Consider the region bounded by the graps of the equations y igual x más 6 , y igual menos x al cuadrado más 5 por x más 6.

The value of envoltorio arriba x is: Respuesta
.
The value of envoltorio arriba y is: Respuesta
.

To solve the problem, we need to determine the points of intersection between the curves described by the equations:

1. \( y = x + 6 \)
2. \( y = -x^2 + 5x + 6 \)

### Step 1: Set the Equations Equal to Each Other
We find the intersection points by setting the equations equal to each other:

\[
x + 6 = -x^2 + 5x + 6
\]

### Step 2: Simplify and Rearrange the Equation
Subtract \( x + 6 \) from both sides to get:

\[
0 = -x^2 + 4x
\]

Factor the equation:

\[
0 = x(-x + 4)
\]

### Step 3: Solve for \( x \)
The solutions are:

\[
x = 0 \quad \text{or} \quad x = 4
\]

### Step 4: Calculate the

Consider the region bounded by the graphs of the equations y = x + 6 and y = -x^2 + 5x + 6.

Solve for the intersection points of the linear equation y = x + 6 and the quadratic equation y = -x^2 + 5x + 6. This detailed guide walks you through key algebraic concepts, including the quadratic formula and factoring. Suitable for students in Grades 10-12.

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