Answer:
By comparing the ratios of sides in similar triangles ΔABC and ΔADB,we can say that 
Step-by-step explanation:
Given that ∠ABC=∠ADC, AD=p and DC=q.
Let us take compare Δ ABC and Δ ADB in the attached file , ∠A is common in both triangles
and given ∠ABC=∠ADB=90°
Hence using AA postulate, ΔABC ≈ ΔADB.
Now we will equate respective side ratios in both triangles.

Since we don't know BD , BC let us take first equality and plugin the variables given in respective sides.

Cross multiply

Hence proved.
Answer:
See below
Step-by-step explanation:
3. What are two ways that a vector can be represented?
Considering a vector
in some vector space
we have

This is the component form. I don't like that way. It is probably used in high school, but
is preferable because the inner product on
is defined to be

You can also write it using linear form such as 
4.
For this question, I think you meant
vectors


Once

Considering that the dot product is

and the norm of
is 
and the norm of
is 
Thus,


Answer:
7) x = 5
8) x = 10
Step-by-step explanation:
7) 2x-3=x+2
x=5
8) 4x=2x+20
2x=20
x=10
Answer:
y = 5x+3
Step-by-step explanation:
a general line is represented by the equation:
y = mx + n
a line with m=5, that goes through (-1,-2), should satisfy the equation:
-2 = 5×(-1) + n
this is because any point on the line, satisfies it's equation.
from this we get n = 3, hence our answer