Could use some help with 11 plus 12 and 13 if its not too mu

Could use some help with #11 (plus 12 and 13 if it\'s not too much) thanks!!!

The x- intercepts are (Type an ordered pair. type an exact answer using radicals as answers as needed) There is no x- intercept use the method of your choice to find all complex- number solutions 16x^2 = -81 (Type an exact answer. using radicals and, as needed. type an integer or a simplified fraction. use a comma to separate answers as needed.) Solve the system x + y + z= -11 2x + 5y + 2z = -40 - x + 6y - 3z = - 19 The solution is (Type an ordered triple.) Find an equation of a parabola that contains the given points. Use a graphing calculator to verify that the graph o your equation contains the points (1.-5). (3.7). (4, 16) The equation of the parabola is y =. Find the domain of the function. Verify the result with a graphing calculator table or graph. f(x) = x- 8/5x^2 - 7X-6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The domain of f(x) is all real numbers except (Use a comma to separate answers as needed. Type integers or simplified fractions.) The domain of f(x) is all real numbers. Simplify the right side of the equation Use a graphing calculator table to verify your work. f(x) = 2x - 10/3x - 15 (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Solution

11) (1, -5) ( 3, 7) and ( 4, 16)

Parabolic equation : y = ax^2 +bx +c

plug the points: -5 = a + b +c ----(1)

7 = 9a +3b +c -----(2)

16 = 16a +4b +c ----(3)

solve equation 1, 2, 3 for a, b and c.

we get a = 1 ; b = 2 ; c = -8

y = x^2 + 2x -8

12) f(x) = (x-8) /(5x^2 -7x -6)

5x^2 -7x -6 =0

solve the quadratic equation : 5x^2 -7x -6 =0

we can write 5x^2 -10x + 3x - 6 =0

taking gcf out of 1st two terms and last two terms

5x(x-2) +3(x-2) = 0

which is equal to

( 5x+3)(x-2) = 0

x = -3/5 ; x= 2

So, f(x) is not defined for x=-3/5 and x=2

So, Domain interval form : ( -inf , -3/5) U ( -3/5 , 2) U ( 2, inf)

Domain is all real except x= -3/5 ; x=2