CPhill

3. The coordinate of the rectangle are (-8,2) (0,4) (1,0) (-7,-2). What is the perimeter of the rectangle to the nearest tenth of a unit? 

(-8,2) = A

(0,4) =B

(1,0)= C

(-7,-2) = D

AB  =  √ [(0+ 8)^2 + (4 -2)^2  ]  = √ [64 + 4 ] = √ 68  = 2√ 17

BC  =  √ [(1- 0)^2 + (4 -0)^2  ]  = √ [1 + 16 ] = √ √ 17

Perimeter  = 2 ( AB + BC)  =  2( 2√ 17  + √ 17 )  = 2 (3√ 17)  = 6√ 17  ≈  24.7  units

2. What is the area of the triangle whose vertices are (4,-6) (9,-6), and (6,-2)

A  = (4,-6)

B =  (9,-6)

C  = (6,-2)

Call AB  the base  = 5 units

The height  = 4 units

Area  = (1/2) B * H  =  (1/2)5 * 4   =  10 units^2

(nC4) = 5(nC3)     we have

n! / [ (n − 4)! 4! ]   =  5  n! / [ (n − 3)! 3! ]    implies that

5 [ [ (n − 4)! 4! ]  =   [ (n − 3)! 3! ]

5 * 4!  * ( n −4)!  = (n − 3)! 3!      rearrange and note that     →    [5 * 4!   = 5!]

5! / 3!   = (n − 3)!  / ( n − 4)!

120/6  = n −  3

20  = n − 3

23  = n

Check

(23C4)   =  8855

5 (23C3)  =  8855

3ⁿ  = 5     log each side

log3ⁿ  = log 5      and we can write

n * log 3  = log 5    divide both sides by log 3

n  = log 5 / log 3  ≈    1.465

1. Addison currently has an account balance of $1,737.83. She opened the account 11 years ago with a deposit of $1,334.62. If the interest compounds semiannually, what is the interest rate on the account?

We have

1737.83  =  1334.62( 1 + R/2)^(11 *2)

1737.83  =  1334.62( 1 + R/2)^(22)       divide both sides by   1334.62

[1737.83 / 1334.62]  = ( 1 + R/2)^(22)    take the 22nd root of both sides 

[1737.83 / 1334.62]^(1/22)  = 1 + R/2    subtract 1 from both sides

[1737.83 / 1334.62]^(1/22) −  1  = R/2      multiply both sides by 2

2 ( [1737.83 / 1334.62]^(1/22) −  1]  =  R ≈  0.0241437  ≈  2.41%

x^2 + 16x  - 225 = 0           factor

(x + 25) (x  − 9 )  =  0

Set each factor to 0

x + 25  = 0  →  x  = − 25          or            x  −  9  = 0  →   x  = 9

(d) is correct

Every time x changes by a positive 1,  y  changes by  positive 2  = rate of change of f(x) is 2

So......we have the points  (3, −10)  (4, − 8) (5, −6) (6, −4)

( 1 + 2 + 4 + 16)^2  =

(7 + 16)^2 

23^2  =

529

P(3 girls)   = C(5,3)(1/2)^5  = 5/16

P(4 girls)  = C(5,4)(1/2)^5  = 5/32

P(5 girls)= C(5,5)(1/2)^5  = 1/32

So  P (3 or more girls)  =  5/16 + 5/32  + 1/32  =   10/32 + 5/32 + 1/32  = 16/32  = 1/2

Just as  NinjaA found.....!!!!!