CPhill

side  =   ∛56  =  3.82586 =  3.83  inches

Question 17 : Given equation 4x² - 7x + 9 = 0, find the value of x.

Because the disriminant < 0,  this has no real roots

Question 16 : Find the value of K in the perfect square 12x² - 6x + K

Write  12x^2 - 6x

Factor  out  the 12

12  ( x^2  -  (1/2)x  )

Take (1/2)  of (1/2)  = 1/4.....square this  =  1/16

So  we  have

12 (x ^2  - (1/2)x  + 1/16)

12x^2  - 6x  + 12/16

12x^2 - 6x  +  3/4

So....  K  =  3/4

Question 15 : Given Ƹ = {1,2,3,4,5,.6,7,8}, A= {1,2,4,8}, B= {1,3,5,7}, C = {2,4,6,8}, find A n B¹ u C¹.

B '  = { 2, 4, 6, 8 }

C' = { 1, 3, 5, 7 }

So

A ∩ B' U C'  =

{ 2, 4, 8 }  U { 1, 3, 5, 7 }  =

{1, 2, 3, 4, 5, 7, 8 }

Question 13 : Find the sum of 28th term of the AP 3+10+17+-----

The 28th  term is given by

3 + 7(27)   =  192

So.....the sum of the first 28 terms is  

(first term + last term)(number of terms) / 2  =

(3 + 192) (28)  / 2  =

(195) * (14)  =

2730

Question 9 : Given that A{prime number less than 20}, B {even numbers less than 15}, C {Multiples of 4 less than 15} then AuBnC is

A  =  { 2, 3, 5, 7, 11, 13, 17 , 19 }

B =  { 2, 4, 6 , 8 , 10, 12, 14 }

C =  { 4, 8, 12 }

So  A U B ∩ C  

{ 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13 14, 17, 19}  ∩ { 4, 8, 12}   =

{ 4, 8, 12 }

Question 8 : Determine the value of x and y simultaneously given that x + y = 10 and xy = 21

x + y  = 10     subtract x from both sides

y  = 10 - x  

Sub this into the other equation

x ( 10 - x)  =  21

10x - x^2  =  21         rearrange as

x^2 - 10x  +  21   =  0   factor

(x - 7) ( x - 3)  =  0

Setting each factor to 0   and solving for x  we have that

x = 7   and   x  = 3

Question 7 : The sum of eight times a number and 15 is less than thrice the same number minus 10, find the number.

8x + 15  <  3x - 10        add 10 to both sides, subtract 8x from both sides

25 < -5x            divide both sides by -5  and reverse the inequality sign

-5 > x     →    x < -5

Question 6 : If A= {3,5,7,9} B = {2,3,4,8,7,9} then AuB is
 

A U B    =  { 2,3,4,5,7,8, 9 }

Question 5 : Using factorization method solve for x, 5x²+ 12x +7 = 0

(5x  + 7) ( x + 1)   = 0

Setting both factors to 0  and solving for x we have that

x = -7/5   =   - 1  2/5        or  x   =  -1