Find all the points if any where y-4x=12 intersects 2-y=2(x+2)^2 a) there are no points of intersection b) (-3,0) c) (3,0) d) (-3,0) and (3,0)

B

Step-by-step explanation:

given the 2 equations

y - 4x = 12 → (1)

2 - y = 2(x + 2)² → (2)

rearrange (1) expressing y in terms of x

y = 12 + 4x

Simplify (2) by expanding factor and substituting y = 12 + 4x

2 - (12 + 4x) = 2(x² + 4x + 4)

2 - 12 - 4x = 2x² + 8x + 8

- 10 - 4x = 2x² + 8x + 8 ← rearrange into standard form

add 10  + 4x to both sides

2x² + 12x + 18 = 0 ← in standard form

divide through by 2

x² + 6x + 9 = 0

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

Point of intersection = (- 3, 0 ) → B

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.

what is

step-by-step explanation: