Answer:
see explanation
Step-by-step explanation:
to find the intersection equate g(x) and h(x) , that is
(x + 7)(x - 5) = x - 5 ← expand left side using FOIL
x² + 2x - 35 = x - 5 ( subtract x - 5 from both sides )
x² + x - 30 = 0 ← in standard quadratic form
(x + 6)(x - 5) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 5 = 0 ⇒ x = 5
substitute these values into either g(x) or h(x) for corresponding values of y
substituting into h(x)
h(- 6) = - 6 - 5 = - 11 ⇒ (- 6, - 11 )
h(5) = 5 - 5 = 0 ⇒ (5, 0 )
