Algebra

15  

(a) Area  =    L * W   =  (x + 2) ( x + 1)   = x^2 + 3x + 2

(b) Assuming this is a right triangle....find x     ....

x^2  + (x + 3)^2   = 225

x^2 + x^2  + 6x + 9  = 225

2x^2 + 6x −216  = 0

x^2 + 3x − 108  = 0

(x + 12) (x − 9)  = 0    →   set both factors to 0 and solve   x  = 9    or  x = −12 [reject]

So

Area = [B * H] / 2  =  [x (x + 3)] / 2  =  [ 9 ( 9 + 3)] / 2  =  [9 * 12] / 2  =  108 / 2  =  54  units^2

16 

f(x)  = x^2 − 7x + 3       take 1/2  of 7 = 7/2  square it   = 49/44   add it and subtract it

f(x)  = x^2 − 7x + 49/4  + 3   −  49/4     factor the first three terms and simplify

f(x) =  ( x − 7/2)^2  + [ 12 − 49] / 4

f(x) =  ( x − 7/2)^2   − 37 / 4