CPhill

Nice, Ninja.....!!!!!

Very nice, Isabelle.....!!!!

See your earlier post for the answers

Use the arctangent here

arctan ( −1.5)   +  180°  = x   =    −56.31°  + 180 =  123.69°

Hard to see this but I think we have 

a)    g(x)  = ( x + 2)^2  + 2

c)   g(−1 )   =  ( −1   + 2) ^2  + 2   =   1^2   + 2   =  3

Here's the graph  :  https://www.desmos.com/calculator/cacudo2xos

3. A rhombus has an area of 40 cm^2 and adjacent angles of 50 degrees and 130 degrees. find the length of the side of the rhombus.

We can use this :

(1/2) Area  =  (1/2) side^2  sin(50°)    multiply by 2 on both sides

Area  =  side^2  sin(50°)

40  = side^2 sin(50°)       divide both sides by sin(50)

40 / sin (50°)   = side^2       take the sq root of both sides

√ [40 / sin (50°) ]   = side ≈    7.226  cm

Looks good. Isabella......they might also want this  [ which is just a matter of semantics]

4x   + 2y  = 200

4. Find the area of a regular pentagon of side 8 cm.

Area  ≈  1.720 * side^2   =  1.720 * [8 cm]^2  =  [1.720 * 64 ] cm^2   ≈  110.08 cm^2

It comes from the following "formula"  for the area of an equilateral triangle

Area =  (1/2) *  side^2  *  sin(60°)       and  sin(60°)  = [√3 / 2 ]

So we have

Area =  (1/2) *  side^2  * [√3 / 2 ]

5. A circle of radius 5 cm is inscribed inside a square as shown. Find the area shaded.

(the radius is not exactly 5 cm in the picture)

Shaded area   =   area of square −  area of circle  =      [10 cm]^2   − pi [5cm]^2  =

100 cm^2   −  25 pi  cm^2   =    [ 100  −  25 pi]  cm^2  ≈  21.46 cm^2