5+3 = 34km

Question 3

1. log4 = 2log2

   2log2/log2 = 2

   log16 = 4log2

   4log2/2log2 = 2

2. log1024 + log256 - log4 = t

   10log2 + 8log2 - 2log2 = t

   16log2 = t

   t = log2^16

   = log65,536

3. log2 + 2log2 + 4log2 + 8log2 + 16log2 + 32log2 = 63log2

Question 4

1. b/sin60 = 3/sin105

   b = sin60 (3/sin105)

   b = 2.689

   b = 2.69m

2. 1

3. y = a(x-2)^2 + 1

   2.6 = a(0-2)^2 +1

   2.6 = 4a+1

   4a = 1.6

   a = 0.4

4. y = 0.4(x-2)^2 + 1

   1.4 = 0.4(x-2)^2 + 1

   0.4 = 0.4(x-2)^2

   1 = x^2 - 2x + 4

   x^2 - 2x + 3 = 0

   (x+1)(x-3) = 0

   x = -1 or x = 3

   L = 3m

Question 5

1. G’ C

   does not have 2 red hair genes and do not have red hair