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Break it upas shown.....   3 .rectangles       area =  l x w

    triangle area  = 1/2  b * h       = 1/2 (7)(2)  

Area of  sector  AOB  =   pi (8)^2  (90/360)  =  16pi

Atea of triangle AOB    =  (1/2) (8)^2   =  32

Purple area =   16pi  - 32   =  16 (pi - 2)  units^2

The answer is 27!

So glad I got it in within a minute it is posted!

Hope this helped,

Math Whiz

oops, I solved for Mary's.  Jolie's would be 100.0% – 37.5%  =  62.5%  

_.

 ( pi r^2   of large basin  -    pi r^2  of smaller basin  ) *  3 ft  =     ........... pi  ft³

^{NOTE :}   r = 1/2 of the diameter

23a

Let   y  be  the  total  number  at the  dance who AREN'T  freshman...let x be the number of  freshmen

So...initially

x  / ( x + y)  =    .40      cross-multiply

x = .40x +  .40y

x - .40x  =.40y

.60x  = .40y

y  = (3/2)x

After  15  more freshmen arrive, we  have  that

(x + 15)  / ( x +  (3/2)x  + 15)  =  .52

(x + 15) / ( 5/2 x  + 15)  = .52     cross-multiply

x + 15  =  .52 ( 5/2x  + 15)

x + 15 =  1.3x  + 7.8

1.3x - x  =  15 - 7.8

,3x  =  7.2

3x  = 72

x = 24 =  number of original freshmen

24(3/2)  = 36  = number not freshmen

Proof

Initially  there were  24  + (3/2)24)  = 60 students at the  dance

(24) / 60   = ,40  = 40%

After 15 more freshmen arrive.....there are  60 + 15  =  75 students

(24 + 15)  / ( 60 + 15)  =    39 / 75   =  .52 = 52%

One base rectangle    6 x 5 = 30 cm²

      PLUS

triangle area = 1/2  base * height   =   1/2 *5 * 4   cm²

 40 is 120% of what number?    

Call the number x.  Thus,     (1.20)(x)  =  40  

                                                         x  =  40/1.20  

                                                         x  =  33.333 • • •   

_.

Complementary means they sum to 90 degrees

8x+5       +         3x+8 = 90

11x           + 13             = 90

11x = 77

x = 7    degrees

5 out of 8 squares are shaded     5/8 = .625     which means   62.5 % is shaded

From a previous post:

https://web2.0calc.com/questions/i-am-following-ep-s-suggestion#r1

they add to 180 ( supplenetary)

2x+3      +   x-6     =     180

3x = 183

x = 61      now you can compute the angles   

20.  Mary has 40% fewer marbles than Jolie. If they combine all their marbles in a single bag, what percent of the marbles in the bag are Jolie's?     

Say Jolie has 100 marbles.  That means Mary has 60 marbles.  

The total in the bag is 160 marbles, and 60 of them are Mary's. 

60/160 = 0.375  so  37.5% are Mary's  

_.

Thanks so much. If I don't mind asking, do you know how to do the acute one too? 

Let x = CA. By the triangle inequality, \(5-3 . There are  \(\boxed{5}\) integer solutions.

hello there Mr.CPhill i have a humble request after this question I have 2 diagram questions would you pls answer them??

The area of the whole rectangle was 2 x 4 = 8  until you cut that right triangle off the corner. 

The legs of that right triangle are 2 – 1 = 1  and  4 – 2 = 2   

Area of a triangle is (1/2)(base)(height) = (1/2)(1)(2) = 1  

So the area of the shape is 8 – 1  =  7 units²    

_.

x = 72.

Lets split the polygon into a rectangle and a triangle. The rectangle area is 18, as 2 x 9 = 18. Meanwhile, the triangle area would be 4, as the base is 4, 9-5=4, and the height is two. 4-2=2. However, we divide, so the area of the small triangle is 4. The answer is 22. Hope that helped! 

The area is 32*pi - 32.

Lets see. 
First, lets divide the polygon into the upper triangle, and the rectangle below
The rectangle is 60 area, as we know, as 5 x 12 is 60.
The triangle area is 6. We know this because the base is 3, 12-9=3, and the height is 4. 9-5=4. Divide that by 2, and you get 6. So the area is 66. 

Well, I do believe since the Area is equal to base times height divided by two, The base should be 12, because 12 times 8 divided by two is 96. If this is wrong, I am sorry.