Graph the absolute value by using the vertex and a few selected points
Point One: X= -1, Y= -8
Point Two: X= 0, Y= -2
Point Three: X= 1, Y= 4
Point Four: X= 2, Y= -2
Point Five: X= 3, Y= -8
The graph should look something like a mountain or an upside down V
Let A( t , f( t ) ) be the point(s) at which the graph of the function has a horizontal tangent => f ' ( t ) = 0.
But, f ' ( x ) = [ ( x^2 ) ' * ( x - 1 ) - ( x^2 ) * ( x - 1 )' ] / ( x - 1 )^2 =>
f ' ( x ) = [ 2x( x - 1 ) - ( x^2 ) * 1 ] / ( x - 1 )^2 => f ' ( x ) = ( x^2 - 2x ) / ( x - 1 )^2;
f ' ( t ) = 0 <=> t^2 - 2t = 0 <=> t * ( t - 2 ) = 0 <=> t = 0 or t = 2 => f ( 0 ) = 0; f ( 2 ) = 4 => A 1 ( 0 , 0 ) and A 2 ( 2 , 4 ).
Since we know a triangle only has 180 degrees we can say:
99+3x+x+5=180
Then we can solve for x:
4x+104=180
4x=76
x=19
When Sam is 13 his mother will be 39 which is 3 times as old as he is. So Sam's mother will be 3 times as old as Sam will be in 11 years. (Your answer is 11 years.)
Answer:
6 possible integers
Step-by-step explanation:
Given
A decreasing geometric sequence
Required
Determine the possible integer values of m
Assume the first term of the sequence to be positive integer x;
The next sequence will be 
The next will be; 
The nth term will be 
For each of the successive terms to be less than the previous term;
then 
must be a proper fraction;
This implies that:
<em>Where 7 is the denominator</em>
<em>The sets of </em><em> is </em>
<em> and their are 6 items in this set</em>
<em>Hence, there are 6 possible integer</em>
