Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. her graph is shown below. what are the solutions of –x2 + 4x = x – 4? a.–5 and 0 b.–5 and –1 c.–1 and 4 d.0 and 4

Answer

C.–1 and 4

Explanation

Solving the equations  y = –x² + 4x and y = x – 4

–x² + 4x = x – 4

x² - 4x + x = 4

x² - 3x = 4

x² - 3x + (3/2)² = 4 +  (3/2)²

(x - 3/2)² = 4 +  9/4

              = 6.25

x - 3/2 = √6.25                      or  x - 3/2 = -√6.25

x = 2.5 + 1.5                                        x = -2.5 + 1.5

 = 4                                                        = -1

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol