CPhill

12[(2/3)^2 ÷ 1/3 - 5/6 × 1/2] =

12 [ (4/9 ) ÷ (1/3) - (5/6) * (1/2) ]  =

12 [ (4/9) * (3/1) - (5/6) * (1/2) ] =

12 [ 12/9  - 5/12] =

12 [ (12)(12) - (5)(9) ] / 108  =

(12/108) [ 144 - 45] =

(1/9) [ 99] =

99/9 =

11

e^(8x + 8)  = 2    take the ln of oth sides

ln e^(8x + 8)  = ln (2)   and we can write....

(8x + 8) * ln e  = ln (2)     and ln e  = 1, so we can forget this....and we have

8x + 8   =  ln (2)   subtract 8 from both sides

8x = ln (2) - 8    divide both sides by 8

x  = [ ln (2) - 8 ] / 8   ≈    - 0.913

Thanks , hectictar.......you probably did a little more than you were obligated to, here.....

8, 3, 2, 22    ......34

One possibility....

8/2 * 3  + 22  =

4 * 3  +  22   =

12 + 22  =

34

We're looking for the secant of an angle whose sin = 4/7

Sec =  r /x    and x  =  sqrt (7^2 - 4^2)   = sqrt (49 - 16)  = sqrt (33)

So.....sec  (theta)   = 7 / sqrt(33)   =  (7/33)*sqrt(33)

[Since the sine inverse only has a range of -pi/2 to pi/2, theta must fall in either the 1st or 4th quadrant......so......the secant is positive in both of these ]

As long as TM is parallel to OR

ST/TO  = SM/MR    so

2 /4   = x / 10 

1/2  = x /10       so.....x must be 5

2:5:9   means that there are 16 equal parts

And green pepper is 2/16  =  1/8 of this

So    (1/8) * 36  =  36/8 cups  = 9/2 cups  = 4.5 cups

Their vertical angles are equal  and  both have another equal angle......so.....similar by AA similarity

Triangle HTM  is similar to triangle MTA ....so....

HT/TM  = TM/TA     and TA  = x   ....so...

12/5 = 5/x

12x = 25

x = 25/12

And

HT/HM  = MT/ MA      and MA  = y.....so....

12/13  = 5/y     cross-multiply

12y = 13*5

12y = 65

y = 65 / 12

1. Don't know how to solve this.......maybe someone else knows....

2. m<DBC =m<DCB - m<BDC  =  90 - 35   = 55

3.  We can use the fact that the procucts of chord segments in a circle are equal....so

4 * 6  = 3 * n

24 = 3n   divide both sides by 3

8 = n

4. Based on my answer to 3......can you do this one???....if,not....let me know....

5. BC is not a tangent line because m<ABC  less than  90dg

To see this....note that the other two angles of triangle ABC =    48 + 47  =  95

So  m<ABC  =   180  - 95   =  85.....and remember, if BC is tangent, then m<ABC  must = 90