Graph #1: No
Graph #2: Yes
Graph #3: No
Graph #4: No
Graph #5: No
Graph #6: Yes
Reasoning:
The vertical line test is a test that determines wether a graph is a function or a relation. The vertical line test shows that if you construct a vertical line through any point on the graph, then the vertical line should only intercept the graph once for it to be a function.
Answer:
the first one is 8 and 9
the second one is 13 and 14
Step-by-step explanation:
8^2 is equal to the square root of 64 and 9^2 is equal to the square root of 81.
13^2 is equal to the square root of 169 and 14^2 is equal to the square root of 196.
hope this helps and is correct.
is in quadrant I, so 
.
is in quadrant II, so 
.
Recall that for any angle 
,
Then with the conditions determined above, we get
and
Now recall the compound angle formulas:
as well as the definition of tangent:
Then
1. 
2. 
3. 
4. 
5. 
6. 
7. A bit more work required here. Recall the half-angle identities:
Because is in quadrant II, we know that 
is in quadrant I. Specifically, we know 
, so 
. In this quadrant, we have 
, so
8. 
Ab = (7x-6) → b = (7x-6)/a (1)
bc = (12-2x) → b = (12-2x)/c (2)
Since (1) = (2) → (7x-6)/a = (12-2x)/c OR a/c = (7x-6)/(12-2x) (3)
Multiply both numerators of (3) by the SQUARE of their respective denominators;
(a*c²)/c = (7x-6)(12-2x)²/(12-2x)
Now simplify:
ac = (7x-6)(12x-2x) or ac = -14x² + 96x - 72
