△DEF is rotated about point N to △D′E′F′.
A rotation is a transformation that turns a figure about a fixed point called the center of rotation. In your case the center of rotation is point N. A rotation is an isometric transformation: the original figure and the image are congruent. Main properties of rotation:
1) A rotation preserves lengths of segments.
2) A rotation preserves degrees of angles.
3) A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.
Therefore, option C is true (because the original figure and the image are congruent) and option D is false (because the original figure and the image must be congruent).
All corresponding points on the image and pre-image are equidistant to point N. This option is true (because rotation preserves lengths of segments), thus, DN≅D'N'.
If we expand the product, we have
The x-coordinate of the vertex is given by
Plug this value in the equation to find the correspondant y-value:
Answer:
(x+10)/5
Step-by-step explanation:
Given the function
g(x) = 5(x-2)
Open the parenthesis
g(x) = 5x-10
To find the inverse we need to follow the steps;
Step 1; make y as g(x)
y = 5x-10
Step 2; replace y with x;
x = 5y - 10
Step 3; make y the subject of the formula;
x = 5y-10
5y = x+10
y = (x+10)/5
Step 4: substitute y as g^(-1)(x)
g^(-1)(x) = (x+10)/5
Hence the inverse of the function is (x+10)/5
Answer: They both equal 30
Solving Steps:
1. Solve for x
40-4x=50-8x
-4x+8x=50-40
4x=10
x=2.5
2. Find <1 and <2
40-4(2.5)
40-10
=30
