Bosco

   how do you find the y intercept     

   Substitute zero for x in the equation, then solve it for y.     

   Example:                       y = x – 13     

   set x equal to zero         y = 0 – 13     

                                         y = – 13        <<==  the y-intercept is y = – 13     

   _.     

   The first term of an arithmetic sequence is 2. The sum of the third and the sixth terms is 14. What is the third term?     

   (a₁ + 2d) + (a₁ + 5d)  =  14     

   ( 2 + 2d)  + ( 2 + 5d)  =  14     

                         7d + 4  =  14     

                               7d  =  10     

                                 d  =  10 / 7     

                    2 + 20 / 7  =  34 / 7     

   check answer     

   Does (34 / 7) + (64 / 7)  =  14  ?     

                             98 / 7   =  14  ?     

                                   14  =  14  True     

   _.     

   What is the greatest prime factor of the sum of the arithmetic sequence 1 + 2 + 3?     

   1 + 2 + 3 = 6  The factors of 6 are 1, 2, 3, & 6.  Two prime factors, the greater is 3.     

   _.     

What real value of $t$ produces the smallest value of the quadratic $t^2 -9t - 36 + 13t - 60$?     

                                                                         t² – 9t – 36 + 13t – 60     

collect like terms                                               t² + 4t – 96     

The lowest value will be the vertex, can be     

found by setting the 1st derivitive to zero        2t + 4 = 0   ==>>   t = – 2     

At t = –2, the quadratic equals –100.     

_.     

   All the sides of a triangle are integers.  If the perimeter of the triangle is $3,$     

   then how many different possible triangles are there?     

   Three sides, all integers, total three.  Only one triangle can fit that description.     

   _.     

   The distance from Capital City to Little Village is 5 miles.     

   The distance from Capital City to Mytown is 2 miles.     

   The distance from Mytown to Yourtown is 3 miles.     

   The distance from Little Village to Yourtown is 4 miles.     

   Find the distance from Capital City to Yourtown, in miles.     

   My Town ----- 2 ----- Capital City ----- 1 ----- Your Town ----- 4 ----- Little Village     

   _.     

   find the exact area of the circle with a circumference of 8pi yards.     

   C = π d      ==>>     8 π  =  π d   ==>>     d  = 8     

    r =  d / 2    ==>>     r  =  8 / 2      ==>>     r  = 4     

   A = π r²     ==>>     A = (3.1416) (4²)     

                                      =  3.1416 x 16     

                                      =  50.27 yd³      

   _.