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I think I messed up:

Every whole number is a rational number: for example, 3 = 3 1 . So it is rational. Every whole number n can be written as a fraction of integers: n = n 1 . We aren't required to write it that way; we just need to know that it is possible to express every whole number as a fraction of integers, and hence it is rational.

Yes....all whole numbers are rational.....the whole numbers are {0, 1, 2, 3, 4.......}.....and every one of these can be expressed as a rational quantity...Examples :     6 = 12/2   0= 0/4, etc.

CPhill, did you block my answer?

6*{[35-(4+x)]*4}=600 

6* [ (35 - 4 - x) * 4 ] = 600

6* [ (31 - x) * 4  ]  = 600

6* [ 124 - 4x]  = 600

744 - 24x  = 600     rearrange as

744 - 600  = 24x

144  = 24x    divide both sides by 24

6  = x

Hit the "2nd" button......the "atan" key is the inverse tangent

Let Elizabeth's age = x

And Jacob's age =

2x - 12  = 28

Add 12 to both sides

2x = 40

Divide both sides by 2

x = 20   = Elizabeth's age

90x*3+9x*2-139x-70   is not factorable

sqrt(pi) = 1.7724538509055159

Remember to FLIP the greater than/less than sign if you multiply or divide by a negative. So, really, x>2

If it does, then:

\(({\frac{3}{2} + \frac{i\sqrt{5}}{4}})({\frac{3}{2} + \frac{i\sqrt{5}}{4}})\)

Foil it out:

\((\frac{3}{2}\times\frac{3}{2}) + (\frac{3}{2}\times\frac{i\sqrt{5}}{4}) + (\frac{3}{2}\times\frac{i\sqrt{5}}{4}) + (\frac{i\sqrt{5}}{4}\times\frac{i\sqrt{5}}{4})\)

Simplify the multiplication parts:

\(\frac{6}{4} + \frac{3i\sqrt{5}}{4} + \frac{3i\sqrt{5}}{4} - \frac{5}{16}\)

Combine like terms:

\(\frac{24}{16} + \frac{6i\sqrt{5}}{4} - \frac{5}{16}\)

Combine more like terms:

\(\frac{19}{16} + \frac{3i\sqrt{5}}{2}\)

And there you have it. I hope I understood the original question correctly.

\(489.\overline{89}\)

(36)

The height of the triangle is given by 6*sin(35)

So the area = (1/2)b*h    = (1/2)(10)* [6 *sin(35) ]  = about 17.21  square units

(37)

The height of the parallelogram is given by  7*sin (40)

So...the area   = b* h   = 15* [ 7*sin(40) ]   = about 67.5 sq units

First subtract 4 from both sides to get:

-3x<-6

Then divide both sides by negative 3 to get:

x<2

First subtract 132 from both sides to get:

2x+3=48

Then subtract 3 from both sides to get:

2x=45

Then divide both sides by 2 to get:

x=22.5

6+(-6)=0

Because 6 and -6 are oppisites they cancel eachother out

   93.85

-27.5

   66.35

Just line each number up and subtract

Does it look like this?

\(({\frac{3}{2} + \frac{i\sqrt{5}}{4}})^{2}\)

Jacobs age is 28, Elizabeths age is twice more than Jacobs age which is 28 plus 12 which is 42. 42 divided by 2 is 21 and this is the answer, sorry I'm not good at explaining but I hope this helps!

Thanks! 

Geometric mean  = √( 10 * 6)   = √60  = about 7.7 ft

P.S. - notice that the geometric mean makes the ratios  10/ √60   and  √60 / 6    equal  ......check this for yourself....!!!!

2 pie r

Thanks, rarinstraw......here are the "numbers" for 52

x is the shortest side opposite the 30 degree angle  = 7

y ....across from the 60 degree angle will be √3  times as long as this = 7√3

z  ...across from the 90 degree angle will be twice as long as x  = 2*7   = 14

(53)

x will be 1/√3 as long as y =  14/√3     ....z will be twice as long as x = 28/√3

54 is similar

For 55......since the angles opposite p and q are equal, then p and q are also equal

So    q = 1      and the other side, r,  in a 45-45-90  triangle will always be √2 times as long as the equal sides....so r =1 *√2  =√2

56 should be easy

57  - the unknown sides are  1/√2   as long as r .....  so they  equal 16 * 1/√2  = 16/ √2

The area of the new figure is 9 times that of the old.....each dimension - width and length - is 3 times as great, so......3W * 3L  = 9 (W * L)    where (W * L) was the area before dilation