CPhill

Let the  number  of dimes  =  D

Then the number  of  nickels is  25 - D

So   we  have this

value of a nickel * number  +  value  of a dime * number  = toal value

.05 (25 - D)  +  .10 (D)   = 1.65     simplify

1.25 - .05D  + .10D  = 1.65

1.25 + .05D  = 1.65     subtract 1.25 from both sides

.05D  = .40         divide both sides  by .05

D = 8 = number of dimes

And  25 - 8  =  17   nickels

We  have  this

tan (50°)  =  x  / 40

40 * tan (50°)  = x

The  height of the  flagpole  =

5.5   +   x   =

5.5  +  40 * tan (50°)    ≈   53.2  ft 

We can solve  this  using the Law of Sines

We have   that

x / sin (73°)  = 29.6 / sin (33°)      multiply both sides by  sin (73°)

x =  29.6*sin (73°)  / sin (33°)  ≈  51.97 = 52 ft

If  f((0)  =  47.....then  the  constant term  is  47

If f(1)  =   32......then the  sum of the coefficients +  the  constant term    = 32

This  implies that

sum of coefficients  + constant term =   32

sum of coefficients  + 47  =  32         subtract  47  from both sides

sum of the coefficients    =    -15

Last one

Area =  (1/2)  (XZ)(YZ)  * sin ( Z)   =  (1/2) (9)(4) sin (58°)  =  18 * sin (58°)  ≈  15.3  units^2

Second one

Area of sector   =  (1/2) r^2  ( theta in rads)   =  (1/2) (5^2) (5pi/12)      =

125 pi

_____    in^2

  24

As before  using Heron's formula

s =   [7 + 7 + 6 ]  /2  =  20 /2  =10

Area  =   √[10 * (10 - 7) (10 - 7) (10- 6)  ]  = √[10 * 3 * 3 * 4  ]  = √ 360  = √ [36 * 10 ] = 

6√10  units^2

We  have a right triangle  with legs of   10  and 24

To find the remaining side  ( the side opposite the right angle = the hypotenuse )  we  have that

hypotenuse  =  √  [ ( leg 1) ^2   + ( leg 2) ^2 ]  = √ [10^2 + 24^2 ] = √ [100 + 576 ]  =

√ [ 676 ]  = 

26

Second one

One  equation  is

a / 3  = 5 / 8

Another one  is just a variation of this

a / 5 =  3 / 8

First one ....not possible

All the   sides of the smaller figure  would  have to be  1/2  the length of the corresponding sides of the larger figure

But  note  that    AE / VZ  =  10 /12  =  5 /6

So.....we cannot dilate  the first figure  to get the second