Answer to Question #217181 in Algebra for Vanessam

Question

We consider a=(1)/[(2/3)+(5/7)]. Which of the following statements is correct?

A. 0.5<a<0.7

B. 0.7<a<1

C.1<a<1.2

D.1.2<a<1.5

Answer 1

Taking into accounrt that

$a=\frac{1}{\frac{2}{3}+\frac{5}{7}}=\frac{1}{\frac{14+15}{21}}=\frac{ 1 }{\frac{29}{21}}=\frac{21}{29}<\frac{29}{29}=1$ and $0.7=\frac{7}{10}=\frac{21}{30}<\frac{21}{29}=a,$

we conclude that $0.7<a<1.$

Answer: B