To start, the equation has to be converted to slope-intercept form, or . Start by subtracting x from both sides;
,
. Switch 4 and -x around to conform to the formula;
. Then divide by 2 to isolate y;
. This is the final equation. Because the slope of a line perpendicular is always the opposite reciprocal (i.e. The opposite reciprocal of 4 is
, the opposite reciprocal of
is 5) the opposite reciprocal of
is 2. So the equation of the line is
, and the answer is A.
Answer:
= 3n + 3
Step-by-step explanation:
The sequence is arithmetic with explicit formula
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
From the recursive formula
a₁ = 6 and d = 3 [ the constant being added to A(n - 1) ] , then
= 6 + 3(n - 1) = 6 + 3n - 3 = 3n + 3
Composing functions means that the input of the outer functions is the output of the inner function.
In fact, you can rewrite the circle notation as
So, we can substitute g(x) with its expression:
And since f(x)=x+5, we simply have to add 5 to its input:
Similarly, we have, substituting f with its expression,
And since g(x)=4x+2, we have to multiply the input by 4 and add 2: