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Which formulas represent linear relationships? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A)the area of a circle, $A = \pi r^2$ $\newline$ (B)the perimeter of a regular hexagon, $P = 6s$ $\newline$ (C)the volume of a sphere, $V = \frac{4}{3} \pi r^3$ $\newline$ (D)the perimeter of an isosceles right triangle, $P = (2 + \sqrt{2})s$

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Write equations of cosine functions using properties

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Q. Which formulas represent linear relationships? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)the area of a circle,

A = \pi r^2

\newline

(B)the perimeter of a regular hexagon,

P = 6s

\newline

(C)the volume of a sphere,

V = \frac{4}{3} \pi r^3

\newline

(D)the perimeter of an isosceles right triangle,

P = (2 + \sqrt{2})s

Linear Relationship Definition: Linear relationships are represented by equations where the dependent variable changes at a constant rate with respect to the independent variable. The equation should be of the first degree.
Choice (A) Area of Circle: Choice (A) $A = \pi r^2$ describes the area of a circle, which depends on the square of the radius $(r^2)$ . This is not a linear relationship because it involves a square term.
Choice (B) Perimeter of Hexagon: Choice (B) $P = 6s$ describes the perimeter of a regular hexagon, where $P$ changes linearly with each change in side length $s$ . This is a linear relationship because it involves only the first power of $s$ .
Choice (C) Volume of Sphere: Choice (C) $V = \frac{4}{3} \pi r^3$ describes the volume of a sphere, which depends on the cube of the radius $(r^3)$ . This is not a linear relationship because it involves a cube term.
Choice (D) Perimeter of Triangle: Choice (D) $P = (2 + \sqrt{2})s$ describes the perimeter of an isosceles right triangle, where $P$ changes linearly with each change in side length $s$ . This is a linear relationship because it involves only the first power of $s$ .

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