Pythagorean Theorem: a^2 + b^2 = c^2
-A and B are legs of the triangle
-C is the hypotenuse
#1.
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
c = 10
#2.
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
c = 13
#4.
10^2 + 4^2 = c^2
100 + 16 = c^2
116 = c^2
c = 
#5.
15^2 + 9^2 = c^2
225 + 81 = c^2
306 = c^2
c = 
#6.
120^2 + b^2 = 150^2
14400 + b^2 = 22500
b^2 = 8100
b = 90
#7.
144^2 + b^2 = 194^2
20736 + b^2 = 37636
b^2 = 16900
b = 130
Hope this helps!! :)
Answer:
C. The 6th term is positive/negative 80
Step-by-step explanation:
Given
Geometric Progression


Required

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;
To solve the common ratio;
Divide the 7th term by the 5th term; This gives

Divide the numerator and the denominator of the fraction by 40
----- equation 1
Recall that the formula of a GP is

Where n is the nth term
So,


Substitute the above expression in equation 1
becomes


Square root both sides

r = ±
Next, is to solve for the first term;
Using 
By substituting 160 for T5 and ±
for r;
We get


Multiply through by 16



Now, we can easily solve for the 6th term
Recall that the formula of a GP is

Here, n = 6;



r = ±
So,
or 
or 
or 
±80
Hence, the 6th term is positive/negative 80
100 is the correct answer
The slope is 2 please mark brainliest