Need help with a few geometry questions !?!?

1. ACB, CDB and ADC are all similar to eachother.

2. 10

3. CD=8, AD=10.666667, AC=13.33333

4. X=2.4

5. X=√10

6. X=√15

Step-by-step explanation:

1. To prove triangles are similar, prove they share at least two angles.

Triangle ACB is similar to triangle CDB because they both share a 90° angle and ∠B.

Triangle ACB is similar to triangle ADC because they both share a 90° angle and ∠A.

Since ACB is similar to both CDB and ADC respectively, CDB is similar to ADC.

2. Use similar triangles to find AB

ACB is similar to CDB

AB/CB=CB/DB

AB/10=10/6

AB=100/6=16.666667

Geometric mean: √(16.66667*6)=10

3.

Find CD using Pythagorus:

10²=6²+CD²

CD²=100-36

CD=√64=8

Use similar triangle ratios to find AD:

CDB is similar to ADC.

CD/DB=AD/DC

8/6=AD/8

AD=8(8/6)=10.6666666667

Find AC using Pythagorus:

AC²=10.66666666667²+8²

AC=√177.7777777778

AC=13.333333333

4. √(40²+30²)=50

30/50=X/40

X=2.4

5. (√35)²=X²+5²

35=X²+25

X=√10

6. √((√10)²-(√6)²=√(10-6)=2

√6/2=X/√10

6/4=X²/10

X²=10(1.5)

X=√15

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of