A family is coloring Easter eggs and wants to make 2 shades

A family is coloring Easter eggs and wants to make 2 shades of purple, \"light purple\" and \"deep purple.\" They have 30 tablespoons of deep red solution and 2 tablespoons of blue solution and \"deep purple\" consists 10% blue solution, how much of each version of purple solution can be created? The line y = mx + b connects the points (-2,4) and (4, -2). Find the values of m and b. Find b and c such that the parabola y = x^2 + bx + c go through the points (2, 7) and (-6, 7). Find b and c such that the parabola y = bx^2 + bx + c goes through the points (4, 46) and (-2, 10). Apply a graphing utility to graph the two equations y = -1.25x + 17.5 and y = 2.3x - 14.1. Approximate solution to this system of linear equations. Apply a graphing utility to graph the two equations y = 14.76x + 19.43 and y = 2.76x + 5.22. Approximate the solution to this system of linear equations. Apply a graphing utility to graph the two equations 23x + 15y = 7 and 46x + 30y = 14. Approximate the solution to this system of linear equations.

Solution

91)

given y=bx²+bx+c passes through (4,46),(-2,10)

put (4,46),(-2,10) in the equation

46=b4²+b4+c,10=b(-2)²+b(-2)+c

46=16b+4b+c,10=4b-2b+c

46=20b+c ,10=2b+c

c=46-20b ,c=10-2b

=>46-20b =10-2b

=>20b-2b=46-10

=>18b=36

=>b=36_/18

=>b=2

c=10-2b ,b=2

=>c=10-2(2)

=>c=10-4

=>c=6