a square with an area of 25 in.^2 is plotted on a grid so that the bottom-left corner is at the origin. The side of the square are horizontal and vertical. A reflection over what line maps the square onto itself?

Reflection about the vertical line x = 2.5 inches will map the square unto itself

Step-by-step explanation:

The given parameters are;

The area of the square = 25 in²

The orientation of the sides of the square are horizontal and vertical

Therefore, we have;

The area, A, of the square given by the following relation;

A = Side²

A = 25 in²

Therefore;

The area of the square = 25 = side²

The length of the sides of the square = √A = √25 = 5

The length of the sides of the square = 5 inches

The reflection of a figure that maps the figure unto itself is a reflection along the line of symmetry

One of the line of symmetry that divides the square into two similar halves is the vertical straight that passes half way through the horizontal side, which is the point 2.5 inches to the right on the x-axis with the coordinates (2.5, 0)

Therefore, reflection about the line x = 2.5 inches will map the square unto itself.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.