CPhill

M =  (3, 5)      N  = (9,2)   L  =  (-3,2)

Distance from  M to N  =  sqrt  [ (9 - 3)^2 + ( 5 - 2)^2 ]  = sqrt [ 36 + 9 ] = sqrt (45 )

Because of symmetry.....the distance from M to L  is the same

Distance from  L to N  =  9 - (-3)  = 12

So....the perimter is  2sqrt (45) + 12   ≈  25 units  (to the nnearest unit )

4.

C(60, 3)                34220              6844

________    =      ______   =      ______

C (15, 3)                 455                 91

5.  The otal ways that voters can choose judges  is:

  C(6,0) + C(6,1) + C(6,2) + C(6,3) + C(6,4)  =   57  ways

1)Sarah has an average of 92.5 for her 3 sciences tests. What does she need to make on her 4th test to get a 94% average?

This is easy....she needs  94 (4)  =   376 total points

So far....she has  92.5 (3)  =  277.5 points

So...she needs   376 - 277.5  = 98.5 points on the 4th test

2) The Pep Club is selling flower arrangements with a choice of 4 different kinds of flower, 3 kinds of greenery, and with or without babies breath. How many different flower arrangements do they offer?

I'm taking a guess as to what is meant here, Manuel...but...I believe the answer is  4 * 3 * 2  = 24 diferent arrangements

3)The athletic director has 6 trophies won by school teams this year, but only enough space in the trophy case to display 3 at a time. How many different ways can he display the trophies if order is important?

If order is important we have an arrangement in each possible set....this indicates a permutation...so we want to choose any 3 of the 6 trophies ans pay attention to their arrangement...so the answer  is:

P(6,3)   =  120  ways

h(x)  =  - ( x+ 1) ( x - 7)   simpliy

- (x^2 - 6x - 7)  =

-x^2 + 6x + 7

In the form -x^2 + bx + c     the number of seconds to reach ax height  is given by :

-b / (2 * -1)   ...so we have

-6 / ( 2 * -1)  =   - 6 / -2   =   3 seconds

This graph confirms this  : https://www.desmos.com/calculator/x2ghsrm5tb

No minutes  or miles  show  up    .....    

f(x)  =  -x^2 + 8x - 15

f(x)  = -x^2 + 2x - 3 

The x value of the vertex of the first function is  -8 / (2 * -1)  = 4

And the max  is  -(4)^2 + 8(4) - 15  =  1

The x value of the vertex  of the second function is  -2 / (2 * -1) = 1

And the max is   - (1)^2 + 2(1) - 3  =  - 2

So  Function  1  has the greater max

\( (3+\sqrt{2},5)$ and $(4,7)\)

\( (6-\sqrt{2},3)$ and $(3,5)\)

Midpoint of the 1st segment  = ( [3 + √2 + 4']/2 , [7 + 5]/2 ) =  ( [7 + √2] / 2 , 6)

Midpoint of the second segment  = ( [ 6 - √2+ 3] / 2 , [5 + 3] / 2 ) =  ( [ 9 - √2] / 2 , 4 )

The midpoint of these two segments is  (  [ (7 + 9) / 2)/2 , [ 6 + 4 ]/ 2 )  =

(16/4, 10/2) = 

(  4,  5 )

The area of the base is composed of six congruent  isosceles triangles with sides of 14cm  and an included angle of 60°

So....the area   =

6 (1/2) (14)^2*sin (60)  =

3 * 196 * √3 / 2  =

(3/2) * 196 * √3  =

294√3  cm ^2

Call Wilma's speed,  W

So when Wilma runs 100m, Betty runs 100 - 10 = 90m

So...Betty's speed is 9/10 of Wilma's =  (9/10)W

Note that Wilma rums 110 m  and her rate  = W

Call the distance that  Betty runs, D,   and her rate is  (9/10)W

So ...D /R  = Time

so....equating times, we have

110 / W  =  D / [(9/10)W]         multiply both sides by [ (9/10)W ]

110 (9/10)W / W  =  D

110 (9/10)  = D

[(110/ 10) * 9]   =  D

11 * 9     = D

99  = D

So....Betty  runs 99m  in the same time that Betty runs 110m....so....Betty is 1  m   from the finish line when Wilma finishes the 110m

B + D   =  180    ....so...

[ 2x + 3 ]   +  [ 4x + 3  ] =  180

6x + 6  =  180

6x  =  174      divide both sides by 6

x  = 29

So 

C  =  2(29)  + 1   =   59°