Slope = (y2 - y1)/(x2 - x1)
Slope = (7-5)/(9-4)
Slope = 2/5
A compass and straightedge are supposed to be part of the required equipment for your class. You are expected to use them here. Your assignment paper should be complete with pencil marks and holes from the compass point. Nobody can do it for you on-line.
Here is a picture of the first one worked. The remaining ones are just like it. The whole assignment should take about 3 minutes, tops.
Term to be added is: + 121/4
t^2 + 11t + 121/4
(t + 11/2) (t + 11/2)
Good.
She wants to pay 20% down:
= 20 / 100 * 840 = 168.
The remainder = 840 - 168 = 672
She wants to pay the remainder in six equal payments = 672 / 6 = 112.
= $112 (B).
The partial fraction expansion takes the form
-6<em>x</em>/((<em>x</em> + 2) (<em>x</em> + 8)) = <em>a</em>/(<em>x</em> + 2) + <em>b</em>/(<em>x</em> + 8)
Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.
Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:
-6<em>x</em> = <em>a</em> (<em>x</em> + 8) + <em>b</em> (<em>x</em> + 2)
Expand the right side and collect terms by powers of <em>x</em> :
-6<em>x</em> = (<em>a</em> + <em>b</em>) <em>x</em> + (8<em>a</em> + 2<em>b</em>)
It follows that
<em>a</em> + <em>b</em> = -6 and 8<em>a</em> + 2<em>b</em> = 0
==> <em>a</em> = -2 and <em>b</em> = 8
So we end up with
-6<em>x</em>/((<em>x</em> + 2) (<em>x</em> + 8)) = -2/(<em>x</em> + 2) + 8/(<em>x</em> + 8)
