Bosco

    In what quadrant does the point (-5, -8) lie?     

    Since x = –5 it's left of the origin    

    Since y = –8 it's below the origin     

    Left and Down puts the point in the 3^rd Quadrant     

_.     

The x-intercepts of the parabola y = x^2 + bx + c are (-3,0) and (-5,0) Find the equation of the parabola, and submit your answer in y = x^2 + bx + c form.     

     y = x² + bx + c     We know that when x = –5, y = 0     

                                                 and when x = –3, y = 0      so substitute those in the equation     

     (–5)²  +  (–5) b  +  c  =  0     –>   25 – 5b + c  =  0     

     (–3)²  +  (–3) b  +  c  =  0     –>     9 – 3b + c  =  0     

     subtract                                            – 2b        =  – 16     

                                                                         b  =  8         so substitute that in the equation     

                                                          25 – 40 + c  =  0     

                                                                          c  =  15     

     therefore we get      y  =  x² + 8x + 15     I wasn't a 100% sure of this answer so I drew it     

                                                                      on Desmos and the resulting curve looked good.     

.     

[T]he points of this 3-by-3 grid are equally spaced horizontally and vertically. How many different sets of three points of this grid can be the three vertices of a triangle?     

     9C3  =        84     

     minus             8     

     answer         72     

I based this answer on the reasoning that a     

triangle can be drawn using any three points     

in the grid, except when those three points lie     

in a straight line.     

_.     

   How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?     

   60     51       42       321     

            510     420     3210     

   I thought of these seven . . . maybe you can come up with some more.     

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