Suppose that the functions g and h are defined for all real numbers x as follows. g(x) =x-6 h (x) = 2x^2 Write the expressions for (g- h)(x) and (g h)(x) and evaluate (g+h)(-1). (g - h) (x) = (g+h)(-1)=

Step-by-step explanation:

Given the functions g(x) =x-6 and h(x) = 2x², we are to find the following expression;

a) (g- h)(x)

(g- h)(x) = g(x)- h(x)

(g- h)(x) = x-6- 2x²

(g- h)(x) = -2x²+x-6

b) (g+ h)(x)

(g+ h)(x) = g(x)+ h(x)

(g- h)(x) = x-6+ 2x²

(g- h)(x) = 2x²+x-6

c) To evaluate  (g+h)(-1)

(g+h)(-1) = g(-1)+h(-1)

(g+h)(-1) = -1-6+ 2(-1)²

(g+h)(-1) = -7+2(1)

(g+h)(-1) = -5

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

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.