Given:
Equation of a line is
To find:
The equation of line in slope intercept form that is parallel to line a and goes through point (24, 6).
Solution:
If a linear equation is , then
In the equation , a=3 and b=-4, thus the slope of the line is
We know that, slope of two parallel lines are same. So, slope of parallel line is
The parallel line passes through (24, 6) and have slope , so the equation of line is
Add 6 on both sides.
Therefore, the equation of parallel line in slope intercept form is .
EXPLANATION
The nth term of the sequence is given by
Where
is the first term and
is the constant difference.
We were given that,
S we just need the common difference to write the nth term.
We can get that from another information given to us.
We were also given that the 4th term is 6. This gives the equation.
We substitute
to obtain
Or
This implies,
We substitute these values into the general formula to obtain,
This gives us,
Hence the nth term of the sequence is,
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If , then .
Let's simplify that.
Distribute with :
Combine the end like terms :
Use identity for :
Combine like terms and :
We are given .
So we have that .
The vertex happens at .
Compare to to determine .
Let's plug it in.
So the coordinate is 5.
Let's find the corresponding coordinate by evaluating our expression named at :
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is where the vertex is .
Let's put into this form.
We are given .
We will need to complete the square.
I like to use the identity .
So If you add something in, you will have to take it out (and vice versa).
So we have in vertex form is:
.
The vertex is (3,-6).
So if we are dealing with the function .
This means we are going to move the vertex of right 2 units to figure out the vertex of which puts us at (3+2,-6)=(5,-6).
The coordinate was not effected here because we were only moving horizontally not up/down.
Answer:
$412.91
Step-by-step explanation:
<u><em>A(t) = P(1+r/n)^nt </em></u>(equation)
A(8) = 300(1+0.04/12)^12(8) (plugging it in)
A(8) = 300(1+0.04/12)^96 (simplifying)
A(8) = 300(1.033)^96 (adding up everything)
A(8) = $412.91 (answer)