The given functions are :
f(x) = x²
g(x) = x² + 5
∴ g(x) = f(x) + 5
g(x) is obtained by shifting f(x) 5 units upward. See the attached figure
<span>So, The function g(x) is obtained by adding
5 to f(x)</span>
I think the correct answer would be C. A validation of congruency between two polygons would be that if by applying rigid motions you can make them coincide. Two figures are said to be congruent if and only if these figures have the same shape and the same size. All of their sides and angles are the same. Rigid motion is a motion done to a figure that preserves distance or length. If all the rigid motions like rotation, reflection, translation and glide reflection are done and the figures are the same or the lengths are preserved, then the polygons should be congruent.
Answer d: 3 pails
The area of the ceiling:
A = 142 = 196 f2
We need plaster to cover 196 $2
196: 90 = 2.17778
Answer: We have to buy 3 pails of plaster
X+y+z=11, x-y+z=5, x-z=y+1 and solve it by any of the methods: isolation, elimination or determinants. isolation (or back substitution, would be for instance: z = 11-x-y, z=5-x+y, z = x-y-1 and then impose z=z:
11-x-y=5-x+y,
11-x-y=x-y-1,
The first takes you to: 6=2y or y=3, then the second to 12=2x or x=6, so that:
x=6, y=3, z=2.
You can see that it checks out