CPhill

Here's 10

2L  + 2W = 20      divide both sides by 2

W + L   = 10    →  W = 10 - L     .....the original area   =  W*L  = [10 - L]L   =  10L - L^2

And we have that

[L + 2 ] * [ W + 3}  = 10L - L^2 + 30

[L + 2] * [ 10 - L + 3]   = 10L - L^2 + 30   simplify

[ L + 2] * [ 13 - L]  = 10L - L^2 + 30

-L^2 + 26 + 13L -2L   = 10L - L^2 + 30

26 + 11L  = 10L + 30       subtract  26 , 10L from both sides

L  = 4 m       and   W  = 10 - L   =  6 m      and these are the original dimensions

Here's 8

L = W + 3

So

2 [ L + W ]   = perimeter

2 [ (W + 3) + W  ]  = 30   simplify....divide both sides by 2

2W + 3  = 15        subtract 3 from both sides

2W   =  12     so W = 6  and L = W + 3 = 9

And area  = L * W    =     9 * 6   = 54  cm^2

Here's 4

L = 3W + 2

And the prerimeter  =  2[L + W]  = 2[ (2W + 2) + W ]    and we have

2 [ (3W + 2) + W ]  = 36   simplify

2 [ 4W + 2 ]   = 36       divide both sides by 2

4W + 2  = 18       subtract  2 from both sides

4W  = 16         divide both sides by  4

W = 4 cm

L= 3(4)) + 2   =  12 + 2   = 14  cm

Here's 2

Call the first side, x

The second side  is  x+ 3

The third side is 3(x + 3)  - 2

And we have

x + [x + 3}  + 3(x + 3)  - 2  = 45     simplify

x + x + 3 + 3x + 9  - 2  = 45

5x + 10   = 45     subtract 10 from both sides

5x = 35     divide both sides by 5

x = 7   cm

And the third side = 3(7 + 3) - 2  = 3(10)  - 2   =  28 cm

The other leg  =   sqrt[ 13^2  - 12^2]  = sqrt [ 25]  =  5

And the area =  (1/2)(12)(5)   = (1/2)(60)  = 30 sq. units

Angle 1 = Angle 4  ........alternating interior angles are equal   [congruent]......

Let x be Jack's age now and y be Jill's age now....and we know that :

y + 3 = 2 [ x + 2]     →   y  =  2x +1      (1)

3x - 9 =  y - 2    →    y = 3x - 7  (2)

Set (1)  = (2)

2x + 1  =  3x - 7       add 7 to both sides, subtract 2x  from both sides]

8 = x       and this is Jack's age now       and Jill's age = 2(8)  + 1   = 17 

a₁₂ = 7(12) + 4 =  88

2.6 * 10^-5 * 0.0000052  =  1.352 x 10^-10

25  = 10 *( log i + 16)   divide both sides by 10

25/10   =  log  i + 16    subtract 16 from both sides

2.5 - 16  = log i

-13.5 = log i   in exponential form, we have

10^(-13.5)  = i   = about  0.00000000000003162  W/cm^2