Which of the following statements are true for this initial value problem? Select all that apply. dy (y - 4) = x - 6 with y (6) = 4 dx O y = x - 2 is the only solution of this initial-value problem. O y = x - 2 and y = 10 - x are both solutions of this initial value problem. This initial-value problem cannot have a solution because the conditions of the existence and uniqueness theorem for first-order linear equations are not satisfied. □ A locally unique solution is not guaranteed to exist by the local existence and uniqueness theorem for first-order x-6 differential equations because is not continuous at the point (6, 4). y-4 O The existence and uniqueness theorem for first-order linear equations ensures the existence of a unique local solution of this initial value problem because x - 6 is continuous at the point (6,4).

Consider the following functions. f₁(x) = 0, f₂(x) = x, f(x) = ex g(x) = c₁f₁(x) + C₂f₂(x) + C3f3(x) Solve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution [0, 0, 0}.) ={1 {C₁, C₂, C3} = Determine whether f₁, f₂, f3 are linearly independent on the interval (-∞, ∞). O linearly dependent O linearly independent Need Help? Read It

Please solve no. 27 in the photo

cnav.com/client/nuek. uTube Maps -> Review E W Bookmark 目 PGCPS BENCHMARK 2 ALGEBRA II / ALGEBRA II/ 7 OF 20 You may use a calculator for this item. Consider the equations f (x) = = and g (x) = (x – 1) –1 To the nearest tenth, what is the solution of f (x) = g (x)? Enter your answer in the space provided. search