in the right triangle shown below, the hypotenuse has a length of 10, one of the length of 5, what is the length of the other leg?

(- 2, - 7) and (3, 13)

Step-by-step explanation:

Given the 2 equations

y = x² + 3x - 5 → (1)

y = 4x + 1 → (2)

Substitute y = 4x + 1 into (1)

x² + 3x - 5 = 4x + 1 ( subtract 4x + 1 from both sides )

x² - x - 6 = 0 ← in standard form

(x - 3)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 2 = 0 ⇒ x = - 2

Substitute these values into (2) for corresponding values of y

x = 3 : y = 4(3) + 1 = 12 + 1 = 13 ⇒ (3, 13)

x = - 2 : y = 4(- 2) + 1 = - 8 + 1 = - 7 ⇒ (- 2, - 7)

The graphs intersect at (- 2, - 7) and (3, 13)