CPhill

Slight typo on the first one

7x-6w+4x+6y+5y+4w =

[7x + 4x] + [ 6y+ 5y ] + [ 4w - 6w ]  =

11x  + 11y  - 2w 

Probability of taking two red sweets in succession =

(3/8)  (2/7)  =  6 / 56  =  3 / 28

I think this is correct.....

Shape Q is a dilation of P with a scale factor of 3 shifted to the right by 2 units and up 2 units  

The area as shown is   5cm^2

The area after enlarging by a scale factor of 2 will be :

[ Old area ] * [ Scale factor ] ^2  =

[ 5 cm^2  ]  *  [ 2 ]*2  =

[ 5 cm^2 ] *  4  =  

20 cm ^2

Note, NSS....if we multiply the first equation through by - 3 we get the second one

Any time one equation is a multiple of another....we have infinite solutions !!!

Area  = side ^2    .....so......

√ Area  = side  = √ 479  ≈ 22 ft  [ rounded to the nearest foot ]  

y  =  x/2

This line will  intersect the square at x values  -a  and a

So....the associated y values are

y =  (-a)/2  =  -a/2     and   (a)/2  

So....the perimeter of one of the quadrilaterals =

2a  +  [(a) -  (-a/2)] + [(a) - a/2 ]  +  sqrt  [ ( a - (-a)) ^2 + ( a/2 - (-a/2)^2]  =

2a  + 3a/2  + a/2  +  sqrt  [ 4a^2  + a^2 ]  =

4a  +  a√ 5    dividing this by a  produces  =

4  + √ 5

 (x - 3)^2 + (y - 3)^2 = 6

This is a circle with a center of  (3, 3)    and a radius  = √ 6

I don't know how to prove this but WolframAlpha gives the answer as

{ x , y }  =  ( 2 - √ 2 , 2 + √ 2 )

And   y / x   ≈   [ 2 + √ 2 ]  / [ 2  - √ 2 ]  ≈  5.828

The area of the triangle formed is

(1/2) [ 1/2 ] * [1]  =  1/4  units^2

The area of the square is  2 unirs on each side  =    2^2  =   4 units"2

So....the area of the pentagon is

4 - 1/4 = 

4 - .25  = 

3.75 units^2

Total possible arrangements  =  7!  = 5040

Total ways to choose 4 of the paintings  = C(7,4)  = 35 ways

Total arrangements of any 4  = 4!  =  24  ways

 Probability of Luis scoring 2 touchdowns  =  [ 7 ] / [ 6 + 10 + 7 + 5 ]  =  7/28  =  1 / 4

 Probability of Luis scoring more than 1 touchdown  =  [ 7 + 5 ] / 28  =   12/28 = 3 / 7

Estimated value  =  weighted average  =

[ 6*0 + 10*1 + 7*2  + 5*3 ] /  28  \

[ 10  + 14  + 15 ] / 28  =

[ 39 ] / [28 ]  ≈   1.4  touchdowns