Question

type the correct answer in each box. use numerals instead of words. for linear functions v and w, v(10) = 12, and w(10) = 9. (v + w)(10) = (v - w)(10) = (vw)(10) =

Explanation:

Step1: Calculate \((v + w)(10)\)

By the property of function addition, \((v + w)(x)=v(x)+w(x)\). So when \(x = 10\), \((v + w)(10)=v(10)+w(10)\). Given \(v(10) = 12\) and \(w(10)=9\), then \((v + w)(10)=12 + 9=21\).

Step2: Calculate \((v - w)(10)\)

By the property of function subtraction, \((v - w)(x)=v(x)-w(x)\). When \(x = 10\), \((v - w)(10)=v(10)-w(10)\). Substituting the values, we get \((v - w)(10)=12-9 = 3\).

Step3: Calculate \((vw)(10)\)

By the property of function multiplication, \((vw)(x)=v(x)\times w(x)\). When \(x = 10\), \((vw)(10)=v(10)\times w(10)\). Substituting \(v(10) = 12\) and \(w(10)=9\), we have \((vw)(10)=12\times9 = 108\).

Answer:

21, 3, 108