Answer :
Answer:
see explanation
Step-by-step explanation:
given
10 [tex]\frac{1}{2}[/tex] : 2 [tex]\frac{1}{2}[/tex]
Change both mixed numbers into improper fractions
[tex]\frac{2(10)+1}{2}[/tex] : [tex]\frac{2(2)+1}{2}[/tex]
= [tex]\frac{20+1}{2}[/tex] : [tex]\frac{4+1}{2}[/tex]
= [tex]\frac{21}{2}[/tex] : [tex]\frac{5}{2}[/tex] ( multiply both parts by 2 )
= 21 : 5 ← in the form 21 : x
with x = 5
------------------------------------------------------------
given
[tex]\frac{11}{\sqrt{x} }[/tex] = [tex]\frac{9}{\sqrt{y} }[/tex] ( square both sides )
[tex](\frac{11}{\sqrt{x} }) ^{2}[/tex] = [tex](\frac{9}{\sqrt{y}}) ^{2}[/tex]
[tex]\frac{121}{x}[/tex] = [tex]\frac{81}{y}[/tex] ( multiply both sides by x )
121 = [tex]\frac{81x}{y}[/tex] (divide both sides by 81 )
[tex]\frac{121}{81}[/tex] = [tex]\frac{x}{y}[/tex]
