Mathematics: The distance between the two islands showed on the map is 210 miles a ruler measure distance on the map as 3 1/2 inches how many miles would be represented by 1 3/4 inches on the map

The distance between the two islands showed on

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smkw04p3ao0n

04.01.2022

let's firstly convert the mixed fractions to improper fractions.

$\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} \stackrel{size}{actual~miles}&\stackrel{size}{map~inches}\\ \cline{1-2} 210&\frac{7}{2}\\\\ x&\frac{7}{4} \end{array} \implies \cfrac{210}{x}=\cfrac{~~\frac{7}{2}~~}{\frac{7}{4}}$

$\bf \cfrac{210}{x}=\cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies \cfrac{210}{x}=2\implies 210=2x\implies \cfrac{210}{2}=x\implies 105=x$

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Ответ:

natalie2sheffield

29.02.2020

Mathematics

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=\stackrel{bases}{parallel~sides}\\ h=height\\[-0.5em] \hrulefill\\ a=29\\ h=9\\ A=193.5 \end{cases}\implies 193.5=\cfrac{9(29+b)}{2} \\\\\\ 387=9(29+b)\implies \cfrac{387}{9}=29+b\implies 43=29+b\implies 14=b$

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The distance between the two islands showed on the map is 210 miles a ruler measure distance on the map as 3 1/2 inches how many miles would be represented by 1 3/4 inches on the map

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