CPhill

(1 - 2x^2)^5        

The x^4 term will be

C(5,2)[1]^3 [2x^2]^2  = 10 [1] [ 2x^2]^2  =  [10*4]x^4

So...the coefficient is 40

I'm assuming simple interest here

The interest we earn  is 1440 - 1200  =$240

So

I = Prt        Where P = 1200 and r = .04    {4%}

240  = 1200(.04)t   simplify

240 = 48t     divide both sides by 48

240/48 = t = 5 years 

2.5 cups makes 24 cookies   {2 dozen}

72 is three times as many.

So  3 x 2.5  = 7.5 cups to make 72.

Mathematically, we have

2.5 / 24 = x / 72     cross-multiply

180 = 24x       divide both sides by 24

x = 7.5

s = [7 + 8 + 9] /2  =  24/2 = 12

And using Heron's formula, we have

A = √[12 * (12-7) * (12 - 8) * (12 - 9)] =

√[12 * 5 * 4 * 3] =

√[12 * 5 * 12] =

√[144 * 5 ] =

12√5 sq units

Since one car travels at 118 and one at 103....and the average speed is 100....we might estimate the third car's speed to  be 100 - 18 = about 82 mph

To find the exact speed:

We have

[103 + 118 + Z] / 3 = 100   multiply both sides by 3

103 + 118 + Z = 300   simpify

221 + Z  = 300 subtract 221 from each side

Z = 79 mph

We still wouldn't have at triangle because  a + c = b .....but....by the Triangle Inequality....a + c must be greater than b....

If 5x - 4y = 7  and xy = 6    find  125x^3 - 64y^3

Note   (5x - 4y)^2  = 7^2    →     25x^2 - 40xy  + 16y^2  = 49    →   25x^2  + 16y^2  = 49 + 40xy

So....factoring  125x^3 - 64y^3  ..... we have..

(5x - 4y) (25x^2 + 20xy  + 16y^2) =

(5x -4) ([25x^2 + 16y^2] + 20xy)  =

(7) ([ 49 + 40xy ]+ 20xy) =

(7)(49 + 60xy) =

(7)(49 + 60(6) ) =

(7) (49 + 360 ) =

(7)(409) =

2863 

7 + 6 ln x - 22.6 = 0     simplify

6 ln x - 15.6  =  0          add 15.6 to both sides

6 ln x = 15.6     divide both sides by 6

ln x = 15.6 / 6

So

x =  e^(15.6 / 6)  = about 13.46

No...but some are silly.....