Answer: Option C
Step-by-step explanation:
If the graph of the function 
represents the transformations made to the graph of 
then, by definition:
If 
the graph moves vertically upwards.
If 
the graph moves vertically down
In this problem we have the function 
and our parent function is 
therefore it is true that 
Therefore the graph of 
is moves vertically upwards by a factor of 5 units.
The answer is the Option C: "The graph of g(x) is the graph of f(x) shifted up 5 units"
Answer is: B
Step-by-step explanation: correct answer is B
b
2
−a
2
Given, acotθ+bcscθ=p
bcotθ+acscθ=q
⇒p
2
−q
2
=(p−q)(p+q)
=[acotθ+bcscθ−bcotθ−acscθ][acotθ+bcscθ+bcotθ+acscθ]
=[cotθ(a−b)−cscθ(a−b)][cotθ(a+b)+cscθ(a+b)]
=(a−b)(cotθ−cscθ)(a+b)(cotθ+cscθ)
=(a
2
−b
2
)(cot
2
θ−csc
2
θ)
=(−1)(a
2
−b
2
)[∵csc
2
θ−cot
2
θ=1]
=(b
2
−a
2
)
Let smaller number be x/2 and the larger number x.
x/2 + x = 81
x/2 + x = 3x/2
3x/2 = 81
3x = 162
x= 54
The smaller number is 54/2= 27 and the larger number is 54.
Answer:
y=[-4]x+[10]
Step-by-step explanation:
For a line to be perpendicular to another it must have the reverse reciprocal of the opposite line, to find the reverse reciprocal you take your slope, flip the numerator and denominator, and multiply it by -1.
The slope 
turns into 
and is then multiplied by -1 to become 
which can be simplified down to: 
Now that we know the slope we need the line to pass through a point, so we will use point slope form:
Substitute in our slope and point values:
Now solve for y:
Then you will find that line 
runs perpendicular to 
and intersects point (2,2).
Answer:
Where's the triangle? Do you have an image?
