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Which formulas represent linear relationships? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A)the area of a triangle whose height and base are the same, $A = \frac{1}{2}h^2$ $\newline$ (B)the perimeter of a regular octagon, $P = 8s$ $\newline$ (C)the surface area of a cube, $SA = 6a^2$ $\newline$ (D)the perimeter of a semicircle, $P = \pi r + 2r$

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Solve trigonometric equations

Full solution

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

\newline

Multi-select Choices:

\newline

(A)the area of a triangle whose height and base are the same,

A = \frac{1}{2}h^2

\newline

(B)the perimeter of a regular octagon,

P = 8s

\newline

(C)the surface area of a cube,

SA = 6a^2

\newline

(D)the perimeter of a semicircle,

P = \pi r + 2r

Identify Relationship Type: Identify the type of relationship in each formula to determine if it's linear. Linear relationships can be represented by equations of the first degree, where variables are not multiplied together or squared.
Check Option (A): Check option (A): $A = \frac{1}{2}h^2$ . This formula represents the area of a triangle where the height and base are the same. The variable $h$ is squared, indicating this is not a linear relationship.
Check Option (B): Check option (B): $P = 8s$ . This formula calculates the perimeter of a regular octagon, where $s$ is the side length. Since $s$ is not raised to any power higher than $1$ , this represents a linear relationship.
Check Option (C): Check option (C): $SA = 6a^2$ . This formula calculates the surface area of a cube, where $a$ is the side length. The variable $a$ is squared, so this is not a linear relationship.
Check Option (D): Check option (D): $P = \pi r + 2r$ . This formula calculates the perimeter of a semicircle. The variables are not squared or multiplied together, making this a linear relationship.

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