CPhill

Let the number of girls  = G

Then, the number of boys =  G + 124

So we have this

[ G + 124 ]/ G  =  11 / 9        cross-multiply

9 G + 1116 = 11G            subtract 9G from both sides

1116  =  2G                   divide both sides by 2

558  =  number of girls

And   558 + 124  = 682  =  number of boys

And     682 / 558  =  11/9

So....there are  682 + 558  =  1240  total students

This is not a circle....it is an ellipse

The center is (5,1).....

The major axis  is vertical.....the  vertices along this axis are (5, 1 + √32)  and (5, 1 - √32)

The minor axis is horizontal.......the vertices along this axis are ( 5 + √8, 1)  and ( 5 - √8, 1)

Here's the graph :   https://www.desmos.com/calculator/i8bwbkv672

The other three angles will  measure 72° , 108°  and 108°

The vertical angle across from the 72° angle  has the same measure and the other two angles will be supplementary to 72°, i.e., 108°

Here's the second one [ I think ]

Let the width of the top left rectangle = a  and its height  = b

So.....ab = 32   ...so its width is  a = 32/b

Let the height of the bottom right rectangle = d  and its width = 45/d

And d = 11 - b

Now....if we had a "completed" rectangle its area would be  14 * 11  = 154

And 14 =  width of the top left rectangle  + width of bottom right rectangle

So we have

(32/b +  45/d) (11) = 154     sub for d

(32/b + 45/(11-b))   = 14     simplify

32/b (11-b) + 45  = 14 (11 - b)

352/b - 32 + 45  =  154 - 14b

352/b + 13 = 154 - 14b

352/b - 141 + 14b = 0

14b^2 - 141b + 352  = 0   ⇒  b= 5.5  or b  = 32/7

If b = 5.5   then a  = 32/5.5 ≈ 5.81

If b = 32/7  then a =  32 / [32/7]  = 7    which is too large 

So b = 5.5    

And d = 11- b =  11- 5.5  = 5.5

a = 32/5.5   = 64/11

ad =   64/ 11 * 5.5   =   64 * (5.5 / 11)  =  64 * 1/2  = 32

You just need to use the associated inverse functions

Example :

arcsin ( 0.4568)  ≈  27.18°

First one :

10x  +  5y  ≤ 500

Second one :

Amount in inches  = 10  +  2x

-2x - 11y  = 5         add 2x to both sides

-11y  =  2x  + 5     divide everything by -11

y  =  [ -2 / 11 ] x  - 5 / 11           

slope = -2/11          y intercept =  -5/11

Your choice is correct, NSS

Look at it again......doesn't it cross the x axis at  -3, 0 and 4   ???

Your first answer is correct......

X intercepts.....look at this one again, NSS......doesn't the function cross the x axis in three places ???

f(-3)   =     abs [ 2(3) - 1 ]  - 5   =  abs [ 6 - 1]  - 5   = abs [5]  - 5  = 5 - 5   = 0