CPhill

4.

x + 2               x + 4   

____     ÷       _________           factor the denominator on the right

x  - 1              x^2 +4x - 5

x + 2              x + 4

____   ÷         __________         notice that x  cannot be  1  or  -5

x - 1              (x - 1) ( x + 5)  

So....we actually have

x + 2             (x - 1) (x + 5)

_____    x   ____________     =

x  -  1              x + 4

( x + 2) ( x - 1) ( x - 5)

__________________          the  (x -1)'s   cancel and we're left with

  (x - 1) ( x + 4)

( x + 2)( x - 5)

___________       Notice that we have another restriction......x cannot  = -4

      x +  4

So....the final answer is in red...and the restrictions are that x  cannot equal  1,-5, -4

So.....last answer

Remember that

sin x  =  cos(90 - x)

So   cos (90 - x)   =  0.84

1.   Notice, NSS...that p  cannot  =  - 4  because the denominator would be  =   0

Factoring   p^2  - 4p  - 32   we get  ( p + 4) ( p - 8)

This would give us

[ (p + 4) ( p - 8) ]  / (p + 4)     the (p+4) 's   cancel

So we're left with   p - 8

So...the second answer is correct

2.   [ q^2  + 11q   + 24 ]  / [ q^2 - 5q - 24 ]      factor top/bottom

[ (q + 8) (q + 3) ]  / [ (q - 8) (q + 3) ]

Notice that   q cannot equal  either 8 or -3 because these would make the original denominator = 0

Now.... the  (q + 8)   factors "cancel on  top/botom   and we're left with  

(q +8 ) / ( q - 8)

So....the thiird answer is correct

Here's one way of doing this

Cos (90 - x)  =  √3/2

Notice that  

Cos (30°)    = √3/2

So.....x must be  = 60°

So.....sin (60°)  = √3 / 2    !!!!!

Does that make sense, RP???

We want to choose 1 girl out of the 24 and 1 boy out of 12

So.....the total number of ways to do this is :

C(24,1)  * C(12, 1)  =   24 * 12  =    288 ways

Good job, RP and tertre....!!!!!

Notice RP, that p, q, r, s, t, u  are all equal to 45°.....so their sines and cosines are all equal....so all the statements are true  !!!

Volume  =  (4/3) pi  (diameter/2)^3  =

(4/3) (3.14) ( 8/2)^3

(4/3)(3.14)(4)^3

(4/3)(3.14) *64 =  

267.95 in^3

The triangle's new area  =

Old Area * (Scale Factor)^2   =

30  * (3)^2  =

30 * 9  =

270 cm^2

We want to solve this

Principal + Interest  = Principal + Interest

100 + 100 (.10)D  =  150 + 150(.05)D        

Where D  is the number of days that will equalize the debt

Subtract 100 from both sides  and simplify

10D   =  50  + 7.5D         subtract  7.5D  from both sides

2.5D  =  50     divide both sides by 2.5

D =  20 days

3. 

The area, A, of a circle's sector be found as

A  =  (1/2) r^2  (theta in rads)  

A  =  (1/2) (5^2) (pi/4)

A  = (25/8)pi  cm^2   =  9.8 cm^2