CPhill

a + b  = -7   ⇒   b  = -7  - a    (1)

ab  = -7    (2)

Sub  (1)  into (2)

a ( -7 - a)   = -7  

-7a - a^2  =  -7       mutiply through  by  -1

a^2  + 7a   =   7        complete the square  on  a

a^2  + 7a  +  49/4   = 7 +  49/4          factor the left  side   and simplify the  right

(a + 7/2)^2   =  77/4          take the  positive  root

a + 7/2  =  sqrt (77) / 2

a =  sqrt (77)/2   -  7/2

b =  -7  - a  =   -7   - ( sqrt (77/2)  -  7/2)   =       -sqrt (77) / 2  - 7/2

Call the side of the  octagon, S

Area of  octagon  = 2(1 + sqrt (2) ) S^2

Blue  area  = 2 (1/2)  (S/sqrt2)^2    +  (S/sqrt (2))*S  = 

S^2 / 2 +  S^2 / sqrt (2)   =

( 1/2 + 1/sqrt (2)) S^2  =

(1/2)  ( 1 + sqrt (2) ) S^2

Blue Area  / Total Area =    (1/2)  / (2)   = 1/4

First one 

BC   = HK

-3x + 11    =  87 + x

11 - 87 =   4x

-76   = 4x

x   = -19

So  GH  = -2x + 41   =   -2(-19)  + 41  =  79

Second  one

EF  =   XZ

x - 7 = 39  - x

2x  =  46

x  = 23

EG  = 5 + x   =   5 + 23  =  28

Last one

BD  = XZ

2n - 4   =  n + 4

n  =   8

ZW  =3n  -10   = 3(8)   - 10    =    14

4. Linda drove 50 miles from San Jose to San Francisco in 90 minutes. For the first 30 minutes, without much traffic, her average speed was 60 miles an hour. In the second 30 minutes, due to a traffic accident along US 101, her average speed dropped to 35 miles an hour. She was stuck in traffic for the last 30 minutes near San Francisco.What was her average speed, in miles per hour, during the last 30 minutes?

Trick question.....she didn't move  in the  last  30 min.....avg speed during this time  =   0  mph

3. On average customers order one pizza every 3 minutes and 20 seconds from Mathni-fient Pizza, and today (due to a mishap) they only have enough raw materials tomake 45 pizzas. They started selling pizza at 05:10pm. At what time does Math-nificent expect to sell out all pizzas?Please write the answer in the 12-hour hh:mm format. For example,9:30pm would be 09:30.

3 min +  20 sec =    3 + 1/3 min =     10/3  min    for  one pizza

So  45  pizzas take        45 * 10 /3 =  150 min  =    2 hrs 30   min

So

5:10  PM    +   2hrs 30  min  =       7: 40  PM   when they sell out

1. Sophia and Melody were biking together. along a straight bikeway from two positions.At one point Sophia stopped to rest, while Melody continued to bike. Sophia resumed biking again but at a faster pace of 22 miles per hour, while Melody continued at asteady pace of 15 miles per hour to allow Sophia to catch up. Sophia finally caughtup with Melody after 6 minutes. How far behind (in miles) was Sophia when she resumed biking? Please express the answer in decimal points

Notice  that the difference  in rates =  (22  - 15)   = 7 mph =  Sophia's  effective rate

6 min =     1/10 hr

So        rate  * time  = distance

7 (1/10)  =     7/10      =    .7   miles behind 

2. One mile is 5280 feet, and 3 feet is one yard. A professional soccer player runs upto 7 miles in a 90-minute match. It averages to how many yards every 9 seconds?Please round the answer to the nearest yard.

No. of yards run  =        5280 / 3  *  7   =  12320 yards

90 min  =1.5 hrs

No. of seconds  in 1.5  hrs  =   1.5  *  60  min  * 60sec  =  5400 sec

Yds run per second =  12320 /  5400  = 308/135 yds

Yds run in 9 sec =     (308/ 135) * 9    ≈  21 yds in 9 sec

Angle A = Angle B

56  - 3a =   8a + 1    rearrange as

56 -1  = 8a + 3a

55  = 11a

Dived both sides  by  11

5  =a

So angle  B  =8(5) + 1 =   41° 

We know that angle D  =107°

Therefore, angle C   = 180   - 107    - 41   =   32°

f(x)  =(2/3)x^3  -1

y= (2/3)x^3   - 1

get x by itself...."swap"  x and y

add 1 to both sides

y + 1  = (2/3)x^3     mutiply both sides by    3/2

(3/2)y +3/2   = x^3           take the  cbe root of both sides

∛ [ (3y + 3)  / 2  ]   =  x

Inside the radical, nutiply numerator, denominator  by 4

∛ [ (12y + 12)  / 8  ]   = x

∛ (12y + 12)  / 2      =  x      "sap  x and y

∛ (12x + 12)   / 2   =  y   =   the nverse 

Let G  be located on AC  such that  FG is   parallel to   CD

angle GFB  = angle CEB

BF  = BE

And angle CBE  = angle  FBG

So by ASA  triangle FBG  is congruent  to triangle EBC

So  BG  = BC

But since    AF   =  AD   then   GA  also =  GC

But  BC  +  BG   =    GC

And since BG  = BC  then      2BC  =  GC

So 2BC also   =  GA

And  AC =  GC + GA     =    2BC  + 2BC   =  4BC

And AB =   4BC  - BC   = 3BC

So

AB : BC    =   3 : 1            { just as the  guest found !!! }

We just  have a right triangle

The  hypotenuse = 34

One leg =  30

Height  = the other leg   =    sqrt ( 34^2  - 30^2)  =  sqrt  ( 256)   =    16  in