What is the solution to the system of equations?
2 answers:
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Answer:
A
Step-by-step explanation:
We want to solve the equation:
To do so, we can rewrite the equation.
Recall the double-angle for sine:
By substitution:
Distribute:
We can subtract 3cos(x) from both sides:
And factor:
Hence, our answer is A.
*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0, and we cannot divide by 0. Hence, we should subtract and then factor.
(a) The vertices after the reflection in the line x = 5 are F'(4,6) , G'(2,8) , H'(2,3) .
and (b) after translation , the vertices are F''(-1,-3) , G'' (1,-1) , H''(1,-6) .
In the question a triangle FGH with vertices F(6,6) , G(8,8) and H(8,3) is given
Part (a)
the rule for reflection of point (x,y) by the line x = p is
(x,y) → (2×p - x , y)
reflection by the line x = 5 ,
we get
the vertices as
(2×5-6,6) = (4,6)
G'(2×5-8,8) = (2,8)
H'(2×5 - 8 ,3) = (2,3)
Part (b)
the rule of translation is given as (x,y)→ (x - 7, y - 9)
So , the vertices after translation are
F''(6-7 , 6-9) = (-1,-3)
G''(8-7,8-9) = (1,-1)
H''(8-7,3-9) = (1,-6)
Therefore , (a) The vertices after the reflection in the line x = 5 are F'(4,6)
G'(2,8) , H'(2,3) .
and (b) after translation , the vertices are F''(-1,-3) , G'' (1,-1) , H''(1,-6) .
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