3. in the diagram below of right triangle acb, altitudb find the length of cd in simplest radical form4,

ACB, ACD and DCB are all right triangles. We can then represent the relationships of their legs through the Pythagorean theorem. 

For triangle ACB:
7^2=(AC)^2+(BC)^2     (1)

For triangle ACD:
(AC)^2=3^2+(CD)^2     (2)

For triangle DCB:
(BC)^2=(CD)^2+4^2     (3)

To make things simpler, we let
(AC)=x
(BC)=y
(CD)=z

Hence we have:
49=x^2+y^2     (1)
y^2=z^2+16     (2)
x^2=9+z^2       (3)

To solve for the unknown c, let us first substitute equation (2) in (1)
49=x^2+z^2+16
33=x^2+z^2     (4)

Then, we can substitute equation (3) in (4)
33=9+z^2+z^2
24=2z^2
z^2=12
z=2sqrt(3)

Thus, the length of z or (CD) is 2sqrt(3) in simplest radical form.

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Ok here we go ..there are plenty of ways to solve such math problems but we will go for the smartest and easiest ..5x+2y=7  -2x+6y=9we rearrange them into the following ..by multiplying the 1st equation by 2 it becomes 10x + 4y = 14we rearrange it and so it becomes 10x = 14 - 4yas for the second equation we multiply it by 5 and rearrange it so it becomes as to the following ..-10x + 30y = 45rearranging so 10x = 30y -45now 10x equals both 14 - 4y and 30y -45so   14 - 4y = 30y -4531 = 26yy= 31/26 = 1.19 or around 1.2so by now we can calculate x easily as  -2x+6y=9so 2x = 6y -9 = 6 * 31/26 - 9 = -1.84  then x = - 0.92 or around -0.9best luck!