Em cada item, verifique se as grandezas são proporcionais entre si. a) Em uma fábrica, certa máquina produz 98 peças em 2 h de funcionamento e 196 peças em 4 h . b) Aos 14 anos de idade, a altura de Regina media \( 1,57 \mathrm{~m} \), e aos 26 anos, \( 1,77 \mathrm{~m} \). c) Em certo supermercado, 1 pacote de çúcar de 1 kg de determinada marca custa R \( \$ 2,60 \) e o pacote de 2 kg custa \( \mathrm{R} \$ 5,10 \). d) Uma impressora industrial imprime certa quantidade de panfletos em 6 h . Três impres- soras iguais a ela imprimem a mesma quantidade em 2 h .

Write the expression as a single logarithm. \[ 2 \log _{m}(7 w+1)+\frac{1}{2} \log _{m}(w+7) \]

A balanced chemical equation indicates the proportions or ratios of the various reactants and products to one another. From the coefficients in the balanced chemical equation, we can create mole-mole ratios that relate any of the various chemicals to a different chemical. For example, consider the following balanced chemical equation: \[ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g) \] From this equation, there are several possible mole-mole ratios. Two of these mole- mole ratios are the following: \[ \frac{3 \text { moles } \mathrm{H}_{2}}{1 \text { mole } \mathrm{N}_{2}} \text { or } \frac{2 \text { moles } \mathrm{NH}_{3}}{3 \text { moles } \mathrm{H}_{2}} \] How many moles of carbon dioxide, \( \mathrm{CO}_{2} \), are produced if 5.87 mol of glucose, \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \), react? \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(l) \)

Subiect: Mathematics 1. Mr. Yadhav walks 18 km due east from the starting point O . Then he walks 12 km due west towards the point O . a) Show this information in a number line. b) In which direction is he now from the point O ? c) How far is he now from the point O ?

b) \( 5 \frac{2}{3} \)

2) \( x-10=12 \)