<h3>
Answer:</h3>
- left picture (bottom expression): -cot(x)
- right picture (top expression): tan(x)
<h3>
Step-by-step explanation:</h3>
A graphing calculator can show you a graph of each expression, which you can compare to the offered choices.
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You can make use of the relations ...
... sin(a)+sin(b) = 2sin((a+b)/2)cos((a-b)/2)
... cos(a)+cos(b) = 2cos((a+b)/2)cos((a-b)/2)
... cos(a)-cos(b) = -2sin((a+b)/2)sin((a-b)/2)
Then you have ...
and ...
Answer:
-2x + 6 
8x or 5x + 3 < 9
Step-by-step explanation:
-2x + 6 8x -> x
3/5
5x + 3 < 9 -> x < 6/5
Answer:
The Answer to 17 1/3 x 8 is 138.67
There is not enough context to answer the second question.
((There has been a malfunction or this users account may have been deleted)) (deleted) (user)
Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
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<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
