Question

which formulas represent linear relationships? select all that apply. the circumference of a circle, ( c=pi d ) the perimeter of an equilateral triangle, ( p = 3s ) the area of an equilateral triangle, ( a=\frac{sqrt{3}}{4}s^{2} ) the surface area of a sphere, ( sa = 4pi r^{2} )

Explanation:

Step1: Recall the form of a linear equation

A linear equation has the form \(y = mx + b\), where \(m\) and \(b\) are constants and the highest power of the variable is \(1\).

Step2: Analyze \(C=\pi d\)

Here, \(C\) is like \(y\) and \(d\) is like \(x\). The equation \(C=\pi d\) can be written as \(C=\pi d+0\), where \(m = \pi\) and \(b = 0\). The power of \(d\) is \(1\).

Step3: Analyze \(P = 3s\)

Here, \(P\) is like \(y\) and \(s\) is like \(x\). The equation \(P=3s\) can be written as \(P = 3s+0\), where \(m = 3\) and \(b=0\). The power of \(s\) is \(1\).

Step4: Analyze \(A=\frac{\sqrt{3}}{4}s^{2}\)

The power of \(s\) is \(2\). A linear equation has the variable with power \(1\), so this is not linear.

Step5: Analyze \(SA = 4\pi r^{2}\)

The power of \(r\) is \(2\). A linear equation has the variable with power \(1\), so this is not linear.

Answer:

The circumference of a circle \(C=\pi d\) and the perimeter of an equilateral triangle \(P = 3s\) represent linear relationships.