Consider the system of equations below. y = x + 6 y = x^2 + 6x + 6what are the solutions for the system of equations?

(0, 6) and (-5, 1)

Step-by-step explanation:

It is easy enough to try the offered solutions in the equations. The incorrect ones fail to satisfy the first equation. Trying the first offered point for each answer, we can see whether y = x +6:

a: 6 ≠ 2 +6

b: -5 ≠ -7 +6

c: 6 ≠ -5 +6

d: 6 = 0 +6 . . . . . this is the correct answer choice

e: 2 ≠ 5 +6

_____

If you actually want to figure the answer, I recommend a graphing calculator as a quick and easy way to do it. Analytically, you can equate the expressions for y and solve the resulting quadratic:

... y = y

... x +6 = x^2 +6x +6 . . . . substitute the two expressions for y

... 0 = x^2 +5x . . . . . subtract the left side

... 0 = x(x +5) . . . . . . factor

Values of x that make this product zero are x=0 and x=-5. Corresponding values of y can be found using the first equation: add 6 to x.

... (x, y) = (0, 6), (-5, 1)

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

[2, 2.5)

(2.5, 3]

step-by-step explanation:

i think its these two not sure [2, 2.5)

(2.5, 3]