Determine the x-intercept(s) of the rational function: f(x) = (x ^ 2 - 16)/(x ^ 2 - 2x - 3)
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Answer:
Yes lines are intersecting, point of intersection is <4,2,0>.
Step-by-step explanation:
Given parametric equations of line are:
If lines are intersecting then parametric coordinates of (1) are equal to (2)
Considering A and B to find values of t and s
From A
t=4s-3---(D)
Putting in (B)
2(4s-3)=1+s
8s-6=1+s
7s=7
s=1
Then
t=4-3
t=1
If lines are intersecting then these values of s and t must satisfy (C)
2-2(1)=1-1
0=0
This shows lines are intersecting.
At this value of t, (1) becomes
Putting s=1 in (2)
Point of intersection is <4,2,0>.
Given:
The rate of interest on three accounts are 7%, 8%, 9%.
She has twice as much money invested at 8% as she does in 7%.
She has three times as much at 9% as she has at 7%.
Total interest for the year is $150.
To find:
Amount invested on each rate.
Solution:
Let x be the amount invested at 7%. Then,
The amount invested at 8% = 2x
The amount invested at 9% = 3x
Total interest for the year is $150.
Multiply both sides by 100.
Divide both sides by 50.
The amount invested at 7% is .
The amount invested at 8% is
The amount invested at 9% is
Thus, the stockbroker invested $300 at 7%, $600 at 8%, and $900 at 9%.